{"title":"Discrete mathematics Books","description":"","products":[{"product_id":"discrete-mathematics-9780198507178","title":"Discrete Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBiggs'' Discrete Mathematics has been a best-selling textbook since the first and revised editions were published in 1986 and 1990, respectively. This second edition has been developed in response to undergraduate course changes and changes in students'' needs. New to this edition are chapters on statements and proof, logical framework, and natural numbers and the integers, in addition to updated chapters from the previous edition. The new chapters are presented at a level suitable for mathematics and computer science students seeking a first approach to this broad and highly relevant topic. Each chapter contains newly developed tailored exercises, and miscellaneous exercises are presented throughout, providing the student with over 1000 individual tailored exercises. This edition is accompanied by a website www.oup.com\/mathematics\/discretemath containing hints and solutions to all exercises presented in the text, providing an invaluable resource for students and lecturers alike. The b\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThis is a new edition of a successful textbook ... this revision is particularly welcome ... The text is written in a fluent but rigorous style and should appeal to sixthformers and undergraduates who are alienated by more formal presentations. There are plenty of approachable exercises, ranging from easy riders to establish technique to more challenging problems which introduce new ideas, and a bonus is that all the answers are available on a companion web-site. I can thoroughly recommend this text. * The Mathematical Gazette *\u003cbr\u003eA well known definition says that a textbook is a book such that everybody thinks he can write a better one. Biggs' Discrete Mathematics is an exception - not only for its wide range of topics and its clear organization but notably for its excellent style of explanation. * EMS *\u003cbr\u003e... the ideal choice for introductory courses to discrete mathematicians. * Zentralblatt MATH *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eTHE LANGUAGE OF MATHEMATICS; TECHNIQUES; ALGORITHMS AND GRAPHS; ALGEBRAIC METHODS","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732762997079,"sku":"9780198507178","price":62.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198507178.jpg?v=1719998292"},{"product_id":"the-nature-of-complex-networks-9780199695119","title":"The Nature of Complex Networks","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe Nature of Complex Networks provides a systematic introduction to the statistical mechanics of complex networks and the different theoretical achievements in the field that are now finding strands in common.The book presents a wide range of networks and the processes taking place on them, including recently developed directions, methods, and techniques. It assumes a statistical mechanics view of random networks based on the concept of statistical ensembles but also features the approaches and methods of modern random graph theory and their overlaps with statistical physics.This book will appeal to graduate students and researchers in the fields of statistical physics, complex systems, graph theory, applied mathematics, and theoretical epidemiology.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe current volume by Dorogovtsev and Mendes takes quite a broad view of complex networks to include the analysis of finite and infinite graphs, directed and undirected graphs, multigraphs, hypergraphs, and even simplicial complexes, as networks scale according to increasing N or in some other fashion. The writing style is that of physics and especially statistical mechanics with frequent connections made to physical concepts such as Bose-Einstein condensation...The current volume can especially serve as a useful reference on complex networks from a physics perspective. * Lenwood S. Heath, MathSciNet *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface 1: First insight 2: Graphs 3: Classical random graphs 4: Equilibrium networks 5: Evolving networks 6: Connected components 7: Epidemics and spreading phenomena 8: Networks of networks 9: Spectra and communities 10: Walks and search 11: Temporal networks 12: Cooperative systems on networks 13: Inference and reconstruction 14: What's next? Further Reading Appendices A-G References","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732888170839,"sku":"9780199695119","price":89.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199695119.jpg?v=1719998821"},{"product_id":"problems-in-analytic-number-theory-9780387723495","title":"Problems in Analytic Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProblems.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.- Solutions.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eM.R. Murty\u003c\/p\u003e\u003cp\u003e\u003ci\u003eProblems in Analytic Number Theory\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003e\"The reviewer strongly approves of the problem-based approach to learning, and recommends this book to any student of analytic number theory.\"\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003e—\u003c\/i\u003eMATHEMATICAL REVIEWS\u003c\/p\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e“This expanded and corrected second edition of this useful and interesting book has a new chapter on the topic of equidistribution. … this monograph gives important results and techniques for specific topics, together with many exercises. … I do enjoy this book … and I imagine when I take the graduate course in the subject that it will be of a greater benefit, which is why I offered such a high rating.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"The second edition of the book has eleven chapters … . the book can be used both as a problem book (as its title shows) and also as a textbook (as the series in which the book is published shows). … is ideal as a text for a first course in analytic number theory, either at the senior undergraduate or the graduate level. … I believe that this book will be very useful for students, researchers and professors. It is well written … .\" (Mehdi Hassani, MathDL, April, 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eProblems.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.- Solutions.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726179671,"sku":"9780387723495","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387723495.jpg?v=1720001397"},{"product_id":"introduction-to-proofs-and-proof-strategies-9781009096287","title":"Introduction to Proofs and Proof Strategies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eEmphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof as they transition to advanced mathematics. Using several strategies, students will develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'Every student in the sciences should be exposed to the basic language of modern mathematics, and standard courses such as calculus or linear algebra do not play this role. The ideal textbook for such a course should not attempt to be encyclopedic and should not assume special prerequisites. It should cover a carefully chosen selection of topics efficiently, engagingly, thoroughly, without being overbearing. Fuchs' text fits this description admirably. The level is right, the math is rock solid, the writing is very pleasant. The book talks to the reader, without ever sounding patronizing. A vast selection of problems, many including solutions, will be splendidly helpful both in a classroom setting and for self-study.' Paolo Aluffi, Florida State University\u003cbr\u003e'This well-written text strikes a good balance between conciseness and clarity. Students are led from looking more deeply into familiar topics, such as the quadratic formula, to an understanding of the nature, structure, and methods of proof. The examples and problems are a strong point. I look forward to teaching from it.' Eric Gottlieb, Rhodes College\u003cbr\u003e'Fuchs' text is an excellent addition to the 'transitions to proof' literature. I will use it when I next teach such a course. Except for the excellent 'Additional Topics' sections, the content is standard, but the spiraling presentation and helpful narrative around proofs are what truly elevate this text. Fuchs has made every attempt to connect the structure and rigor of mathematics with the intuition of the student. For example, the notion of function arises in three different chapters, with two increasingly rigorous 'provisional definitions,' before a complete definition is given within a wider discussion of relations. I anticipate this approach resonating with students. Fuchs' Chapter 3, which introduces logic and proof strategies, is the most usable presentation of the material I have seen or used. The practice of mathematics and mathematical thinking is communicated well, while opportunities for confusion and obfuscation via a blizzard of symbols are minimized.' Ryan Grady, Montana State University\u003cbr\u003e'This book is a must-have resource for an undergraduate mathematics student or interested reader to learn the fundamental topics in how to prove things. The text is thorough and of top quality, yet it is conversational and easy to absorb. Maybe the most important quality, it offers advice about how to approach problems, making it perfect for an introduction to proofs class.' Andrew McEachern, York University, Canada\u003cbr\u003e'This is a great choice of textbook for any course introducing undergraduates to mathematical proofs. What makes this book stand out are the early chapters, as well as the 'Additional Topics,' both with accompanying exercises. The book begins by gently introducing proof-based thinking by posing well-motivated prompts and exercises concerning familiar arithmetic of real numbers and the integers. It then introduces fields as a playground to practice working with axioms and drawing (sometimes surprising) conclusions from them. The book proceeds with introducing formal logic, mathematical induction, set theory, and relations on sets. The book's design nicely enables framing classes around a choice sampling among the abundant exercises. The book's 'Additional Topics' can serve to engage those students with a brimming imagination and who are already familiar with basic notions of proofs.' David Ayala, Montana State University\u003cbr\u003e'Fuchs' Introduction to Proofs and Proof Strategies is an excellent textbook choice for an undergraduate proof-writing course. The author takes a friendly and conversational approach, giving many worked examples throughout each section. Furthermore, each section is replete with exercises for the reader, along with fully worked solutions at chapter's end. This is exactly the 'get your hands dirty' approach students and readers will benefit greatly from!' Frank Patane, Samford University\u003cbr\u003e'The book Introduction to Proofs and Proof Strategies by Shay Fuchs takes the problem-solving approach to the forefront by accompanying the reader in the construction and deconstruction of proofs through numerous examples and challenging exercises. The fundamental principles of mathematics are introduced in a creative and innovative way, making learning an enjoyable journey.' Roberto Bruni, Università di Pisa\u003cbr\u003e'This textbook is easy to read and designed to enhance students' problem-solving skills in their first year of university. The book really stands out due to the variety and quality of exercises at the end of each chapter. The latter chapters dive into more advanced topics for interested students.' Marina Tvalavadze, University of Toronto Mississauga\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents; Preface; Part I. Core Material; 1. Numbers, Quadratics and Inequalities; 2. Sets, Functions and the Field Axioms; 3. Informal Logic and Proof Strategies; 4. Mathematical Induction; 5. Bijections and Cardinality; 6. Integers and Divisibility; 7. Relations; Part II. Additional Topics; 8. Elementary Combinatorics; 9. Preview of Real Analysis – Limits and Continuity; 10. Complex Numbers; 11. Preview of Linear Algebra; Notes; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738003648855,"sku":"9781009096287","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009096287.jpg?v=1723811673"},{"product_id":"graph-theory-and-additive-combinatorics-9781009310949","title":"Graph Theory and Additive Combinatorics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis graduate level textbook covers classical and modern developments in graph theory and additive combinatorics, presenting arguments as a cohesive whole. Students will appreciate the chapter summaries, many figures and exercises, as well as the complementary set of lecture videos freely available through MIT OpenCourseWare.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'Yufei Zhao does great mathematics and has an uncanny ability to explain the deepest results with clear understandable prose. For anyone interested in the seminal ideas (and their interrelationships) of recent decades - pseudorandomness, graphons, graph regularity, to name a few - this is the book to read and savor.' Joel Spencer, New York University\u003cbr\u003e'This impeccable book should quickly become a classic text in discrete maths. A huge selection of topics is treated elegantly, with beautiful illustrations, and in just the `right' amount of detail to arouse the interest of the reader and leave them well placed to find out more. In particular, the second half of the book is a superb introduction to additive combinatorics, which I will happily recommend to any student in this area.' Ben Green, Oxford University\u003cbr\u003e'This charming text gives an accessible introduction to the connected topics of extremal graph theory and modern additive combinatorics. The focus is very strongly on presenting intuition and restricting attention to the simplest possible instances of methods or classes of results, rather than aiming for maximal generality or the strongest statements; instead, references are given for further reading, or for the proofs of important theorems that are only stated here. Being highly suitable for advanced undergraduates or beginning graduate students, it fills a niche that is currently not occupied by other texts in these highly active areas of current mathematical research.' Terry Tao, University of California, Los Angeles\u003cbr\u003e'A valuable and readable unified treatment of a fast-moving area of combinatorics from one of the world's experts - sure to become a standard resource.' Jordan Ellenberg, University of Wisconsin-Madison\u003cbr\u003e'Yufei Zhao's book is a wonderful book about graph theory, additive combinatorics, and their surprising connections, involving a major theme of modern mathematics: the interplay between structure and randomness. In both areas, the book can take the curious reader, whether an advanced undergraduate or a professional mathematician, on a joyous journey from the very basics to state-of-the-art research. Yufei Zhao himself is a major player in modern research in both these areas and his presentation is a tour de force.' Gil Kalai, Hebrew University of Jerusalem and Reichman University\u003cbr\u003e'This is a beautiful treatment of extremal graph theory and additive combinatorics, focusing on the fruitful interplay between the two. The book covers the classical results as well as recent developments in this active area. It is a fascinating manuscript that would appeal to students and researchers with an interest in discrete mathematics, theoretical computer number theory, and related areas.' Noga Alon, Princeton University\u003cbr\u003e'This is a wonderful, well-written account of additive combinatorics from the graph theoretic perspective. Zhao skillfully ties in this approach to the usual statements and gives a thorough development of the subject. This book is indispensable for any serious researcher in this area. Beginners will find a thorough account of the subject with plenty of motivation. The more experienced reader will appreciate the authors' insights and elegant development of some difficult ideas.' Andrew Granville, University of Montréal\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Notation and Conventions; Appetizer: triangles and equations; 1. Forbidding a subgraph; 2. Graph regularity method; 3. Pseudorandom graphs; 4. Graph limits; 5. Graph homomorphism inequalities; 6. Forbidding 3-term arithmetic progressions; 7. Structure of set addition; 8. Sum-product problem; 9. Progressions in sparse pseudorandom sets; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738030125399,"sku":"9781009310949","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009310949.jpg?v=1723811692"},{"product_id":"equivariant-cohomology-in-algebraic-geometry-9781009349987","title":"Equivariant Cohomology in Algebraic Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'This book is a much-needed introduction to a powerful and central tool in algebraic geometry and related subjects. The authors are masters of clarity and rigor. The important theorems and examples are thoroughly explained, and illuminated with well-chosen exercises. This book is an essential companion for anyone wanting to understand group actions in algebraic geometry.' Ravi Vakil, Stanford University\u003cbr\u003e'Equivariant Cohomology is a tool from algebraic topology that becomes available when groups act on spaces. In Algebraic geometry, the groups are algebraic groups, including tori, and typical spaces are toric varieties and homogeneous varieties such as Grassmannians and flag varieties. This book introduces and studies equivariant cohomology (actually equivariant Chow groups) from the perspective of algebraic geometry, beginning with the artful replacement of Borel's classifying spaces by Totaro's finite-dimensional approximations. After developing the main properties of equivariant Chow groups, including localization and GKM theory, the authors investigate equivariant Chow groups of toric varieties and flag varieties, and the equivariant classes of Schubert varieties. Reflecting the interests of the authors, special attention is paid to Schubert calculus and the links between degeneracy loci and equivariant cohomology. The text also serves as an introduction to flag varieties, their Schubert varieties, and the calculus of Schubert classes in equivariant cohomology.' Frank Sottile, Texas A\u0026amp;M University\u003cbr\u003e'Equivariant Cohomology in Algebraic Geometry by David Anderson and William Fulton offers a comprehensive, accessible exploration of the development, standard examples, and recent contributions in this fascinating field. The authors have successfully struck a balance between rigor and approachability, making it an excellent resource for young researchers in the field. The book's real strength lies in its application to toric varieties and Schubert varieties across various settings, including Grassmannians, flag varieties, degeneracy loci, and extensions to other classical types and Kac–Moody groups. The authors' treatment of Bott-Samelson desingularizations of Schubert varieties is particularly noteworthy, displaying elegance and coherence within the context of the book's material. With over 450 pages of content, Equivariant Cohomology in Algebraic Geometry offers a comprehensive resource for researchers and scholars. It is poised to become a standard reference in the field, leaving a lasting impact on the flourishing area of research for years to come.' Sara Billey, University of Washington\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Preview; 2. Defining equivariant cohomology; 3. Basic properties; 4. Grassmannians and flag varieties; 5. Localization I; 6. Conics; 7. Localization II; 8. Toric varieties; 9. Schubert calculus on Grassmannians; 10. Flag varieties and Schubert polynomials; 11. Degeneracy loci; 12. Infinite-dimensional flag varieties; 13. Symplectic flag varieties; 14. Symplectic Schubert polynomials; 15. Homogeneous varieties; 16. The algebra of divided difference operators; 17. Equivariant homology; 18. Bott–_Samelson varieties and Schubert varieties; 19. Structure constants; A. Algebraic topology; B. Specialization in equivariant Borel–_Moore homology; C. Pfaffians and Q-polynomials; D. Conventions for Schubert varieties; E. Characteristic classes and equivariant cohomology; References; Notation index; Subject index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738033566039,"sku":"9781009349987","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009349987.jpg?v=1723811694"},{"product_id":"basic-mathematics-an-introduction-teach-yourself-9781473651976","title":"Basic Mathematics: An Introduction: Teach Yourself","description":"\u003cp\u003e\u003ci\u003eBasic Mathematics\u003c\/i\u003e teaches you all the maths you need for everyday situations. If you are terrified by maths, this is the book for you.\u003cbr\u003e\u003cbr\u003eDo you shy away from using numbers? Basic Mathematics can help. An easy-to-follow guide, it will ensure you gain the confidence you need to tackle maths and overcome your fears. It offers simple explanations of all the key areas, including decimals, percentages, measurements and graphs, and applies them to everyday situations, games and puzzles to help you understand mathematics quickly and enjoyably.\u003cbr\u003e\u003cbr\u003eEverything you need is here in this one book. Each chapter includes clear explanations, worked examples and test questions. At the end of the book there are challenges and games to give you new and interesting ways to practise your new skills.\u003c\/p\u003e","brand":"John Murray Press","offers":[{"title":"Default Title","offer_id":48739527852375,"sku":"9781473651975","price":13.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781473651975.jpg?v=1720052497"},{"product_id":"algebraic-graph-algorithms-a-practical-guide-using-python-9783030878857","title":"Algebraic Graph Algorithms: A Practical Guide Using Python","description":"\u003cp\u003eThis textbook discusses the design and implementation of basic algebraic graph algorithms, and algebraic graph algorithms for complex networks, employing matroids whenever possible. The text describes the design of a simple parallel matrix algorithm kernel that can be used for parallel processing of algebraic graph algorithms. Example code is presented in pseudocode, together with case studies in Python and MPI. The text assumes readers have a background in graph theory and\/or graph algorithms.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743056114007,"sku":"9783030878856","price":32.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"graph-and-network-theory-an-applied-approach-using-mathematica-r-9783031038563","title":"Graph and Network Theory: An Applied Approach","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics\/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book.  \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThe material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- List of Algorithms.- List of Bibliographical Notes.- Part 1. Topics in network optimisation.- 1. An introduction to graphs.- 2. Graph connectedness.- 3. Algorithmic complexity.- 4. Optimal paths.- 5. Trees.- 6. Location problems.- 7. Maximum flow networks.- 8. Minimum-cost network flows.- Part 2. Topics in classical graph theory.- 9. Matchings.- 10. Eulerian graphs.- 11. Hamiltonian graphs.- 12. Graph connectivity.- 13. Planarity.- 14. Graph colouring.- 15. Oriented graphs. Part 3. Topics in modern graph theory.- 16. Domination in graphs.- 17. Ramsey Theory.-  18. Extremal graph theory.- 19. Graph enumeration.- 20. The probabilistic method.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743065321815,"sku":"9783031038563","price":79.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031038563.jpg?v=1720063959"},{"product_id":"a-primer-for-undergraduate-research-from-groups-and-tiles-to-frames-and-vaccines-9783319660646","title":"A Primer for Undergraduate Research: From Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading.\u003c\/p\u003e\u003cp\u003eThe content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book is a superb resource for students and faculty mentors embarking on undergraduate research in mathematics. Its focus is on topics and applications rarely covered in the traditional undergraduate math curriculum, offering novice researchers a sturdy jumping-off point to a broad array of research problems. … A valuable resource for students and faculty mentors interested in undergraduate research.” (V. K. Chellamuthu, Choice, Vol. 56 (2), October, 2018)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCoxeter Groups and the Davis Complex (T.A. Schroeder).- A Tale of Two Symmetries: Embeddable and Non-Embeddable Group Actions on Surfaces (V. Peterson, A. Wootton).- Tile Invariants for Tackling Tiling Questions (M.P. Hitchman).- Forbidden Minors: Finding the Finite Few (T.W. Mattman).- Introduction to competitive graph coloring (C. Dunn, V. Larsen, J.F. Nordstrom).- Matrioids (E. McNicholas, N.A. Neudauer, C. Starr).- Finite Frame Theory (S. Datta, J. Oldroyd).- Mathematical decision-making with linear and convex programming (J. Kotas).- Computing weight multiplicities (P. E. Harris).- Vaccination strategies for small worlds. (W. Just, H. C. Highlander).- Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations (R. C. Harwood).","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743101366615,"sku":"9783319660646","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"theory-of-computation-simplified-simulate-real-world-computing-machines-and-problems-with-strong-principles-of-computation-9789355510648","title":"Theory of Computation Simplified: Simulate","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"BPB Publications","offers":[{"title":"Default Title","offer_id":48743243776343,"sku":"9789355510648","price":31.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789355510648.jpg?v=1720064748"},{"product_id":"logic-and-discrete-mathematics-9781118751275","title":"Logic and Discrete Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA concise yet rigorous introduction to logic and discrete mathematics.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade.\u003c\/p\u003e \u003cp\u003eThe chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solu\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\"This is a very well-written brief introduction to discrete mathematics that emphasizes logic and set theory and has shorter sections on number theory, combinatorics, and graph theory.\" (\u003ci\u003eMAA Reviews\u003c\/i\u003e, 4 January 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eList of Boxes xiii\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eAcknowledgements xxi\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Preliminaries 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Sets 2\u003c\/p\u003e \u003cp\u003e1.1.1 Exercises 7\u003c\/p\u003e \u003cp\u003e1.2 Basics of logical connectives and expressions 9\u003c\/p\u003e \u003cp\u003e1.2.1 Propositions, logical connectives, truth tables, tautologies 9\u003c\/p\u003e \u003cp\u003e1.2.2 Individual variables and quantifiers 12\u003c\/p\u003e \u003cp\u003e1.2.3 Exercises 15\u003c\/p\u003e \u003cp\u003e1.3 Mathematical induction 17\u003c\/p\u003e \u003cp\u003e1.3.1 Exercises 18\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Sets, Relations, Orders 20\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Set inclusions and equalities 21\u003c\/p\u003e \u003cp\u003e2.1.1 Properties of the set theoretic operations 22\u003c\/p\u003e \u003cp\u003e2.1.2 Exercises 26\u003c\/p\u003e \u003cp\u003e2.2 Functions 28\u003c\/p\u003e \u003cp\u003e2.2.1 Functions and their inverses 28\u003c\/p\u003e \u003cp\u003e2.2.2 Composition of mappings 31\u003c\/p\u003e \u003cp\u003e2.2.3 Exercises 33\u003c\/p\u003e \u003cp\u003e2.3 Binary relations and operations on them 35\u003c\/p\u003e \u003cp\u003e2.3.1 Binary relations 35\u003c\/p\u003e \u003cp\u003e2.3.2 Matrix and graphical representations of relations on finite sets 38\u003c\/p\u003e \u003cp\u003e2.3.3 Boolean operations on binary relations 39\u003c\/p\u003e \u003cp\u003e2.3.4 Inverse and composition of relations 41\u003c\/p\u003e \u003cp\u003e2.3.5 Exercises 42\u003c\/p\u003e \u003cp\u003e2.4 Special binary relations 45\u003c\/p\u003e \u003cp\u003e2.4.1 Properties of binary relations 45\u003c\/p\u003e \u003cp\u003e2.4.2 Functions as relations 47\u003c\/p\u003e \u003cp\u003e2.4.3 Reflexive, symmetric and transitive closures of a relation 47\u003c\/p\u003e \u003cp\u003e2.4.4 Exercises 49\u003c\/p\u003e \u003cp\u003e2.5 Equivalence relations and partitions 51\u003c\/p\u003e \u003cp\u003e2.5.1 Equivalence relations 51\u003c\/p\u003e \u003cp\u003e2.5.2 Quotient sets and partitions 53\u003c\/p\u003e \u003cp\u003e2.5.3 The kernel equivalence of a mapping 56\u003c\/p\u003e \u003cp\u003e2.5.4 Exercises 57\u003c\/p\u003e \u003cp\u003e2.6 Ordered sets 59\u003c\/p\u003e \u003cp\u003e2.6.1 Pre-orders and partial orders 59\u003c\/p\u003e \u003cp\u003e2.6.2 Graphical representing posets: Hasse diagrams 61\u003c\/p\u003e \u003cp\u003e2.6.3 Lower and upper bounds. Minimal and maximal elements 63\u003c\/p\u003e \u003cp\u003e2.6.4 Well-ordered sets 65\u003c\/p\u003e \u003cp\u003e2.6.5 Exercises 67\u003c\/p\u003e \u003cp\u003e2.7 An introduction to cardinality 69\u003c\/p\u003e \u003cp\u003e2.7.1 Equinumerosity and cardinality 69\u003c\/p\u003e \u003cp\u003e2.7.2 Exercises 73\u003c\/p\u003e \u003cp\u003e2.8 Isomorphisms of ordered sets. Ordinal numbers 75\u003c\/p\u003e \u003cp\u003e2.8.1 Exercises 79\u003c\/p\u003e \u003cp\u003e2.9 Application: relational databases 80\u003c\/p\u003e \u003cp\u003e2.9.1 Exercises 86\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Propositional Logic 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Propositions, logical connectives, truth tables, tautologies 90\u003c\/p\u003e \u003cp\u003e3.1.1 Propositions and propositional connectives. Truth tables 90\u003c\/p\u003e \u003cp\u003e3.1.2 Some remarks on the meaning of the connectives 90\u003c\/p\u003e \u003cp\u003e3.1.3 Propositional formulae 91\u003c\/p\u003e \u003cp\u003e3.1.4 Construction and parsing tree of a propositional formula 92\u003c\/p\u003e \u003cp\u003e3.1.5 Truth tables of propositional formulae 93\u003c\/p\u003e \u003cp\u003e3.1.6 Tautologies 95\u003c\/p\u003e \u003cp\u003e3.1.7 A better idea: search for a falsifying truth assignment 96\u003c\/p\u003e \u003cp\u003e3.1.8 Exercises 97\u003c\/p\u003e \u003cp\u003e3.2 Propositional logical consequence. Valid and invalid propositional inferences 101\u003c\/p\u003e \u003cp\u003e3.2.1 Propositional logical consequence 101\u003c\/p\u003e \u003cp\u003e3.2.2 Logically sound rules of propositional inference. Logically correct propositional arguments 104\u003c\/p\u003e \u003cp\u003e3.2.3 Fallacies of the implication 106\u003c\/p\u003e \u003cp\u003e3.2.4 Exercises 107\u003c\/p\u003e \u003cp\u003e3.3 The concept and use of deductive systems 109\u003c\/p\u003e \u003cp\u003e3.4 Semantic tableaux 113\u003c\/p\u003e \u003cp\u003e3.4.1 Exercises 117\u003c\/p\u003e \u003cp\u003e3.5 Logical equivalences. Negating propositional formulae 121\u003c\/p\u003e \u003cp\u003e3.5.1 Logically equivalent propositional formulae 121\u003c\/p\u003e \u003cp\u003e3.5.2 Some important equivalences 123\u003c\/p\u003e \u003cp\u003e3.5.3 Exercises 124\u003c\/p\u003e \u003cp\u003e3.6 Normal forms. Propositional resolution 126\u003c\/p\u003e \u003cp\u003e3.6.1 Conjunctive and disjunctive normal forms of propositional formulae 126\u003c\/p\u003e \u003cp\u003e3.6.2 Clausal form. Clausal resolution 129\u003c\/p\u003e \u003cp\u003e3.6.3 Resolution-based derivations 130\u003c\/p\u003e \u003cp\u003e3.6.4 Optimizing the method of resolution 131\u003c\/p\u003e \u003cp\u003e3.6.5 Exercises 132\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. First-Order Logic 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Basic concepts of first-order logic 136\u003c\/p\u003e \u003cp\u003e4.1.1 First-order structures 136\u003c\/p\u003e \u003cp\u003e4.1.2 First-order languages 138\u003c\/p\u003e \u003cp\u003e4.1.3 Terms and formulae 139\u003c\/p\u003e \u003cp\u003e4.1.4 The semantics of first-order logic: an informal outline 143\u003c\/p\u003e \u003cp\u003e4.1.5 Translating first-order formulae to natural language 146\u003c\/p\u003e \u003cp\u003e4.1.6 Exercises 147\u003c\/p\u003e \u003cp\u003e4.2 The formal semantics of first–order logic 152\u003c\/p\u003e \u003cp\u003e4.2.1 Interpretations 152\u003c\/p\u003e \u003cp\u003e4.2.2 Variable assignment and term evaluation 153\u003c\/p\u003e \u003cp\u003e4.2.3 Truth evaluation games 156\u003c\/p\u003e \u003cp\u003e4.2.4 Exercises 159\u003c\/p\u003e \u003cp\u003e4.3 The language of first-order logic: a deeper look 161\u003c\/p\u003e \u003cp\u003e4.3.1 Translations from natural language into first-order languages 161\u003c\/p\u003e \u003cp\u003e4.3.2 Restricted quantification 163\u003c\/p\u003e \u003cp\u003e4.3.3 Free and bound variables. Scope of a quantifier 164\u003c\/p\u003e \u003cp\u003e4.3.4 Renaming of a bound variable in a formula. Clean formulae 165\u003c\/p\u003e \u003cp\u003e4.3.5 Substitution of a term for a variable in a formula. Capture of a variable 166\u003c\/p\u003e \u003cp\u003e4.3.6 Exercises 167\u003c\/p\u003e \u003cp\u003e4.4 Truth, logical validity, equivalence and consequence in first-order logic 171\u003c\/p\u003e \u003cp\u003e4.4.1 More on truth of sentences in structures. Models and countermodels 171\u003c\/p\u003e \u003cp\u003e4.4.2 Satisfiability and validity of first-order formulae 172\u003c\/p\u003e \u003cp\u003e4.4.3 Logical equivalence in first-order logic 173\u003c\/p\u003e \u003cp\u003e4.4.4 Some logical equivalences involving quantifiers 174\u003c\/p\u003e \u003cp\u003e4.4.5 Negating first-order formulae 175\u003c\/p\u003e \u003cp\u003e4.4.6 Logical consequence in first-order logic 176\u003c\/p\u003e \u003cp\u003e4.4.7 Exercises 180\u003c\/p\u003e \u003cp\u003e4.5 Semantic tableaux for first-order logic 185\u003c\/p\u003e \u003cp\u003e4.5.1 Some derivations using first-order semantic tableau 186\u003c\/p\u003e \u003cp\u003e4.5.2 Semantic tableaux for first-order logic with equality 189\u003c\/p\u003e \u003cp\u003e4.5.3 Discussion on the quantifier rules and on termination of semantic tableaux 189\u003c\/p\u003e \u003cp\u003e4.5.4 Exercises 191\u003c\/p\u003e \u003cp\u003e4.6 Prenex and clausal normal forms 195\u003c\/p\u003e \u003cp\u003e4.6.1 Prenex normal forms 195\u003c\/p\u003e \u003cp\u003e4.6.2 Skolemization 197\u003c\/p\u003e \u003cp\u003e4.6.3 Clausal forms 198\u003c\/p\u003e \u003cp\u003e4.6.4 Exercises 199\u003c\/p\u003e \u003cp\u003e4.7 Resolution in first-order logic 201\u003c\/p\u003e \u003cp\u003e4.7.1 Propositional resolution rule in first-order logic 201\u003c\/p\u003e \u003cp\u003e4.7.2 Substitutions of terms for variables revisited 201\u003c\/p\u003e \u003cp\u003e4.7.3 Unification of terms 202\u003c\/p\u003e \u003cp\u003e4.7.4 Resolution with unification in first-order logic 204\u003c\/p\u003e \u003cp\u003e4.7.5 Examples of resolution-based derivations 205\u003c\/p\u003e \u003cp\u003e4.7.6 Resolution for first-order logic with equality 207\u003c\/p\u003e \u003cp\u003e4.7.7 Optimizations of the resolution method for first-order logic 207\u003c\/p\u003e \u003cp\u003e4.7.8 Exercises 207\u003c\/p\u003e \u003cp\u003e4.8 Applications of first-order logic to mathematical reasoning and proofs 211\u003c\/p\u003e \u003cp\u003e4.8.1 Proof strategies: direct and indirect proofs 211\u003c\/p\u003e \u003cp\u003e4.8.2 Tactics for logical reasoning 215\u003c\/p\u003e \u003cp\u003e4.8.3 Exercises 216\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Number Theory 219\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The principle of mathematical induction revisited 220\u003c\/p\u003e \u003cp\u003e5.1.1 Exercises 222\u003c\/p\u003e \u003cp\u003e5.2 Divisibility 224\u003c\/p\u003e \u003cp\u003e5.2.1 Basic properties of divisibility 224\u003c\/p\u003e \u003cp\u003e5.2.2 Division with a remainder 224\u003c\/p\u003e \u003cp\u003e5.2.3 Greatest common divisor 225\u003c\/p\u003e \u003cp\u003e5.2.4 Exercises 227\u003c\/p\u003e \u003cp\u003e5.3 Computing greatest common divisors. Least common multiples 230\u003c\/p\u003e \u003cp\u003e5.3.1 Euclid’s algorithm for computing greatest common divisors 230\u003c\/p\u003e \u003cp\u003e5.3.2 Least common multiple 232\u003c\/p\u003e \u003cp\u003e5.3.3 Exercises 233\u003c\/p\u003e \u003cp\u003e5.4 Prime numbers. The fundamental theorem of arithmetic 236\u003c\/p\u003e \u003cp\u003e5.4.1 Relatively prime numbers 236\u003c\/p\u003e \u003cp\u003e5.4.2 Prime numbers 237\u003c\/p\u003e \u003cp\u003e5.4.3 The fundamental theorem of arithmetic 238\u003c\/p\u003e \u003cp\u003e5.4.4 On the distribution of prime numbers 239\u003c\/p\u003e \u003cp\u003e5.4.5 Exercises 240\u003c\/p\u003e \u003cp\u003e5.5 Congruence relations 243\u003c\/p\u003e \u003cp\u003e5.5.1 Exercises 246\u003c\/p\u003e \u003cp\u003e5.6 Equivalence classes and residue systems modulo \u003ci\u003en \u003c\/i\u003e248\u003c\/p\u003e \u003cp\u003e5.6.1 Equivalence relations and partitions 248\u003c\/p\u003e \u003cp\u003e5.6.2 Equivalence classes modulo \u003ci\u003en\u003c\/i\u003e. Modular arithmetic 249\u003c\/p\u003e \u003cp\u003e5.6.3 Residue systems 250\u003c\/p\u003e \u003cp\u003e5.6.4 Multiplicative inverses in ℤ\u003ci\u003e\u003csub\u003en\u003c\/sub\u003e \u003c\/i\u003e251\u003c\/p\u003e \u003cp\u003e5.6.5 Exercises 251\u003c\/p\u003e \u003cp\u003e5.7 Linear Diophantine equations and linear congruences 253\u003c\/p\u003e \u003cp\u003e5.7.1 Linear Diophantine equations 253\u003c\/p\u003e \u003cp\u003e5.7.2 Linear congruences 254\u003c\/p\u003e \u003cp\u003e5.7.3 Exercises 256\u003c\/p\u003e \u003cp\u003e5.8 Chinese remainder theorem 257\u003c\/p\u003e \u003cp\u003e5.8.1 Exercises 259\u003c\/p\u003e \u003cp\u003e5.9 Euler’s function. Theorems of Euler and Fermat 261\u003c\/p\u003e \u003cp\u003e5.9.1 Theorems of Euler and Fermat 262\u003c\/p\u003e \u003cp\u003e5.9.2 Exercises 264\u003c\/p\u003e \u003cp\u003e5.10 Wilson’s theorem. Order of an integer 266\u003c\/p\u003e \u003cp\u003e5.10.1 Wilson’s theorem 266\u003c\/p\u003e \u003cp\u003e5.10.2 Order of an integer 266\u003c\/p\u003e \u003cp\u003e5.10.3 Exercises 267\u003c\/p\u003e \u003cp\u003e5.11 Application: public key cryptography 269\u003c\/p\u003e \u003cp\u003e5.11.1 About cryptography 269\u003c\/p\u003e \u003cp\u003e5.11.2 The idea of public key cryptography 269\u003c\/p\u003e \u003cp\u003e5.11.3 The method RSA 270\u003c\/p\u003e \u003cp\u003e5.11.4 Exercises 271\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Combinatorics 274\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Two basic counting principles 275\u003c\/p\u003e \u003cp\u003e6.1.1 Exercises 281\u003c\/p\u003e \u003cp\u003e6.2 Combinations. The binomial theorem 284\u003c\/p\u003e \u003cp\u003e6.2.1 Counting sheep and combinations 284\u003c\/p\u003e \u003cp\u003e6.2.2 Some important properties 286\u003c\/p\u003e \u003cp\u003e6.2.3 Pascal’s triangle 287\u003c\/p\u003e \u003cp\u003e6.2.4 The binomial theorem 287\u003c\/p\u003e \u003cp\u003e6.2.5 Exercises 289\u003c\/p\u003e \u003cp\u003e6.3 The principle of inclusion–exclusion 293\u003c\/p\u003e \u003cp\u003e6.3.1 Exercises 296\u003c\/p\u003e \u003cp\u003e6.4 The Pigeonhole Principle 299\u003c\/p\u003e \u003cp\u003e6.4.3 Exercises 302\u003c\/p\u003e \u003cp\u003e6.5 Generalized permutations, distributions and the multinomial theorem 304\u003c\/p\u003e \u003cp\u003e6.5.1 Arranging nondistinct objects 304\u003c\/p\u003e \u003cp\u003e6.5.2 Distributions 306\u003c\/p\u003e \u003cp\u003e6.5.3 The multinomial theorem 308\u003c\/p\u003e \u003cp\u003e6.5.4 Summary 310\u003c\/p\u003e \u003cp\u003e6.5.5 Exercises 311\u003c\/p\u003e \u003cp\u003e6.6 Selections and arrangements with repetition; distributions of identical objects 312\u003c\/p\u003e \u003cp\u003e6.6.1 Selections with repetition 312\u003c\/p\u003e \u003cp\u003e6.6.2 Distributions of identical objects 314\u003c\/p\u003e \u003cp\u003e6.6.3 Arrangements with repetition 315\u003c\/p\u003e \u003cp\u003e6.6.4 Summary 316\u003c\/p\u003e \u003cp\u003e6.6.5 Exercises 316\u003c\/p\u003e \u003cp\u003e6.7 Recurrence relations and their solution 318\u003c\/p\u003e \u003cp\u003e6.7.1 Recurrence relations. Fibonacci numbers 318\u003c\/p\u003e \u003cp\u003e6.7.2 Catalan numbers 319\u003c\/p\u003e \u003cp\u003e6.7.3 Solving homogeneous linear recurrence relations 322\u003c\/p\u003e \u003cp\u003e6.7.4 Exercises 327\u003c\/p\u003e \u003cp\u003e6.8 Generating functions 329\u003c\/p\u003e \u003cp\u003e6.8.1 Introducing generating functions 329\u003c\/p\u003e \u003cp\u003e6.8.2 Computing coefficients of generating functions 332\u003c\/p\u003e \u003cp\u003e6.8.3 Exercises 335\u003c\/p\u003e \u003cp\u003e6.9 Recurrence relations and generating functions 337\u003c\/p\u003e \u003cp\u003e6.9.1 Exercises 341\u003c\/p\u003e \u003cp\u003e6.10 Application: classical discrete probability 343\u003c\/p\u003e \u003cp\u003e6.10.1 Common sense probability 343\u003c\/p\u003e \u003cp\u003e6.10.2 Sample spaces 343\u003c\/p\u003e \u003cp\u003e6.10.3 Discrete probability 345\u003c\/p\u003e \u003cp\u003e6.10.4 Properties of probability measures 346\u003c\/p\u003e \u003cp\u003e6.10.5 Conditional probability and independent events 348\u003c\/p\u003e \u003cp\u003e6.10.6 Exercises 352\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Graph Theory 356\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction to graphs and digraphs 357\u003c\/p\u003e \u003cp\u003e7.1.1 Graphs 357\u003c\/p\u003e \u003cp\u003e7.1.2 Digraphs 364\u003c\/p\u003e \u003cp\u003e7.1.3 Exercises 367\u003c\/p\u003e \u003cp\u003e7.2 Incidence and adjacency matrices 370\u003c\/p\u003e \u003cp\u003e7.2.1 Exercises 374\u003c\/p\u003e \u003cp\u003e7.3 Weighted graphs and path algorithms 377\u003c\/p\u003e \u003cp\u003e7.3.1 Dijkstra’s algorithm 378\u003c\/p\u003e \u003cp\u003e7.3.2 The Floyd–Warshall algorithm 381\u003c\/p\u003e \u003cp\u003e7.3.3 Exercises 383\u003c\/p\u003e \u003cp\u003e7.4 Trees 385\u003c\/p\u003e \u003cp\u003e7.4.1 Undirected trees 385\u003c\/p\u003e \u003cp\u003e7.4.2 Computing spanning trees: Kruskal’s algorithm 388\u003c\/p\u003e \u003cp\u003e7.4.3 Rooted trees 390\u003c\/p\u003e \u003cp\u003e7.4.4 Traversing rooted trees 392\u003c\/p\u003e \u003cp\u003e7.4.5 Exercises 393\u003c\/p\u003e \u003cp\u003e7.5 Eulerian graphs and Hamiltonian graphs 395\u003c\/p\u003e \u003cp\u003e7.5.1 Eulerian graphs and digraphs 396\u003c\/p\u003e \u003cp\u003e7.5.2 Hamiltonian graphs and digraphs 398\u003c\/p\u003e \u003cp\u003e7.5.3 Exercises 400\u003c\/p\u003e \u003cp\u003e7.6 Planar graphs 404\u003c\/p\u003e \u003cp\u003e7.6.1 Exercises 408\u003c\/p\u003e \u003cp\u003e7.7 Graph colourings 411\u003c\/p\u003e \u003cp\u003e7.7.1 Colourings 411\u003c\/p\u003e \u003cp\u003e7.7.2 The four- and five-colour theorems 413\u003c\/p\u003e \u003cp\u003e7.7.3 Exercises 414\u003c\/p\u003e \u003cp\u003eIndex 419\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48866377302359,"sku":"9781118751275","price":37.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118751275.jpg?v=1722278361"},{"product_id":"graph-theory-new-research-9781628085433","title":"Graph Theory: New Research","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48887064822103,"sku":"9781628085433","price":146.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781628085433.jpg?v=1722542837"},{"product_id":"combinatorics-9780198723493","title":"Combinatorics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHow many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal''s triangle? (it was not Pascal)Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries.ABOUT THE SERIES: The  Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eClear and beautifully written ... this book is much more than a simple introduction ... [Its] great strength is that while examining a number of important concepts in detail, the author does so ... without using complicated abstract formulae. * Mathematics Today *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: What is combinatorics? 2: Four types of problem 3: Permutations and combinations 4: A combinatorial zoo 5: Tilings and polyhedra 6: Graphs 7: Square arrays 8: Designs and geometry 9: Partitions Further Reading Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":49083397833047,"sku":"9780198723493","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198723493.jpg?v=1725548809"},{"product_id":"automated-theorem-proving-after-25-years-9780821850275","title":"Automated Theorem Proving  After 25 Years","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAutomated theorem proving: a quarter century review by D. W. Loveland Citation to Hao Wang Computer theorem proving and artificial intelligence by H. Wang Citation to Lawrence Wos and Steven Winker Open questions solved with the assistance of AURA by L. Wos and S. Winker Some automatic proofs in analysis by W. W. Bledsoe Proof-checking, theorem-proving, and program verification by R. S. Boyer and J. S. Moore A mechanical proof of the turing completeness of pure LISP by R. S. Boyer and J. S. Moore Automating higher-order logic by P. B. Andrews, D. A. Miller, E. L. Cohen, and F. Pfenning Abelian group unification algorithms for elementary terms by D. Lankford, G. Butler, and B. Brady Combining satisfiability procedures by equality sharing by G. Nelson On the decision problem and the mechanization of theorem-proving in elementary geometry by W. Wen-Tsun Some recent advances in mechanical theorem-proving of geometries by W. Wen-Tsun Proving elementary geometry theorems using Wu's algorithm by S.-C. Chou Automated theory formation in mathematics by D. B. Lenat Student use of an interactive theorem prover by J. McDonald and P. Suppes.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":49083683537239,"sku":"9780821850275","price":89.25,"currency_code":"GBP","in_stock":true}]},{"product_id":"enumerative-combinatorics-volume-2-9781009262484","title":"Enumerative Combinatorics Volume 2","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eRichard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This updated edition provides the only comprehensive high-level treatment of enumerative combinatorics, including the theory of symmetric functions, with over 150 new exercises and solutions.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'This is one of the great books; readable, deep and full of gems. It brings algebraic combinatorics to life. I teach out of it and feel that if I can get my students to 'touch Stanley' I have given them a gift for life.' Persi Diaconis, Stanford University\u003cbr\u003e'It is wonderful to celebrate the completion of the second edition of Richard Stanley's Enumerative Combinatorics, one of the finest mathematical works of all time. He has added nearly 200 exercises, together with their answers, to what was already a uniquely masterful summary of a vast and beautiful theory. When paired with the second edition of Volume 1, his two classic volumes will surely be a timeless treasure for generations to come.' Donald E. Knuth, Stanford University\u003cbr\u003e'An updated classic with a mesmerizing array of interconnected examples. Through Stanley's masterful exposition, the current and future generations of mathematicians will learn the inherent beauty and pleasures of enumeration.' June Huh, Princeton University\u003cbr\u003e'I have used Richard Stanley's books on Enumerative Combinatorics numerous times for the combinatorics classes I have taught. This new edition contains many new exercises, which will no doubt be extremely useful for the next generation of combinatorialists.' Anne Schilling, University of California, Davis\u003cbr\u003e'Richard Stanley's Enumerative Combinatorics, in two volumes, is an essential reference for researchers and graduate students in the field of enumeration. Volume 2, newly revised, includes comprehensive coverage of composition and inversion of generating functions, exponential and algebraic generating functions, and symmetric functions. The treatment of symmetric functions is especially noteworthy for its thoroughness and accessibility. Engaging problems and solutions, and detailed historical notes, add to the value of this book. It provides an excellent introduction to the subject for beginners while also offering advanced researchers new insights and perspectives.' Ira Gessel, Brandeis University\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface to Second Edition; Preface; 5. Trees and the Composition of Generating Functions; 6. Algebraic Generating Functions; 7. Symmetric Functions; Appendices: References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49083792687447,"sku":"9781009262484","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009262484.jpg?v=1725550039"},{"product_id":"an-invitation-to-combinatorics-9781108476546","title":"An Invitation to Combinatorics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eActive student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author  an award-winning teacher  writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'I would certainly accept this 'invitation.' The text covers essentially all of the basic combinatorial subjects in a both gentle and intense way. The extensive problems, examples, and 'projects,' especially the collaborative projects, exemplify current pedagogical research on effective teaching methods. I would expect it to remain as a reference on many shelves.' Bruce Rothschild, University of California, Los Angeles\u003cbr\u003e'Shahriari's voice as an experienced classroom teacher shines through in this brilliantly crafted student-friendly text. Each mini-project provides a guided exploration of an interesting topic in combinatorics. These, together with the plethora of interesting exercises, help the student to build problem-solving muscle and to experience the joy of mathematical discovery.' Jamie Pommersheim, Reed College\u003cbr\u003e'From well-chosen motivating problems in the introduction to deeper material near the book's conclusion, Shahriari invites students encountering combinatorics systematically for the first time to think, to build, and to play. His warm writing style and cross-cultural approach to core topics of the field are sure to engage readers from many backgrounds and levels of preparation.' Joshua Cooper, University of South Carolina\u003cbr\u003e'This book is a mathematically rigorous introductory textbook on combinatorics. It contains an excellent range of problems and exercises that will help students practice and learn the material. It also lists open questions in combinatorics so students can see that the field continues to develop. The really special feature of this book is a lovely collection of mini-projects that let students explore a variety of topics and deepen their understanding.' David Auckly, Kansas State University\u003cbr\u003e'I highly recommend this text. Among its most interesting, unusual, and valuable features, one finds a long list of collaborative mini-projects for students to work on in groups, together with other problems to work on individually; nice historical asides, including references to the work of non-Western mathematicians; and a very accessible conversational style. It fits well with discovery-style or problem-oriented courses on the subject.' William Monty McGovern, University of Washington\u003cbr\u003e'One of the major attractions of this textbook is the writing style - it is designed to be very readable, as though the author were having a conversation with the reader. The result is a text which feels engaging - a quality which is sure to be of great benefit to undergraduate students.' Audie Warren, zbMATH\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Introduction; 1. Induction and Recurrence Relations; 2. The Pigeonhole Principle and Ramsey Theory; 3. Counting, Probability, Balls and Boxes; 4. Permutations and Combinations; 5. Binomial and Multinomial Coefficients; 6. Stirling Numbers; 7. Integer Partitions; 8. The Inclusion-Exclusion Principle; 9. Generating Functions; 10. Graph Theory; 11. Posets, Matchings, and Boolean Lattices; Appendices; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49083829485911,"sku":"9781108476546","price":54.13,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108476546.jpg?v=1725550148"},{"product_id":"logical-methods-the-art-of-thinking-abstractly-and-mathematically-9783030637767","title":"Logical Methods: The Art of Thinking Abstractly","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMany believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. \u003cp\u003eThis book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science,  its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more.\u003c\/p\u003e  \u003cp\u003eIn the book you will, among other things, find answers to:\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eWhat is a proof? What is a counterexample?\u003c\/li\u003e\n\u003cli\u003eWhat does it mean to say that something follows logically from a set of premises?\u003c\/li\u003e\n\u003cli\u003eWhat does it mean to abstract over something?\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eHow can knowledge and information be represented and used in calculations?\u003c\/li\u003e\n\u003cli\u003eWhat is the connection between Morse code and Fibonacci numbers?\u003c\/li\u003e\n\u003cli\u003eWhy could it take billions of years to solve Hanoi's Tower?\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eLogical Methods\u003c\/i\u003e is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The definitions are followed by examples to help explain their meaning, along with counterexamples ... . Therefore, very little basic knowledge is required for this introduction to logical methods ... which is written in an accessible style ... . contained in the book are several hundred small figures; arrow, Venn, and Hasse diagrams; and simplifies visual representations ... . The author has also elected to use color to draw the reader's attention ... .\" \u003cbr\u003e“From personal teaching experience, knowledge of these mathematical areas is necessary for disparate fields of CS and informatics. These foundations are needed for many fields, from database theory to various domains of information systems applications. The book’s presentation of topics and incentives for problem-solving, along with its exercises, is very useful for university-level instructors and students. The compact chapters contain clear explanations, diagrams, and brief descriptions of interesting facts.” (Bálint Molnár, Computing Reviews, July 27, 2021)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 0 The Art of Thinking Abstractly and Mathematically.- 1 Basic Set Theory.- 2 Propositional Logic.- 3 Semantics from Propositional Logic.- 4 Concepts in Propositional Logic.- 5 Proofs, Conjectures, and Counterexamples.- 6 Relations.- 7 Functions.- 8 A Little More Set Theory.- 9 Closures and Inductively Defined Sets.- 10 Recursively Defined Functions.- 11 Mathematical Induction.- 12 Structural Induction.- 13 First-Order Languages.- 14 Representation of Quantified Statements.- 15 Interpretation in Models.- 16 Reasoning About Models.- 17 Abstraction with Equivalences and Partitions.- 18 Combinatorics.- 19 A Little More Combinatorics.- 20 A Bit of Abstract Algebra.- 21 Graph Theory.- 22 Walks in Graphs.- 23 Formal Languages and Grammars.- 24 Natural Deduction.- The Road Ahead.- Index. Symbols.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49084751479127,"sku":"9783030637767","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030637767.jpg?v=1725553226"},{"product_id":"graph-and-network-theory-an-applied-approach-using-mathematica-r-9783031038594","title":"Graph and Network Theory: An Applied Approach","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics\/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book.  \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThe material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- List of Algorithms.- List of Bibliographical Notes.- Part 1. Topics in network optimisation.- 1. An introduction to graphs.- 2. Graph connectedness.- 3. Algorithmic complexity.- 4. Optimal paths.- 5. Trees.- 6. Location problems.- 7. Maximum flow networks.- 8. Minimum-cost network flows.- Part 2. Topics in classical graph theory.- 9. Matchings.- 10. Eulerian graphs.- 11. Hamiltonian graphs.- 12. Graph connectivity.- 13. Planarity.- 14. Graph colouring.- 15. Oriented graphs. Part 3. Topics in modern graph theory.- 16. Domination in graphs.- 17. Ramsey Theory.-  18. Extremal graph theory.- 19. Graph enumeration.- 20. The probabilistic method.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084752396631,"sku":"9783031038594","price":55.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031038594.jpg?v=1725553228"},{"product_id":"advanced-graph-theory-9783031225642","title":"Advanced Graph Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084754133335,"sku":"9783031225642","price":43.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031225642.jpg?v=1725553234"},{"product_id":"discrete-mathematics-a-concise-introduction-9783031304873","title":"Discrete Mathematics: A Concise Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. “Safe” – that is, paradox-free – informal set theory is introduced following on the heels of Russell’s Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor’s diagonalisation technique. Predicate logic “for the user” is introduced along with axioms and rules and extensive examples. Partial orders and the \u003ci\u003eminimal condition\u003c\/i\u003e are studied in detail with the latter shown to be equivalent to the \u003ci\u003einduction principle\u003c\/i\u003e. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of \u003ci\u003efunctions\u003c\/i\u003e \u003ci\u003eand\u003c\/i\u003e \u003ci\u003esets\u003c\/i\u003e. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics. \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eElementary Informal Set Theory.- Safe Set Theory.- Relations and Functions.- A Tiny Bit of Informal Logic.- Inductively Defined Sets and Structural Induction.- Recurrence Equations.- Trees and Graphs.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084755738967,"sku":"9783031304873","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031304873.jpg?v=1725553236"},{"product_id":"why-machines-learn-9780593185742","title":"Why Machines Learn","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Penguin Publishing Group","offers":[{"title":"Default Title","offer_id":49396197130583,"sku":"9780593185742","price":18.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780593185742.jpg?v=1730415065"},{"product_id":"discrete-mathematics-9780128206560","title":"Discrete Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Discrete Mathematics is adequately written and well-documented....  This book presents the material on the topic in a cogently coherent manner thereby serving and justifying the purpose of writing books such as this one.  The classroom-tested pedagogy and its 400 examples speak a lot about the kind and amount of sweat that must have gone into it.\" --zbMATH Open\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I: Logic 1. Propositional Logic 2. Predicate Logic   Part II: Set Theory and Related Topics 3. Sets 4. Matrices 5. Relations 6. Functions 7. Boolean Algebra   Part III: Proof Methods 8. Sequences 9. Recursion 10. Induction 11. General Proof Methods   Part IV: Number Theory and Applications 12. Elementary Number Theory 13. Cryptography   Part V: Probability 14. Counting Methods 15. Discrete Probability 16. Discrete Random Variables   Part VI: Graph Theory 17. Graphs 18. Trees 19. Network Models   Part VII: Algorithms and Finite State Machines 20. Algorithms","brand":"Elsevier Science Publishing Co Inc","offers":[{"title":"Default Title","offer_id":49399839031639,"sku":"9780128206560","price":56.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780128206560.jpg?v=1730468875"},{"product_id":"machine-learning-9780323898591","title":"Machine Learning","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Elsevier Science \u0026 Technology","offers":[{"title":"Default Title","offer_id":49401782894935,"sku":"9780323898591","price":75.95,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780323898591.jpg?v=1730478507"},{"product_id":"evolutionary-optimization-algorithms-9780470937419","title":"Evolutionary Optimization Algorithms","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA clear and lucid bottom-up approach to the basic principles of evolutionary algorithms\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003eEvolutionary algorithms (EAs) are a type of artificial intelligence. EAs are motivated by optimization processes that we observe in nature, such as natural selection, species migration, bird swarms, human culture, and ant colonies. \u003c\/p\u003e\u003cp\u003eThis book discusses the theory, history, mathematics, and programming of evolutionary optimization algorithms. Featured algorithms include genetic algorithms, genetic programming, ant colony optimization, particle swarm optimization, differential evolution, biogeography-based optimization, and many others. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eEvolutionary Optimization Algorithms:\u003c\/i\u003e \u003c\/p\u003e\u003cul\u003e \u003cli\u003eProvides a straightforward, bottom-up approach that assists the reader in obtaining a clear?but theoretically rigorous?understanding of evolutionary algorithms, with an emphasis on implementation\u003c\/li\u003e \u003cli\u003eGives a careful treatment of recently developed EAs?including opposition-based learning, arti\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAcknowledgments xxi\u003cbr\u003e \u003cbr\u003e Acronyms xxiii\u003cbr\u003e \u003cbr\u003e List of Algorithms xxvii\u003cbr\u003e \u003cbr\u003e \u003cb\u003ePart I: Introduction to Evolutionary Optimization\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 1 Introduction 1\u003cbr\u003e \u003cbr\u003e 2 Optimization 11\u003cbr\u003e \u003cbr\u003e \u003cb\u003ePart II: Classic Evolutionary Algorithms\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 3 Generic Algorithms 35\u003cbr\u003e \u003cbr\u003e 4 Mathematical Models of Genetic Algorithms 63\u003cbr\u003e \u003cbr\u003e 5 Evolutionary Programming 95\u003cbr\u003e \u003cbr\u003e 6 Evolution Strategies 117\u003cbr\u003e \u003cbr\u003e 7 Genetic Programming 141\u003cbr\u003e \u003cbr\u003e 8 Evolutionary Algorithms Variations 179\u003cbr\u003e \u003cbr\u003e \u003cb\u003ePart III: More Recent Evolutionary Algorithms\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e 9 Simulated Annealing 223\u003cbr\u003e \u003cbr\u003e 10 Ant Colony Optimization 241\u003cbr\u003e \u003cbr\u003e 11 Particle Swarm Optimization 265\u003cbr\u003e \u003cbr\u003e 12 Differential Evolution 293\u003cbr\u003e \u003cbr\u003e 13 Estimation of Distribution Algorithms 313\u003cbr\u003e \u003cbr\u003e 14 Biogeography-Based Optimization 351\u003cbr\u003e \u003cbr\u003e 15 Cultural Algorithms 377\u003cbr\u003e \u003cbr\u003e 16 Opposition-Based Learning 397\u003cbr\u003e \u003cbr\u003e 17 Other Evolutionary Algorithms 421\u003cbr\u003e \u003cbr\u003e \u003cb\u003ePart IV: Special Type of Optimization Problems\u003c\/b\u003e \u003cbr\u003e \u003cbr\u003e 18 Combinatorial Optimization 449\u003cbr\u003e \u003cbr\u003e 19 Constrained Optimization 481\u003cbr\u003e \u003cbr\u003e 20 Multi-Objective Optimization 517\u003cbr\u003e \u003cbr\u003e 21 Expensive, Noisy and Dynamic Fitness Functions 563\u003cbr\u003e \u003cbr\u003e \u003cb\u003eAppendices\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e A Some Practical Advice 607\u003cbr\u003e \u003cbr\u003e B The No Free Lunch Theorem and Performance Testing 613\u003cbr\u003e \u003cbr\u003e C Benchmark Optimization Functions 641\u003c\/p\u003e \u003cp\u003eReferences 685\u003c\/p\u003e \u003cp\u003eTopic Index 727\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402461552983,"sku":"9780470937419","price":99.86,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470937419.jpg?v=1730480481"},{"product_id":"essential-discrete-mathematics-for-computer-science-9780691179292","title":"Essential Discrete Mathematics for Computer","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"I want to share with everybody my enjoyment of this excellent textbook.\"\u003cb\u003e---Narciso Marti-Oliet, \u003ci\u003eEuropean Math Society\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Those teaching computer scientists who take discrete mathematics alongside other mathematics modules such as linear algebra and calculus (as is the case with the CS20 students at Harvard), and who need a book with an emphasis on proof, will likely and this book a very good choice for their students.\"\u003cb\u003e---London Mathematical Society, \u003ci\u003eGlenn Hawe\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403854127447,"sku":"9780691179292","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691179292.jpg?v=1730484725"},{"product_id":"finite-mathematics-9781119015536","title":"Finite Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eThis set includes \u003ci\u003eFinite Mathematics: Models and Applications\u003c\/i\u003e \u0026amp; \u003ci\u003eSolutions Manual to accompany Finite Mathematics: Models and Applications\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eFinite Mathematics: Models and Applications \u003c\/i\u003e emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.\u003c\/p\u003e \u003cp\u003eThe book features coverage including: Algebra Skills; Mathematics of Finance; Matrix Algebra; Geometric Solutions; Simplex Methods; Application Models; Set and Probability Relationships; Random Variables and Probability Distributions; Markov Chains; Mathematical Statistics; Enrichment in Finite Mathematics\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003eAbout the Authors xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Linear Equations and Mathematical Concepts 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Solving Linear Equations 2\u003c\/p\u003e \u003cp\u003e1.2 Equations of Lines and Their Graphs 7\u003c\/p\u003e \u003cp\u003e1.3 Solving Systems of Linear Equations 15\u003c\/p\u003e \u003cp\u003e1.4 The Numbers \u003ci\u003e𝜋 \u003c\/i\u003eand \u003ci\u003ee\u003c\/i\u003e 21\u003c\/p\u003e \u003cp\u003e1.5 Exponential and Logarithmic Functions 24\u003c\/p\u003e \u003cp\u003e1.6 Variation 32\u003c\/p\u003e \u003cp\u003e1.7 Unit Conversions and Dimensional Analysis 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Mathematics of Finance 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Simple and Compound Interest 47\u003c\/p\u003e \u003cp\u003e2.2 Ordinary Annuity 55\u003c\/p\u003e \u003cp\u003e2.3 Amortization 59\u003c\/p\u003e \u003cp\u003e2.4 Arithmetic and Geometric Sequences 63\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Matrix Algebra 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Matrices 72\u003c\/p\u003e \u003cp\u003e3.2 Matrix Notation, Arithmetic, and Augmented Matrices 78\u003c\/p\u003e \u003cp\u003e3.3 Gauss–Jordan Elimination 89\u003c\/p\u003e \u003cp\u003e3.4 Matrix Inversion and Input–Output Analysis 100\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Linear Programming – Geometric Solutions 116\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 116\u003c\/p\u003e \u003cp\u003e4.1 Graphing Linear Inequalities 117\u003c\/p\u003e \u003cp\u003e4.2 Graphing Systems of Linear Inequalities 121\u003c\/p\u003e \u003cp\u003e4.3 Geometric Solutions to Linear Programs 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Linear Programming – Simplex Method 136\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Standard Maximization Problem (SMP) 137\u003c\/p\u003e \u003cp\u003e5.2 Tableaus and Pivot Operations 142\u003c\/p\u003e \u003cp\u003e5.3 Optimal Solutions and the Simplex Method 149\u003c\/p\u003e \u003cp\u003e5.4 Dual Programs 161\u003c\/p\u003e \u003cp\u003e5.5 Non-SMP Linear Programs 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Linear Programming – Application Models 182\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Set and Probability Relationships 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Sets 204\u003c\/p\u003e \u003cp\u003e7.2 Venn Diagrams 210\u003c\/p\u003e \u003cp\u003e7.3 Tree Diagrams 216\u003c\/p\u003e \u003cp\u003e7.4 Combinatorics 221\u003c\/p\u003e \u003cp\u003e7.5 Mathematical Probability 231\u003c\/p\u003e \u003cp\u003e7.6 Bayes’ Rule and Decision Trees 245\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Random Variables and Probability Distributions 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Random Variables 259\u003c\/p\u003e \u003cp\u003e8.2 Bernoulli Trials and the Binomial Distribution 265\u003c\/p\u003e \u003cp\u003e8.3 The Hypergeometric Distribution 273\u003c\/p\u003e \u003cp\u003e8.4 The Poisson Distribution 279\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Markov Chains 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Transition Matrices and Diagrams 286\u003c\/p\u003e \u003cp\u003e9.2 Transitions 291\u003c\/p\u003e \u003cp\u003e9.3 Regular Markov Chains 295\u003c\/p\u003e \u003cp\u003e9.4 Absorbing Markov Chains 304\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Mathematical Statistics 314\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Graphical Descriptions of Data 315\u003c\/p\u003e \u003cp\u003e10.2 Measures of Central Tendency and Dispersion 323\u003c\/p\u003e \u003cp\u003e10.3 The Uniform Distribution 331\u003c\/p\u003e \u003cp\u003e10.4 The Normal Distribution 334\u003c\/p\u003e \u003cp\u003e10.5 Normal Distribution Applications 348\u003c\/p\u003e \u003cp\u003e10.6 Developing and Conducting a Survey 363\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Enrichment in Finite Mathematics 371\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Game Theory 372\u003c\/p\u003e \u003cp\u003e11.2 Applications in Finance and Economics 385\u003c\/p\u003e \u003cp\u003e11.3 Applications in Social and Life Sciences 394\u003c\/p\u003e \u003cp\u003e11.4 Monte Carlo Method 403\u003c\/p\u003e \u003cp\u003e11.5 Dynamic Programming 422\u003c\/p\u003e \u003cp\u003eAnswers to Odd Numbered Exercises 439\u003c\/p\u003e \u003cp\u003eUsing Technology 502\u003c\/p\u003e \u003cp\u003eGlossary 506\u003c\/p\u003e \u003cp\u003eIndex 513\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406967185751,"sku":"9781119015536","price":116.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119015536.jpg?v=1730497724"},{"product_id":"integer-programming-9781119606536","title":"Integer Programming","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe revised second edition of \u003ci\u003eInteger Programming\u003c\/i\u003e explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing\/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders' decompositi\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface to the Second Edition xii\u003c\/p\u003e \u003cp\u003ePreface to the First Edition xiii\u003c\/p\u003e \u003cp\u003eAbbreviations and Notation xvii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Formulations \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 What Is an Integer Program? 3\u003c\/p\u003e \u003cp\u003e1.3 Formulating IPs and BIPs 5\u003c\/p\u003e \u003cp\u003e1.4 The Combinatorial Explosion 8\u003c\/p\u003e \u003cp\u003e1.5 Mixed Integer Formulations 9\u003c\/p\u003e \u003cp\u003e1.6 Alternative Formulations 12\u003c\/p\u003e \u003cp\u003e1.7 Good and Ideal Formulations 15\u003c\/p\u003e \u003cp\u003e1.8 Notes 18\u003c\/p\u003e \u003cp\u003e1.9 Exercises 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Optimality, Relaxation, and Bounds \u003c\/b\u003e\u003cb\u003e25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Optimality and Relaxation 25\u003c\/p\u003e \u003cp\u003e2.2 Linear Programming Relaxations 27\u003c\/p\u003e \u003cp\u003e2.3 Combinatorial Relaxations 28\u003c\/p\u003e \u003cp\u003e2.4 Lagrangian Relaxation 29\u003c\/p\u003e \u003cp\u003e2.5 Duality 30\u003c\/p\u003e \u003cp\u003e2.6 Linear Programming and Polyhedra 32\u003c\/p\u003e \u003cp\u003e2.7 Primal Bounds: Greedy and Local Search 34\u003c\/p\u003e \u003cp\u003e2.8 Notes 38\u003c\/p\u003e \u003cp\u003e2.9 Exercises 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Well-Solved Problems \u003c\/b\u003e\u003cb\u003e43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Properties of Easy Problems 43\u003c\/p\u003e \u003cp\u003e3.2 IPs with Totally Unimodular Matrices 44\u003c\/p\u003e \u003cp\u003e3.3 Minimum Cost Network Flows 46\u003c\/p\u003e \u003cp\u003e3.4 Special Minimum Cost Flows 48\u003c\/p\u003e \u003cp\u003e3.4.1 Shortest Path 48\u003c\/p\u003e \u003cp\u003e3.4.2 Maximum \u003ci\u003es \u003c\/i\u003e− \u003ci\u003et \u003c\/i\u003eFlow 49\u003c\/p\u003e \u003cp\u003e3.5 Optimal Trees 50\u003c\/p\u003e \u003cp\u003e3.6 Submodularity and Matroids 54\u003c\/p\u003e \u003cp\u003e3.7 Two Harder Network Flow Problems 57\u003c\/p\u003e \u003cp\u003e3.8 Notes 59\u003c\/p\u003e \u003cp\u003e3.9 Exercises 60\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Matchings and Assignments \u003c\/b\u003e\u003cb\u003e63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Augmenting Paths and Optimality 63\u003c\/p\u003e \u003cp\u003e4.2 Bipartite Maximum Cardinality Matching 65\u003c\/p\u003e \u003cp\u003e4.3 The Assignment Problem 67\u003c\/p\u003e \u003cp\u003e4.4 Matchings in Nonbipartite Graphs 73\u003c\/p\u003e \u003cp\u003e4.5 Notes 74\u003c\/p\u003e \u003cp\u003e4.6 Exercises 75\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Dynamic Programming \u003c\/b\u003e\u003cb\u003e79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Some Motivation: Shortest Paths 79\u003c\/p\u003e \u003cp\u003e5.2 Uncapacitated Lot-Sizing 80\u003c\/p\u003e \u003cp\u003e5.3 An Optimal Subtree of a Tree 83\u003c\/p\u003e \u003cp\u003e5.4 Knapsack Problems 84\u003c\/p\u003e \u003cp\u003e5.4.1 0–1 Knapsack Problems 85\u003c\/p\u003e \u003cp\u003e5.4.2 Integer Knapsack Problems 86\u003c\/p\u003e \u003cp\u003e5.5 The Cutting Stock Problem 89\u003c\/p\u003e \u003cp\u003e5.6 Notes 91\u003c\/p\u003e \u003cp\u003e5.7 Exercises 92\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Complexity and Problem Reductions \u003c\/b\u003e\u003cb\u003e95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Complexity 95\u003c\/p\u003e \u003cp\u003e6.2 Decision Problems, and Classes \u003ci\u003eNP\u003c\/i\u003e and \u003ci\u003eP\u003c\/i\u003e 96\u003c\/p\u003e \u003cp\u003e6.3 Polynomial Reduction and the Class \u003ci\u003eNPC\u003c\/i\u003e 98\u003c\/p\u003e \u003cp\u003e6.4 Consequences of P =NP orP ≠NP 103\u003c\/p\u003e \u003cp\u003e6.5 Optimization and Separation 104\u003c\/p\u003e \u003cp\u003e6.6 The Complexity of Extended Formulations 105\u003c\/p\u003e \u003cp\u003e6.7 Worst-Case Analysis of Heuristics 106\u003c\/p\u003e \u003cp\u003e6.8 Notes 109\u003c\/p\u003e \u003cp\u003e6.9 Exercises 110\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Branch and Bound \u003c\/b\u003e\u003cb\u003e113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Divide and Conquer 113\u003c\/p\u003e \u003cp\u003e7.2 Implicit Enumeration 114\u003c\/p\u003e \u003cp\u003e7.3 Branch and Bound: an Example 116\u003c\/p\u003e \u003cp\u003e7.4 LP-Based Branch and Bound 120\u003c\/p\u003e \u003cp\u003e7.5 Using a Branch-and-Bound\/Cut System 123\u003c\/p\u003e \u003cp\u003e7.6 Preprocessing or Presolve 129\u003c\/p\u003e \u003cp\u003e7.7 Notes 134\u003c\/p\u003e \u003cp\u003e7.8 Exercises 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Cutting Plane Algorithms \u003c\/b\u003e\u003cb\u003e139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 139\u003c\/p\u003e \u003cp\u003e8.2 Some Simple Valid Inequalities 140\u003c\/p\u003e \u003cp\u003e8.3 Valid Inequalities 143\u003c\/p\u003e \u003cp\u003e8.4 A Priori Addition of Constraints 147\u003c\/p\u003e \u003cp\u003e8.5 Automatic Reformulation or Cutting Plane Algorithms 149\u003c\/p\u003e \u003cp\u003e8.6 Gomory’s Fractional Cutting Plane Algorithm 150\u003c\/p\u003e \u003cp\u003e8.7 Mixed Integer Cuts 153\u003c\/p\u003e \u003cp\u003e8.7.1 The Basic Mixed Integer Inequality 153\u003c\/p\u003e \u003cp\u003e8.7.2 The Mixed Integer Rounding (MIR) Inequality 155\u003c\/p\u003e \u003cp\u003e8.7.3 The Gomory Mixed Integer Cut 155\u003c\/p\u003e \u003cp\u003e8.7.4 Split Cuts 156\u003c\/p\u003e \u003cp\u003e8.8 Disjunctive Inequalities and Lift-and-Project 158\u003c\/p\u003e \u003cp\u003e8.9 Notes 161\u003c\/p\u003e \u003cp\u003e8.10 Exercises 162\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Strong Valid Inequalities \u003c\/b\u003e\u003cb\u003e167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 167\u003c\/p\u003e \u003cp\u003e9.2 Strong Inequalities 168\u003c\/p\u003e \u003cp\u003e9.3 0–1 Knapsack Inequalities 175\u003c\/p\u003e \u003cp\u003e9.3.1 Cover Inequalities 175\u003c\/p\u003e \u003cp\u003e9.3.2 Strengthening Cover Inequalities 176\u003c\/p\u003e \u003cp\u003e9.3.3 Separation for Cover Inequalities 178\u003c\/p\u003e \u003cp\u003e9.4 Mixed 0–1 Inequalities 179\u003c\/p\u003e \u003cp\u003e9.4.1 Flow Cover Inequalities 179\u003c\/p\u003e \u003cp\u003e9.4.2 Separation for Flow Cover Inequalities 181\u003c\/p\u003e \u003cp\u003e9.5 The Optimal Subtour Problem 183\u003c\/p\u003e \u003cp\u003e9.5.1 Separation for Generalized Subtour Constraints 183\u003c\/p\u003e \u003cp\u003e9.6 Branch-and-Cut 186\u003c\/p\u003e \u003cp\u003e9.7 Notes 189\u003c\/p\u003e \u003cp\u003e9.8 Exercises 190\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Lagrangian Duality \u003c\/b\u003e\u003cb\u003e195\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Lagrangian Relaxation 195\u003c\/p\u003e \u003cp\u003e10.2 The Strength of the Lagrangian Dual 200\u003c\/p\u003e \u003cp\u003e10.3 Solving the Lagrangian Dual 202\u003c\/p\u003e \u003cp\u003e10.4 Lagrangian Heuristics 205\u003c\/p\u003e \u003cp\u003e10.5 Choosing a Lagrangian Dual 207\u003c\/p\u003e \u003cp\u003e10.6 Notes 209\u003c\/p\u003e \u003cp\u003e10.7 Exercises 210\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Column (and Row) Generation Algorithms \u003c\/b\u003e\u003cb\u003e213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 213\u003c\/p\u003e \u003cp\u003e11.2 The Dantzig–Wolfe Reformulation of an IP 215\u003c\/p\u003e \u003cp\u003e11.3 Solving the LP Master Problem: Column Generation 216\u003c\/p\u003e \u003cp\u003e11.4 Solving the Master Problem: Branch-and-Price 219\u003c\/p\u003e \u003cp\u003e11.5 Problem Variants 222\u003c\/p\u003e \u003cp\u003e11.5.1 Handling Multiple Subproblems 222\u003c\/p\u003e \u003cp\u003e11.5.2 Partitioning\/Packing Problems with Additional Variables 223\u003c\/p\u003e \u003cp\u003e11.5.3 Partitioning\/Packing Problems with Identical Subsets 224\u003c\/p\u003e \u003cp\u003e11.6 Computational Issues 225\u003c\/p\u003e \u003cp\u003e11.7 Branch-Cut-and-Price: An Example 226\u003c\/p\u003e \u003cp\u003e11.7.1 A Capacitated Vehicle Routing Problem 226\u003c\/p\u003e \u003cp\u003e11.7.2 Solving the Subproblems 229\u003c\/p\u003e \u003cp\u003e11.7.3 The Load Formulation 230\u003c\/p\u003e \u003cp\u003e11.8 Notes 231\u003c\/p\u003e \u003cp\u003e11.9 Exercises 232\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Benders’ Algorithm \u003c\/b\u003e\u003cb\u003e235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 235\u003c\/p\u003e \u003cp\u003e12.2 Benders’ Reformulation 236\u003c\/p\u003e \u003cp\u003e12.3 Benders’ with Multiple Subproblems 240\u003c\/p\u003e \u003cp\u003e12.4 Solving the Linear Programming Subproblems 242\u003c\/p\u003e \u003cp\u003e12.5 Integer Subproblems: Basic Algorithms 244\u003c\/p\u003e \u003cp\u003e12.5.1 Branching in the (\u003ci\u003ex, \u003c\/i\u003e\u003ci\u003e𝜂, y\u003c\/i\u003e)-Space 244\u003c\/p\u003e \u003cp\u003e12.5.2 Branching in (\u003ci\u003ex, \u003c\/i\u003e\u003ci\u003e𝜂\u003c\/i\u003e)-Space and “No-Good” Cuts 246\u003c\/p\u003e \u003cp\u003e12.6 Notes 247\u003c\/p\u003e \u003cp\u003e12.7 Exercises 248\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Primal Heuristics \u003c\/b\u003e251\u003c\/p\u003e \u003cp\u003e13.1 Introduction 251\u003c\/p\u003e \u003cp\u003e13.2 Greedy and Local Search Revisited 252\u003c\/p\u003e \u003cp\u003e13.3 Improved Local Search Heuristics 255\u003c\/p\u003e \u003cp\u003e13.3.1 Tabu Search 255\u003c\/p\u003e \u003cp\u003e13.3.2 Simulated Annealing 256\u003c\/p\u003e \u003cp\u003e13.3.3 Genetic Algorithms 257\u003c\/p\u003e \u003cp\u003e13.4 Heuristics Inside MIP Solvers 259\u003c\/p\u003e \u003cp\u003e13.4.1 Construction Heuristics 259\u003c\/p\u003e \u003cp\u003e13.4.2 Improvement Heuristics 261\u003c\/p\u003e \u003cp\u003e13.5 User-Defined MIP heuristics 262\u003c\/p\u003e \u003cp\u003e13.6 Notes 265\u003c\/p\u003e \u003cp\u003e13.7 Exercises 266\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 From Theory to Solutions \u003c\/b\u003e\u003cb\u003e269\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 269\u003c\/p\u003e \u003cp\u003e14.2 Software for Solving Integer Programs 269\u003c\/p\u003e \u003cp\u003e14.3 How Do We Find an Improved Formulation? 272\u003c\/p\u003e \u003cp\u003e14.4 Multi-item Single Machine Lot-Sizing 277\u003c\/p\u003e \u003cp\u003e14.5 A Multiplexer Assignment Problem 282\u003c\/p\u003e \u003cp\u003e14.6 Integer Programming and Machine Learning 285\u003c\/p\u003e \u003cp\u003e14.7 Notes 287\u003c\/p\u003e \u003cp\u003e14.8 Exercises 287\u003c\/p\u003e \u003cp\u003eReferences 291\u003c\/p\u003e \u003cp\u003eIndex 311\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407098224983,"sku":"9781119606536","price":95.9,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119606536.jpg?v=1730498170"},{"product_id":"combinatorial-pattern-matching-algorithms-in-computational-biology-using-perl-and-r-9781420069730","title":"Combinatorial Pattern Matching Algorithms in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eEmphasizing the search for patterns within and between biological sequences, trees, and graphs, \u003cstrong\u003eCombinatorial Pattern Matching Algorithms in Computational Biology Using Perl and R\u003c\/strong\u003e shows how combinatorial pattern matching algorithms can solve computational biology problems that arise in the analysis of genomic, transcriptomic, proteomic, metabolomic, and interactomic data. It implements the algorithms in Perl and R, two widely used scripting languages in computational biology. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe book provides a well-rounded explanation of traditional issues as well as an up-to-date account of more recent developments, such as graph similarity and search. It is organized around the specific algorithmic problems that arise when dealing with structures that are commonly found in computational biology, including biological sequences, trees, and graphs. For each of these structures, the author makes a clear distinction between problems that arise in the analysis of one str\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eI like the hands-on approach this book offers, and the very pedagogical structure it follows … . The book also has tons of examples, thoughtfully chosen and beautifully laid out … the book is very well-written and accessible, undoubtedly written by an author who takes great care in preparing his manuscripts and teaching about an area he enjoys working on.\u003cbr\u003e—Anthony Labarre, \u003cem\u003eSIGACT News\u003c\/em\u003e, July 2012\u003c\/p\u003e\u003cp\u003eThis text provides a solid foundation to the field. It will work as a practical handbook for pattern matching applications in computational biology. \u003cbr\u003e—Michael Goldberg, \u003cem\u003eComputing Reviews\u003c\/em\u003e, February 2010\u003c\/p\u003e\u003cp\u003e… the book makes a clear distinction between problems that emerge in the analysis of the structure and in the comparative analysis of two or more structures. … Well-known computational biology tools that allow searching nucleotide and protein databases for local sequence alignment are based on CPM algorithms only. The techniques presented in this book go beyond that. … detailed algorithm solutions in pseudocode, full Perl and R implementation, and pointers to software and implementation are presented. This … is what makes Valiente’s effort unique. …\u003cbr\u003e—Ernesto D’Avanzo, \u003cem\u003eComputing Reviews\u003c\/em\u003e, February 2010\u003c\/p\u003e\u003cp\u003e… It is a well-sorted collection of pattern matching algorithms that are used to work with problems in computational biology. … You can find all of the sources on the author’s website, which come in handy when you actually want to use them, since you do not have to retype them. And there is an introduction to Perl as well as to R, showing how to decode DNA\/RNA-triplets to amino acids and giving some basic overview over standard functions. … I certainly recommend this as an introduction and reference to some algorithms of pattern matching in computational biology. You actually learn how algorithms over the most important data types are designed in a straightforward, logical way. …\u003cbr\u003e—Jannik Pewny, \u003cem\u003eIACR Book Reviews\u003c\/em\u003e, 2009\u003c\/p\u003e\u003cp\u003e…after a few minutes of random browsing, I was left with a feeling of total appreciation of the book, admiration for Prof. Gabriel Valiente, and a realization that this book will be part of my fundamental library for me and my group from the moment it is published. There are so many good things to say that I do not know where to start. The organization is straightforward with major sections that extend from simple sequences to trees to graphs. … This parallel structure makes it easy to apply lessons used on the simplest object (sequences) to objects of medium (trees) and significant (graphs) difficulty. …a wonderful way to learn leveraging … The Perl is beautifully clear and the examples have already taught me how to improve my own code.\u003cbr\u003e—Michael Levitt, Professor and Chair, Department of Structural Biology, Stanford University, California, USA\u003c\/p\u003e\u003cp\u003e…Balancing a careful mixture of formal methods, programming, and examples, Gabriel Valiente has managed to harmoniously bridge languages and contents into a self-contained source of lasting influence. It is not difficult to predict that this book will be studied indifferently by the specialist of biology and computer science, helping each to walk a few steps toward the other. It will entice new generations of scholars to engage in its beautiful subject.\u003cbr\u003e—From the Foreword, Alberto Apostolico, Professor, College of Computing, Georgia Tech, Atlanta, USA\u003c\/p\u003e\u003cp\u003eUnlocks the power for R for Perl programmers, and vice versa. Reveals R to be a powerful and accessible tool for bioinformatics. The title is a mouthful, but the use of both R and Perl for bioinformatics is revealing.\u003cbr\u003e—Steven Skiena, Professor, Department of Computer Science, Stony Brook University, New York, USA\u003c\/p\u003e\u003cbr\u003e\u003cp\u003eI like the hands-on approach this book offers, and the very pedagogical structure it follows … . The book also has tons of examples, thoughtfully chosen and beautifully laid out … the book is very well-written and accessible, undoubtedly written by an author who takes great care in preparing his manuscripts and teaching about an area he enjoys working on.\u003cbr\u003e—Anthony Labarre, \u003cem\u003eSIGACT News\u003c\/em\u003e, July 2012\u003c\/p\u003e\u003cp\u003eThis text provides a solid foundation to the field. It will work as a practical handbook for pattern matching applications in computational biology. \u003cbr\u003e—Michael Goldberg, \u003cem\u003eComputing Reviews\u003c\/em\u003e, February 2010\u003c\/p\u003e\u003cp\u003e… the book makes a clear distinction between problems that emerge in the analysis of the structure and in the comparative analysis of two or more structures. … Well-known computational biology tools that allow searching nucleotide and protein databases for local sequence alignment are based on CPM algorithms only. The techniques presented in this book go beyond that. … detailed algorithm solutions in pseudocode, full Perl and R implementation, and pointers to software and implementation are presented. This … is what makes Valiente’s effort unique. …\u003cbr\u003e—Ernesto D’Avanzo, \u003cem\u003eComputing Reviews\u003c\/em\u003e, February 2010\u003c\/p\u003e\u003cp\u003e… It is a well-sorted collection of pattern matching algorithms that are used to work with problems in computational biology. … You can find all of the sources on the author’s website, which come in handy when you actually want to use them, since you do not have to retype them. And there is an introduction to Perl as well as to R, showing how to decode DNA\/RNA-triplets to amino acids and giving some basic overview over standard functions. … I certainly recommend this as an introduction and reference to some algorithms of pattern matching in computational biology. You actually learn how algorithms over the most important data types are designed in a straightforward, logical way. …\u003cbr\u003e—Jannik Pewny, \u003cem\u003eIACR Book Reviews\u003c\/em\u003e, 2009\u003c\/p\u003e\u003cp\u003e…after a few minutes of random browsing, I was left with a feeling of total appreciation of the book, admiration for Prof. Gabriel Valiente, and a realization that this book will be part of my fundamental library for me and my group from the moment it is published. There are so many good things to say that I do not know where to start. The organization is straightforward with major sections that extend from simple sequences to trees to graphs. … This parallel structure makes it easy to apply lessons used on the simplest object (sequences) to objects of medium (trees) and significant (graphs) difficulty. …a wonderful way to learn leveraging … The Perl is beautifully clear and the examples have already taught me how to improve my own code.\u003cbr\u003e—Michael Levitt, Professor and Chair, Department of Structural Biology, Stanford University, California, USA\u003c\/p\u003e\u003cp\u003e…Balancing a careful mixture of formal methods, programming, and examples, Gabriel Valiente has managed to harmoniously bridge languages and contents into a self-contained source of lasting influence. It is not difficult to predict that this book will be studied indifferently by the specialist of biology and computer science, helping each to walk a few steps toward the other. It will entice new generations of scholars to engage in its beautiful subject.\u003cbr\u003e—From the Foreword, Alberto Apostolico, Professor, College of Computing, Georgia Tech, Atlanta, USA\u003c\/p\u003e\u003cp\u003eUnlocks the power for R for Perl programmers, and vice versa. Reveals R to be a powerful and accessible tool for bioinformatics. The title is a mouthful, but the use of both R and Perl for bioinformatics is revealing.\u003cbr\u003e—Steven Skiena, Professor, Department of Computer Science, Stony Brook University, New York, USA\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction. SEQUENCE PATTERN MATCHING: Sequences. Simple Pattern Matching in Sequences. General Pattern Matching in Sequences. TREE PATTERN MATCHING: Trees. Simple Pattern Matching in Trees. General Pattern Matching in Trees. GRAPH PATTERN MATCHING: Graphs. Simple Pattern Matching in Graphs. General Pattern Matching in Graphs. Appendices. References. Index.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":49408097878359,"sku":"9781420069730","price":180.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781420069730.jpg?v=1730501573"},{"product_id":"set-theoretical-aspects-of-real-analysis-9781482242010","title":"Set Theoretical Aspects of Real Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eSet Theoretical Aspects of Real Analysis\u003c\/strong\u003e is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary between fundamental concepts of measurability and nonmeasurability for point sets and functions. The remainder of the book deals with more specialized material on set theoretical real analysis. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe book focuses on certain logical and set theoretical aspects of real analysis. It is expected that the first eleven chapters can be used in a course on Lebesque measure theory that highlights the fundamental concepts of measurability and non-measurability for point sets and functions. Provided in the book are problems of varying difficulty that range from simple observations to advanced results. Relatively difficult \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eZF theory and some point sets on the real line. Countable versions of AC and real analysis. Uncountable versions of AC and Lebesgue nonmeasurable sets. The Continuum Hypothesis and Lebesgue nonmeasurable sets. Measurability properties of sets and functions. Radon measures and nonmeasurable sets. Real-valued step functions with strange measurability properties. Relationships between certain classical constructions of Lebesgue nonmeasurable sets. Measurability properties of Vitali sets. A relationship between the measurability and continuity of real-valued functions. A relationship between absolutely nonmeasurable functions and Sierpinski-Zygmund functions. Sums of absolutely nonmeasurable injective functions. A large group of absolutely nonmeasurable additive functions. Additive properties of certain classes of pathological functions. Absolutely nonmeasurable homomorphisms of commutative groups. Measurable and nonmeasurable sets with homogeneous sections. A combinatorial problem on translation invariant extensions of the Lebesgue measure. Countable almost invariant partitions of G-spaces. Nonmeasurable unions of measure zero sections of plane sets. Measurability properties of well-orderings. Appendices. Bibliography. Subject Index.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409114046807,"sku":"9781482242010","price":175.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781482242010.jpg?v=1730505488"},{"product_id":"buildings-and-schubert-schemes-9781498768290","title":"Buildings and Schubert Schemes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck''s SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eGrassmannians and Flag Varieties. Schubert Cell Decomposition of Grassmannians and Flag Varieties. Resolution of Singularities of a Schubert Variety. The Singular Locus of a Schubert Variety. The Flag Complex. Configurations and Galleries Varieties. Configurations Varieties as Galleries Varieties. The Coxeter Complex. Minimal Generalized Galleries in a Coxeter Complex. Minimal Generalized Galleries in a Reductive Group Building. Parabolic Subgroups in a Reductive Group Scheme. Associated Schemes to the Relative Building. Incidence Type Schemes of the Relative Building. Smooth Resolutions of Schubert Schemes. Contracted Products and Galleries Configurations Schemes. Functoriality of Schubert Schemes Smooth Resolutions and Base Changes. About the Coxeter Complex. Generators and Relations and the Building of a Reductive Group.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409295090007,"sku":"9781498768290","price":175.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498768290.jpg?v=1730506318"},{"product_id":"a-bridge-to-higher-mathematics-9781498775250","title":"A Bridge to Higher Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cem\u003eA Bridge to Higher Mathematics\u003c\/em\u003e is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis is one of the shorter books for a course that introduces students to the concept of mathematical proofs. The brevity is due to the \"bare-bones\" nature of the treatment. The number of topics covered, the number of examples, and the number of exercises are not smaller than what appears in competing textbooks; what is shorter is the text that one finds between theorems, lemmas, examples, and exercises. Besides the topics found in similar textbooks (i.e., proof techniques, logic, set theory, relations, and functions), there are chapters on (very) elementary number theory, combinatorial counting techniques, and Peano axioms on the set of positive integers. Several chapters are devoted to the construction of various kinds of numbers, such as integers, rationals, real numbers, and complex numbers. Answers to around half the exercises are included at the end of the book, and a few have complete solutions. This reviewer finds the book more enjoyable than the average competing textbook.\u003c\/p\u003e\u003cp\u003e\u003cem\u003e \u003cbr\u003e\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003e--M. Bona, University of Florida\u003c\/em\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eElements of logic\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eTrue and false statements\u003c\/p\u003e\u003cp\u003eLogical connectives and truth tables\u003c\/p\u003e\u003cp\u003eLogical equivalence\u003c\/p\u003e\u003cp\u003eQuantifiers\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eProofs: Structures and strategies\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eAxioms, theorems and proofs\u003c\/p\u003e\u003cp\u003eDirect proof\u003c\/p\u003e\u003cp\u003eContrapositive proof\u003c\/p\u003e\u003cp\u003eProof by equivalent statements\u003c\/p\u003e\u003cp\u003eProof by cases\u003c\/p\u003e\u003cp\u003eExistence proofs\u003c\/p\u003e\u003cp\u003eProof by counterexample\u003c\/p\u003e\u003cp\u003eProof by mathematical induction\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eElementary Theory of Sets. Functions\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eAxioms for set theory\u003c\/p\u003e\u003cp\u003eInclusion of sets\u003c\/p\u003e\u003cp\u003eUnion and intersection of sets\u003c\/p\u003e\u003cp\u003eComplement, difference and symmetric difference of sets\u003c\/p\u003e\u003cp\u003eOrdered pairs and the Cartersian product\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFunctions\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eDefinition and examples of functions\u003c\/p\u003e\u003cp\u003eDirect image, inverse image\u003c\/p\u003e\u003cp\u003eRestriction and extension of a function\u003c\/p\u003e\u003cp\u003eOne-to-one and onto functions\u003c\/p\u003e\u003cp\u003eComposition and inverse functions\u003c\/p\u003e\u003cp\u003e*Family of sets and the axiom of choice\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eRelations\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eGeneral relations and operations with relations\u003c\/p\u003e\u003cp\u003eEquivalence relations and equivalence classes\u003c\/p\u003e\u003cp\u003eOrder relations\u003c\/p\u003e\u003cp\u003e*More on ordered sets and Zorn's lemma\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAxiomatic theory of positive integers\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003ePeano axioms and addition\u003c\/p\u003e\u003cp\u003eThe natural order relation and subtraction\u003c\/p\u003e\u003cp\u003eMultiplication and divisibility\u003c\/p\u003e\u003cp\u003eNatural numbers\u003c\/p\u003e\u003cp\u003eOther forms of induction\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eElementary number theory\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eAboslute value and divisibility of integers\u003c\/p\u003e\u003cp\u003eGreatest common divisor and least common multiple\u003c\/p\u003e\u003cp\u003eIntegers in base 10 and divisibility tests\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCardinality. Finite sets, infinite sets\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eEquipotent sets\u003c\/p\u003e\u003cp\u003eFinite and infinite sets\u003c\/p\u003e\u003cp\u003eCountable and uncountable sets\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCounting techniques and combinatorics\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eCounting principles\u003c\/p\u003e\u003cp\u003ePigeonhole principle and parity\u003c\/p\u003e\u003cp\u003ePermutations and combinations\u003c\/p\u003e\u003cp\u003eRecursive sequences and recurrence relations\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eThe construction of integers and rationals\u003c\/strong\u003e \u003c\/p\u003e\u003cp\u003eDefinition of integers and operations\u003c\/p\u003e\u003cp\u003eOrder relation on integers\u003c\/p\u003e\u003cp\u003eDefinition of rationals, operations and order\u003c\/p\u003e\u003cp\u003eDecimal representation of rational numbers\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eThe construction of real and complex numbers\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eThe Dedekind cuts approach\u003c\/p\u003e\u003cp\u003eThe Cauchy sequences approach\u003c\/p\u003e\u003cp\u003eDecimal representation of real numbers\u003c\/p\u003e\u003cp\u003eAlgebraic and transcendental numbers\u003c\/p\u003e\u003cp\u003eComples numbers\u003c\/p\u003e\u003cp\u003eThe trigonometric form of a complex number\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409296335191,"sku":"9781498775250","price":73.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498775250.jpg?v=1730506323"},{"product_id":"matrix-inequalities-for-iterative-systems-9781498777773","title":"Matrix Inequalities for Iterative Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eIntroduction. \u003c\/strong\u003eNotation and Basic Facts. Motivation.\u003cstrong\u003e \u003c\/strong\u003eDiagonalization and Spectral Decomposition. \u003cstrong\u003eUndirected Graphs \/ Hermitian Matrices. \u003c\/strong\u003eGeneral Results. Restricted Graph Classes. \u003cstrong\u003eDirected Graphs \/ Nonsymmetric\u003c\/strong\u003e. Walks and Alternating Walks in Directed Graphs. Powers of Row and Column Sums.\u003cstrong\u003e Applications.\u003c\/strong\u003e Bounds for the Largest Eigenvalue. Iterated Kernels.\u003cstrong\u003e \u003c\/strong\u003eConclusion. Bibliography. Index.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409296728407,"sku":"9781498777773","price":142.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498777773.jpg?v=1730506325"},{"product_id":"aqa-a-level-further-mathematics-discrete-9781510433342","title":"AQA A Level Further Mathematics Discrete","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eExam board: AQA\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eLevel: A level\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eSubject: Maths\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eFirst teaching: September 2017\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eFirst exams: Summer 2019\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eProvide full support for the AQA Discrete content of the new specification with worked examples, stimulating activities and assessment support to help develop understanding, reasoning and problem solving. \u003c\/b\u003e\u003cbr\u003e- Help prepare students for assessment with skills-building activities and fully worked examples and solutions tailored to the changed criteria.\u003cbr\u003e- Build understanding through carefully worded expositions that set out the basics and the detail of each topic, with call-outs to add clarity.\u003cbr\u003e- Test knowledge and develop understanding, reasoning and problem solving with banded Exercise questions that increase in difficulty (answers provided in the back of the book and online). \u003cbr\u003e- Gain a full understanding of the logical steps that are used in creating each individual algorithm \u003cbr\u003e- Encourages students to track their progress using learning outcomes and Key Points listed at the end of each chapter.\u003c\/p\u003e","brand":"Hodder Education","offers":[{"title":"Default Title","offer_id":49409619755351,"sku":"9781510433342","price":27.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781510433342.jpg?v=1730507453"},{"product_id":"practical-discrete-mathematics-discover-math-principles-that-fuel-algorithms-for-computer-science-and-machine-learning-with-python-9781838983147","title":"Practical Discrete Mathematics: Discover math","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science\u003c\/b\u003e\u003c\/p\u003eKey Features\u003cul\u003e\n\u003cli\u003eApply the math of countable objects to practical problems in computer science\u003c\/li\u003e\n\u003cli\u003eExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematics\u003c\/li\u003e\n\u003cli\u003eLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidance\u003c\/li\u003e\n\u003c\/ul\u003eBook Description\u003cp\u003eDiscrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks.\u003c\/p\u003e \u003cp\u003ePractical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level.\u003c\/p\u003e \u003cp\u003eAs you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science.\u003c\/p\u003e \u003cp\u003eBy the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.\u003c\/p\u003eWhat you will learn\u003cul\u003e\n\u003cli\u003eUnderstand the terminology and methods in discrete math and their usage in algorithms and data problems\u003c\/li\u003e\n\u003cli\u003eUse Boolean algebra in formal logic and elementary control structures\u003c\/li\u003e\n\u003cli\u003eImplement combinatorics to measure computational complexity and manage memory allocation\u003c\/li\u003e\n\u003cli\u003eUse random variables, calculate descriptive statistics, and find average-case computational complexity\u003c\/li\u003e\n\u003cli\u003eSolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first search\u003c\/li\u003e\n\u003cli\u003ePerform ML tasks such as data visualization, regression, and dimensionality reduction\u003c\/li\u003e\n\u003c\/ul\u003eWho this book is for\u003cp\u003eThis book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eTable of Contents\u003col\u003e\n\u003cli\u003eKey Concepts, Notation, Set Theory, Relations, and Functions\u003c\/li\u003e\n\u003cli\u003eFormal Logic and Constructing Mathematical Proofs\u003c\/li\u003e\n\u003cli\u003eComputing with Base-n Numbers\u003c\/li\u003e\n\u003cli\u003eCombinatorics Using SciPy\u003c\/li\u003e\n\u003cli\u003eElements of Discrete Probability\u003c\/li\u003e\n\u003cli\u003eComputational Algorithms in Linear Algebra\u003c\/li\u003e\n\u003cli\u003eComputational Requirements for Algorithms\u003c\/li\u003e\n\u003cli\u003eStorage and Feature Extraction of Graphs, Trees, and Networks\u003c\/li\u003e\n\u003cli\u003eSearching Data Structures and Finding Shortest Paths\u003c\/li\u003e\n\u003cli\u003eRegression Analysis with NumPy and Scikit-Learn\u003c\/li\u003e\n\u003cli\u003eWeb Searches with PageRank\u003c\/li\u003e\n\u003cli\u003ePrincipal Component Analysis with Scikit-Learn\u003c\/li\u003e\n\u003c\/ol\u003e","brand":"Packt Publishing Limited","offers":[{"title":"Default Title","offer_id":49413212176727,"sku":"9781838983147","price":46.54,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781838983147.jpg?v=1730519440"},{"product_id":"optimization-of-logistics-9781848214248","title":"Optimization of Logistics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book aims to help engineers, Masters students and young researchers to understand and gain a general knowledge of logistic systems optimization problems and techniques, such as system design, layout, stock management, quality management, lot-sizing or scheduling. It summarizes the evaluation and optimization methods used to solve the most frequent problems. In particular, the authors also emphasize some recent and interesting scientific developments, as well as presenting some industrial applications and some solved instances from real-life cases.\u003cbr\u003ePerformance evaluation tools (Petri nets, the Markov process, discrete event simulation, etc.) and optimization techniques (branch-and-bound, dynamic programming, genetic algorithms, ant colony optimization, etc.) are presented first. Then, new optimization methods are presented to solve systems design problems, layout problems and buffer-sizing optimization. Forecasting methods, inventory optimization, packing problems, lot-sizing quality management and scheduling are presented with examples in the final chapters.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“On the other hand, this book constitutes a valuable guide and convenient introduction to the fied of operations research applications for professionals, which deal with real production and logistic system design and management. It can be also recommended as a textbook for students of production management.”  (\u003ci\u003eZentralblatt Math\u003c\/i\u003e, 1 May 2013)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction xiii\u003c\/p\u003e \u003cp\u003eChapter 1. Modeling and Performance Evaluation 1\u003c\/p\u003e \u003cp\u003e1.1. Introduction 1\u003c\/p\u003e \u003cp\u003e1.2. Markovian processes 2\u003c\/p\u003e \u003cp\u003e1.2.1. Overview of stochastic processes 2\u003c\/p\u003e \u003cp\u003e1.2.2. Markov processes 3\u003c\/p\u003e \u003cp\u003e1.2.2.1. Basics 3\u003c\/p\u003e \u003cp\u003e1.2.2.2. Chapman–Kolmogorov equations 4\u003c\/p\u003e \u003cp\u003e1.2.2.3. Steady-state probabilities 5\u003c\/p\u003e \u003cp\u003e1.2.2.4. Graph associated with a Markov process 6\u003c\/p\u003e \u003cp\u003e1.2.2.5. Application to production systems 6\u003c\/p\u003e \u003cp\u003e1.2.3. Markov chains 8\u003c\/p\u003e \u003cp\u003e1.2.3.1. Basics 8\u003c\/p\u003e \u003cp\u003e1.2.3.2. State probability vectors 9\u003c\/p\u003e \u003cp\u003e1.2.3.3. Fundamental equation of a Markov chain 9\u003c\/p\u003e \u003cp\u003e1.2.3.4. Graph associated with a Markov chain 10\u003c\/p\u003e \u003cp\u003e1.2.3.5. Steady states of ergodic Markov chains 11\u003c\/p\u003e \u003cp\u003e1.2.3.6. Application to production systems 12\u003c\/p\u003e \u003cp\u003e1.3. Petri nets 14\u003c\/p\u003e \u003cp\u003e1.3.1. Introduction to Petri nets 14\u003c\/p\u003e \u003cp\u003e1.3.1.1. Basic definitions 14\u003c\/p\u003e \u003cp\u003e1.3.1.2. Dynamics of Petri nets 15\u003c\/p\u003e \u003cp\u003e1.3.1.3. Specific structures 16\u003c\/p\u003e \u003cp\u003e1.3.1.4. Tools for Petri net analysis 18\u003c\/p\u003e \u003cp\u003e1.3.1.5. Properties of Petri nets 19\u003c\/p\u003e \u003cp\u003e1.3.2. Non-autonomous Petri nets 20\u003c\/p\u003e \u003cp\u003e1.3.3. Timed Petri nets 20\u003c\/p\u003e \u003cp\u003evi Optimization of Logistics\u003c\/p\u003e \u003cp\u003e1.3.4. Continuous Petri nets 23\u003c\/p\u003e \u003cp\u003e1.3.4.1. Fundamental equation and performance analysis 24\u003c\/p\u003e \u003cp\u003e1.3.4.2. Example 25\u003c\/p\u003e \u003cp\u003e1.3.5. Colored Petri nets 27\u003c\/p\u003e \u003cp\u003e1.3.6. Stochastic Petri nets 28\u003c\/p\u003e \u003cp\u003e1.3.6.1. Firing time 29\u003c\/p\u003e \u003cp\u003e1.3.6.2. Firing selection policy 29\u003c\/p\u003e \u003cp\u003e1.3.6.3. Service policy 30\u003c\/p\u003e \u003cp\u003e1.3.6.4. Memory policy 30\u003c\/p\u003e \u003cp\u003e1.3.6.5. Petri net analysis 30\u003c\/p\u003e \u003cp\u003e1.3.6.6. Marking graph 31\u003c\/p\u003e \u003cp\u003e1.3.6.7. Generator of Markovian processes 31\u003c\/p\u003e \u003cp\u003e1.3.6.8. Fundamental equation 32\u003c\/p\u003e \u003cp\u003e1.3.6.9. Steady-state probabilities 32\u003c\/p\u003e \u003cp\u003e1.3.6.10. Performance indices (steady state) 35\u003c\/p\u003e \u003cp\u003e1.4. Discrete-event simulation 36\u003c\/p\u003e \u003cp\u003e1.4.1. The role of simulation in logistics systems analysis 36\u003c\/p\u003e \u003cp\u003e1.4.2. Components and dynamic evolution of systems 37\u003c\/p\u003e \u003cp\u003e1.4.3. Representing chance and the Monte Carlo method 38\u003c\/p\u003e \u003cp\u003e1.4.3.1. Uniform distribution U [0, 1] 38\u003c\/p\u003e \u003cp\u003e1.4.3.2. The Monte Carlo method 39\u003c\/p\u003e \u003cp\u003e1.4.4. Simulating probability distributions 41\u003c\/p\u003e \u003cp\u003e1.4.4.1. Simulating random events 41\u003c\/p\u003e \u003cp\u003e1.4.4.2. Simulating discrete random variables 44\u003c\/p\u003e \u003cp\u003e1.4.4.3. Simulating continuous random variables 47\u003c\/p\u003e \u003cp\u003e1.4.5. Discrete-event systems 52\u003c\/p\u003e \u003cp\u003e1.4.5.1. Key aspects of simulation 52\u003c\/p\u003e \u003cp\u003e1.5. Decomposition method 57\u003c\/p\u003e \u003cp\u003e1.5.1. Presentation 57\u003c\/p\u003e \u003cp\u003e1.5.2. Details of the method 58\u003cbr\u003e  \u003cbr\u003e Chapter 2. Optimization 61\u003c\/p\u003e \u003cp\u003e2.1. Introduction 61\u003c\/p\u003e \u003cp\u003e2.2. Polynomial problems and NP-hard problems 62\u003c\/p\u003e \u003cp\u003e2.2.1. The complexity of an algorithm 62\u003c\/p\u003e \u003cp\u003e2.2.2. Example of calculating the complexity of an algorithm 63\u003c\/p\u003e \u003cp\u003e2.2.3. Some definitions 64\u003c\/p\u003e \u003cp\u003e2.2.3.1. Polynomial-time algorithms 64\u003c\/p\u003e \u003cp\u003e2.2.3.2. Pseudo-polynomial-time algorithms 64\u003c\/p\u003e \u003cp\u003e2.2.3.3. Exponential-time algorithms 64\u003c\/p\u003e \u003cp\u003e2.2.4. Complexity of a problem 64\u003c\/p\u003e \u003cp\u003e2.2.4.1. Polynomial-time problems 64\u003c\/p\u003e \u003cp\u003e2.2.4.2. NP-hard problems 64\u003c\/p\u003e \u003cp\u003e2.3. Exact methods 64\u003c\/p\u003e \u003cp\u003e2.3.1. Mathematical programming 64\u003c\/p\u003e \u003cp\u003e2.3.2. Dynamic programming 65\u003c\/p\u003e \u003cp\u003e2.3.3. Branch and bound algorithm 65\u003c\/p\u003e \u003cp\u003e2.4. Approximate methods 66\u003c\/p\u003e \u003cp\u003e2.4.1. Genetic algorithms 67\u003c\/p\u003e \u003cp\u003e2.4.1.1. General principles 67\u003c\/p\u003e \u003cp\u003e2.4.1.2. Encoding the solutions 67\u003c\/p\u003e \u003cp\u003e2.4.1.3. Crossover operators 68\u003c\/p\u003e \u003cp\u003e2.4.1.4. Mutation operators 70\u003c\/p\u003e \u003cp\u003e2.4.1.5. Constructing the population in the next generation 70\u003c\/p\u003e \u003cp\u003e2.4.1.6. Stopping condition 70\u003c\/p\u003e \u003cp\u003e2.4.2. Ant colonies 70\u003c\/p\u003e \u003cp\u003e2.4.2.1. General principle 70\u003c\/p\u003e \u003cp\u003e2.4.2.2. Management of pheromones: example of the traveling salesman problem 71\u003c\/p\u003e \u003cp\u003e2.4.3. Tabu search 72\u003c\/p\u003e \u003cp\u003e2.4.3.1. Initial solution 73\u003c\/p\u003e \u003cp\u003e2.4.3.2. Representing the solution 73\u003c\/p\u003e \u003cp\u003e2.4.3.3. Creating the neighborhood 74\u003c\/p\u003e \u003cp\u003e2.4.3.4. The tabu list 75\u003c\/p\u003e \u003cp\u003e2.4.3.5. An illustrative example 76\u003c\/p\u003e \u003cp\u003e2.4.4. Particle swarm algorithm 76\u003c\/p\u003e \u003cp\u003e2.4.4.1. Description 76\u003c\/p\u003e \u003cp\u003e2.4.4.2. An illustrative example 77\u003c\/p\u003e \u003cp\u003e2.5. Multi-objective optimization 79\u003c\/p\u003e \u003cp\u003e2.5.1. Definition 79\u003c\/p\u003e \u003cp\u003e2.5.2. Resolution methods 80\u003c\/p\u003e \u003cp\u003e2.5.3. Comparison criteria 81\u003c\/p\u003e \u003cp\u003e2.5.3.1. The Riise distance 81\u003c\/p\u003e \u003cp\u003e2.5.3.2. The Zitzler measure 82\u003c\/p\u003e \u003cp\u003e2.5.4. Multi-objective optimization methods 82\u003c\/p\u003e \u003cp\u003e2.5.4.1. Exact methods 82\u003c\/p\u003e \u003cp\u003e2.5.4.2. Approximate methods 84\u003c\/p\u003e \u003cp\u003e2.6. Simulation-based optimization 89\u003c\/p\u003e \u003cp\u003e2.6.1. Dedicated tools 90\u003c\/p\u003e \u003cp\u003e2.6.2. Specific methods 90\u003c\/p\u003e \u003cp\u003eChapter 3. Design and Layout 93\u003c\/p\u003e \u003cp\u003e3.1. Introduction 93\u003c\/p\u003e \u003cp\u003e3.2. The different types of production system 94\u003c\/p\u003e \u003cp\u003e3.3. Equipment selection 97\u003c\/p\u003e \u003cp\u003eviii Optimization of Logistics\u003c\/p\u003e \u003cp\u003e3.3.1. General overview 97\u003c\/p\u003e \u003cp\u003e3.3.2. Equipment selection with considerations of reliability 99\u003c\/p\u003e \u003cp\u003e3.3.2.1. Introduction to reliability optimization 99\u003c\/p\u003e \u003cp\u003e3.3.2.2. Design of a parallel-series system 100\u003c\/p\u003e \u003cp\u003e3.4. Line balancing 110\u003c\/p\u003e \u003cp\u003e3.4.1. The classification of line balancing problems 111\u003c\/p\u003e \u003cp\u003e3.4.1.1. The simple assembly line balancing model (SALB) 111\u003c\/p\u003e \u003cp\u003e3.4.1.2. The general assembly line balancing model (GALB) 112\u003c\/p\u003e \u003cp\u003e3.4.2. Solution methods 112\u003c\/p\u003e \u003cp\u003e3.4.2.1. Exact methods 112\u003c\/p\u003e \u003cp\u003e3.4.2.2. Approximate methods 113\u003c\/p\u003e \u003cp\u003e3.4.3. Literature review 113\u003c\/p\u003e \u003cp\u003e3.4.4. Example 113\u003c\/p\u003e \u003cp\u003e3.5. The problem of buffer sizing 114\u003c\/p\u003e \u003cp\u003e3.5.1. General overview 116\u003c\/p\u003e \u003cp\u003e3.5.2. Example of a multi-objective buffer sizing problem 116\u003c\/p\u003e \u003cp\u003e3.5.3. Example of the use of genetic algorithms 117\u003c\/p\u003e \u003cp\u003e3.5.3.1. Representation of the solutions 117\u003c\/p\u003e \u003cp\u003e3.5.3.2. Calculation of the objective function 118\u003c\/p\u003e \u003cp\u003e3.5.3.3. Selection of solutions for the archive 119\u003c\/p\u003e \u003cp\u003e3.5.3.4. New population and stopping criterion 119\u003c\/p\u003e \u003cp\u003e3.5.4. Example of the use of ant colony algorithms 119\u003c\/p\u003e \u003cp\u003e3.5.4.1. Encoding 120\u003c\/p\u003e \u003cp\u003e3.5.4.2. Construction of the ant trails 121\u003c\/p\u003e \u003cp\u003e3.5.4.3. Calculation of the visibility 121\u003c\/p\u003e \u003cp\u003e3.5.4.4. Global and local updates of the pheromones 122\u003c\/p\u003e \u003cp\u003e3.5.5. Example of the use of simulation-based optimization 123\u003c\/p\u003e \u003cp\u003e3.5.5.1. Simulation model 125\u003c\/p\u003e \u003cp\u003e3.5.5.2. Optimization algorithms 129\u003c\/p\u003e \u003cp\u003e3.5.5.3. The pairing of simulation and optimization 130\u003c\/p\u003e \u003cp\u003e3.5.5.4. Results and comparison 130\u003c\/p\u003e \u003cp\u003e3.6. Layout 132\u003c\/p\u003e \u003cp\u003e3.6.1. Types of facility layout 132\u003c\/p\u003e \u003cp\u003e3.6.1.1. Logical layout 132\u003c\/p\u003e \u003cp\u003e3.6.1.2. Physical layout 133\u003c\/p\u003e \u003cp\u003e3.6.2. Approach for treating a layout problem 133\u003c\/p\u003e \u003cp\u003e3.6.2.1. Linear layout 134\u003c\/p\u003e \u003cp\u003e3.6.2.2. Functional layout 135\u003c\/p\u003e \u003cp\u003e3.6.2.3. Cellular layout 135\u003c\/p\u003e \u003cp\u003e3.6.2.4. Fixed layout 135\u003c\/p\u003e \u003cp\u003e3.6.3. The best-known methods 135\u003c\/p\u003e \u003cp\u003e3.6.4. Example of arranging a maintenance facility 136\u003c\/p\u003e \u003cp\u003e3.6.5. Example of laying out an automotive workshop 140\u003c\/p\u003e \u003cp\u003eChapter 4. Tactical Optimization 143\u003c\/p\u003e \u003cp\u003e4.1. Introduction 143\u003c\/p\u003e \u003cp\u003e4.2. Demand forecasting 143\u003c\/p\u003e \u003cp\u003e4.2.1. Introduction 143\u003c\/p\u003e \u003cp\u003e4.2.2. Categories and methods 144\u003c\/p\u003e \u003cp\u003e4.2.3. Time series 145\u003c\/p\u003e \u003cp\u003e4.2.4. Models and series analysis 146\u003c\/p\u003e \u003cp\u003e4.2.4.1. Additive models 147\u003c\/p\u003e \u003cp\u003e4.2.4.2. Multiplicative model 149\u003c\/p\u003e \u003cp\u003e4.2.4.3. Exponential smoothing 150\u003c\/p\u003e \u003cp\u003e4.3. Stock management 155\u003c\/p\u003e \u003cp\u003e4.3.1. The different types of stocked products 156\u003c\/p\u003e \u003cp\u003e4.3.2. The different types of stocks 157\u003c\/p\u003e \u003cp\u003e4.3.3. Storage costs 157\u003c\/p\u003e \u003cp\u003e4.3.4. Stock management 159\u003c\/p\u003e \u003cp\u003e4.3.4.1. Functioning of a stock 159\u003c\/p\u003e \u003cp\u003e4.3.4.2. Stock monitoring 161\u003c\/p\u003e \u003cp\u003e4.3.4.3. Stock valuation 162\u003c\/p\u003e \u003cp\u003e4.3.5. ABC classification method 163\u003c\/p\u003e \u003cp\u003e4.3.6. Economic quantities 165\u003c\/p\u003e \u003cp\u003e4.3.6.1. Economic quantity: the Wilson formula 166\u003c\/p\u003e \u003cp\u003e4.3.6.2. Economic quantity with a discount threshold 167\u003c\/p\u003e \u003cp\u003e4.3.6.3. Economic quantity with a uniform discount 168\u003c\/p\u003e \u003cp\u003e4.3.6.4. Economic quantity with a progressive discount 169\u003c\/p\u003e \u003cp\u003e4.3.6.5. Economic quantity with a variable ordering cost 170\u003c\/p\u003e \u003cp\u003e4.3.6.6. Economic quantity with order consolidation 171\u003c\/p\u003e \u003cp\u003e4.3.6.7. Economic quantity with a non-zero delivery time 172\u003c\/p\u003e \u003cp\u003e4.3.6.8. Economic quantity with progressive input 172\u003c\/p\u003e \u003cp\u003e4.3.6.9. Economic quantity with tolerated shortage 173\u003c\/p\u003e \u003cp\u003e4.3.7. Replenishment methods 174\u003c\/p\u003e \u003cp\u003e4.3.7.1. The (r, Q) replenishment method 175\u003c\/p\u003e \u003cp\u003e4.3.7.2. The (T , S) replenishment method 175\u003c\/p\u003e \u003cp\u003e4.3.7.3. The (s, S) replenishment method 175\u003c\/p\u003e \u003cp\u003e4.3.7.4. The (T , r, S) replenishment method 176\u003c\/p\u003e \u003cp\u003e4.3.7.5. The (T , r, Q) replenishment method 177\u003c\/p\u003e \u003cp\u003e4.3.7.6. Security stock 177\u003c\/p\u003e \u003cp\u003e4.4. Cutting and packing problems 178\u003c\/p\u003e \u003cp\u003e4.4.1. Classifying cutting and packing problems 179\u003c\/p\u003e \u003cp\u003e4.4.2. Packing problems in industrial systems 183\u003c\/p\u003e \u003cp\u003e4.4.2.1. Model 183\u003c\/p\u003e \u003cp\u003e4.4.2.2. Solution 185\u003c\/p\u003e \u003cp\u003e4.5. Production and replenishment planning, lot-sizing methods 186\u003c\/p\u003e \u003cp\u003e4.5.1. Introduction 186\u003c\/p\u003e \u003cp\u003ex Optimization of Logistics\u003c\/p\u003e \u003cp\u003e4.5.2. MRP and lot-sizing 186\u003c\/p\u003e \u003cp\u003e4.5.3. Lot-sizing methods 187\u003c\/p\u003e \u003cp\u003e4.5.3.1. The characteristic elements of the models 188\u003c\/p\u003e \u003cp\u003e4.5.3.2. Lot-sizing in the scientific literature 189\u003c\/p\u003e \u003cp\u003e4.5.4. Examples 190\u003c\/p\u003e \u003cp\u003e4.5.4.1. The Wagner–Whitin method 191\u003c\/p\u003e \u003cp\u003e4.5.4.2. The Florian and Klein method 193\u003c\/p\u003e \u003cp\u003e4.6. Quality management 198\u003c\/p\u003e \u003cp\u003e4.6.1. Evaluation, monitoring and improvement tools 198\u003c\/p\u003e \u003cp\u003e4.6.1.1. The objective of metrology 198\u003c\/p\u003e \u003cp\u003e4.6.1.2. Concepts of error and uncertainty 198\u003c\/p\u003e \u003cp\u003e4.6.1.3. Statistical quality control 199\u003c\/p\u003e \u003cp\u003e4.6.1.4. Stages of control 199\u003c\/p\u003e \u003cp\u003e4.6.1.5. Tests of normality 200\u003c\/p\u003e \u003cp\u003e4.6.2. Types of control 205\u003c\/p\u003e \u003cp\u003e4.6.2.1. Reception or final control 205\u003c\/p\u003e \u003cp\u003e4.6.2.2. Reception control by measurement 206\u003c\/p\u003e \u003cp\u003e4.6.2.3. Manufacturing control 209\u003c\/p\u003e \u003cp\u003e4.6.2.4. Control charts 214\u003c\/p\u003e \u003cp\u003eChapter 5. Scheduling 233\u003c\/p\u003e \u003cp\u003e5.1. Introduction 233\u003c\/p\u003e \u003cp\u003e5.2. Scheduling problems 234\u003c\/p\u003e \u003cp\u003e5.2.1. Basic notions 234\u003c\/p\u003e \u003cp\u003e5.2.2. Notation 234\u003c\/p\u003e \u003cp\u003e5.2.3. Definition of the criteria and objective functions 234\u003c\/p\u003e \u003cp\u003e5.2.3.1. Flow time 235\u003c\/p\u003e \u003cp\u003e5.2.3.2. Lateness 235\u003c\/p\u003e \u003cp\u003e5.2.3.3. Tardiness 235\u003c\/p\u003e \u003cp\u003e5.2.3.4. The earliness 236\u003c\/p\u003e \u003cp\u003e5.2.3.5. Objective functions 236\u003c\/p\u003e \u003cp\u003e5.2.3.6. Properties of schedules 238\u003c\/p\u003e \u003cp\u003e5.2.4. Project scheduling 239\u003c\/p\u003e \u003cp\u003e5.2.4.1. Definition of a project 239\u003c\/p\u003e \u003cp\u003e5.2.4.2. Projects with unlimited resources 240\u003c\/p\u003e \u003cp\u003e5.2.4.3. Projects with consumable resources 247\u003c\/p\u003e \u003cp\u003e5.2.4.4. Minimal-cost scheduling 252\u003c\/p\u003e \u003cp\u003e5.2.5. Single-machine problems 254\u003c\/p\u003e \u003cp\u003e5.2.5.1. Minimization of the mean flow time\u003c\/p\u003e \u003cp\u003e5.2.5.2. Minimization of the mean weighted flow time\u003c\/p\u003e \u003cp\u003e5.2.5.3. Minimization of the mean flow time\u003c\/p\u003e \u003cp\u003e5.2.5.4. Minimization of the maximum tardiness\u003cbr\u003e Tmax, 1\/ri = 0\/Tmax 259\u003c\/p\u003e \u003cp\u003e5.2.5.5. Minimization of the maximum tardiness when the jobs have different arrival dates, with pre-emption 1\/ri, pmtn\/Tmax 261\u003c\/p\u003e \u003cp\u003e5.2.5.6. Minimization of the mean tardiness 1\/\/T 261\u003c\/p\u003e \u003cp\u003e5.2.5.7. Minimization of the flow time 1\/ri\/F 265\u003c\/p\u003e \u003cp\u003e5.2.6. Scheduling a flow shop workshop 267\u003c\/p\u003e \u003cp\u003e5.2.6.1. The two-machine problem 267\u003c\/p\u003e \u003cp\u003e5.2.6.2. A particular case of the three-machine problem 268\u003c\/p\u003e \u003cp\u003e5.2.6.3. The m-machine problem 268\u003c\/p\u003e \u003cp\u003e5.2.7. Parallel-machine problems 270\u003c\/p\u003e \u003cp\u003e5.2.7.1. Identical machines, ri = 0, M in F 270\u003c\/p\u003e \u003cp\u003e5.2.7.2. Identical machines, ri = 0, M in Cmax interruptible jobs 271\u003c\/p\u003e \u003cp\u003eBibliography 273\u003c\/p\u003e \u003cp\u003eIndex 285\u003c\/p\u003e","brand":"ISTE Ltd and John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49413711692119,"sku":"9781848214248","price":129.15,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781848214248.jpg?v=1730521129"},{"product_id":"nonlinear-stochastic-integrators-equations-and-flows-9782881247330","title":"Nonlinear Stochastic Integrators, Equations and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHighly technical monograph in which the authors, writing on the basis of their own recent research for the benefit of expert readers, describe a general theory of stochastic integration equations. First published in 1990.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction, Nonlinear Stochastic Integrators, Stochastic Calculus, Dependence on the initial Conditions and Flows.","brand":"Gordon \u0026 Breach Science Publishers SA","offers":[{"title":"Default Title","offer_id":49415542669655,"sku":"9782881247330","price":171.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9782881247330.jpg?v=1730527259"},{"product_id":"descriptive-theory-of-sets-and-functions-functional-analysis-in-semi-ordered-spaces-9782884490122","title":"Descriptive Theory of Sets and Functions.","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book presents articles of L.V. Kantorovich on the descriptive theory of sets and function and on functional analysis in semi-ordered spaces, to demonstrate the unity of L.V. Kantorovich's creative research. It also includes two papers on the extension of Hilbert space.","brand":"Gordon and Breach","offers":[{"title":"Default Title","offer_id":49415543226711,"sku":"9782884490122","price":325.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9782884490122.jpg?v=1730527264"},{"product_id":"geometric-aspects-of-functional-analysis-israel-seminar-gafa-2017-2019-volume-ii-9783030467616","title":"Geometric Aspects of Functional Analysis: Israel","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eContinuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed. \u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- Jean Bourgain: In Memoriam. - A Generalized Central Limit Conjecture for Convex Bodies. - The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding. - Two-Sided Estimates for Order Statistics of Log-Concave Random Vectors. - Further Investigations of Rényi Entropy Power Inequalities and an Entropic Characterization of s-Concave Densities. - Small Ball Probability for the Condition Number of Random Matrices. - Concentration of the Intrinsic Volumes of a Convex Body. - Two Remarks on Generalized Entropy Power Inequalities. - On the Geometry of Random Polytopes. - Reciprocals and Flowers in Convexity. - Moments of the Distance Between Independent Random Vectors. - The Alon–Milman Theorem for Non-symmetric Bodies. - An Interpolation Proof of Ehrhard’s Inequality. - Bounds on Dimension Reduction in the Nuclear Norm. - High-Dimensional Convex Sets Arising in Algebraic Geometry. - Polylog Dimensional Subspaces of lN\/∞. - On a Formula for the Volume of Polytopes.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415621411159,"sku":"9783030467616","price":43.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030467616.jpg?v=1730527547"},{"product_id":"line-graphs-and-line-digraphs-9783030813840","title":"Line Graphs and Line Digraphs","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. \u003cp\u003eA subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs.\u003c\/p\u003e\u003cp\u003e\u003ci\u003eLine Graphs and Line Digraphs\u003c\/i\u003e is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientists who have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I Line Graphs.- 1 Fundamentals of Line Graphs.- 2 Line Graph Isomorphisms.- 3 Characterization of Line Graphs.- 4 Spectral Properties of Line Graphs.- 5 Planarity of Line Graphs.- 6 Connectivity of Line Graphs.- 7 Tranversability in Line Graphs.- 8 Colorability in Line Graphs.- 9 Distance and Transitivity in Line Graphs.- Part II Line Digraphs.- 10 Fundamentals of Line Digraphs.- 11 Characterizations of Line Digraphs.- 12 Iterated Line Digraphs.- Part III Generalizations.- 13 Total Graphs and Total Digraphs.- 14 Path Graphs and Path Digraphs.- 15 Super Line Graphs and Super Line Digraphs.- 16 Line Graphs of Signed Graphs.- 17 The Krausz Dimension of Graph.- Reference. Index of Names.- Index of Definitions.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415643496791,"sku":"9783030813840","price":82.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030813840.jpg?v=1730527626"},{"product_id":"combinatorics-graph-theory-and-computing-seiccgtc-2020-boca-raton-usa-march-9-13-9783031053740","title":"Combinatorics, Graph Theory and Computing:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world – many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia.\u003cbr\u003eThe conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work.\u003cbr\u003eThis volume is intended for the community of pure and applied mathematicians, in academia, industry and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eRatio Balancing Numbers(Bartz et al).- An Unexpected Digit Permutation from Multiplying in any Number Base(Qu et al).- A \u0026amp; Z Sequences for Double Riordan Arrays (Branch et al).- Constructing Clifford Algebras for Windmill and Dutch Windmill Graphs; A New Proof of The Friendship Theorem(Myers).- Finding Exact Values of a Character Sum (Peart et al).- On Minimum Index Stanton 4-cycle Designs (Bunge et al).- k-Plane Matroids and Whiteley’s Flattening Conjectures (Servatius et al).- Bounding the edge cover of a hypergraph (Shahrokhi).- A Generalization on Neighborhood Representatives (Holliday).- Harmonious Labelings of Disconnected Graphs involving Cycles and Multiple Components Consisting of Starlike Trees(Abueida et al).- On Rainbow Mean Colorings of Trees (Hallas et al).- Examples of Edge Critical Graphs in Peg Solitaire (Beeler et al).- Regular Tournaments with Minimum Split Domination Number and Cycle Extendability (Factor et al).- Independence and Domination of Chess Pieces on Triangular Boards and on the Surface of a Tetrahedron(Munger et al).- Efficient and Non-efficient Domination of Z-stacked Archimedean Lattices (Paskowitz et al).- On subdivision graphs which are 2-steps Hamiltonian graphs and hereditary non 2-steps Hamiltonian graphs (Lee et al).- On the Erd}os-S_os Conjecture for graphs with circumference at most k + 1 (Heissan et al).- Regular graph and some vertex-deleted subgraph (Egawa et al).- Connectivity and Extendability in Digraphs (Beasle).-\u003cbr\u003eOn the extraconnectivity of arrangement graphs (Cheng et al).- k-Paths of k-Trees(Bickle).-Rearrangement of the Simple Random Walk(Skyers et al).- On the Energy of Transposition Graphs(DeDeo).- A Smaller Upper Bound for the (4; 82) Lattice Site Percolation Threshold(Wierman).","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415677083991,"sku":"9783031053740","price":97.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031053740.jpg?v=1730527752"},{"product_id":"graph-transformation-15th-international-conference-icgt-2022-held-as-part-of-staf-2022-nantes-france-july-7-8-2022-proceedings-9783031098420","title":"Graph Transformation: 15th International","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book constitutes the refereed proceedings of the 15th International Conference on Graph Transformation, ICGT 2022, which took place Nantes, France in July 2022.\u003cp\u003eThe 10 full papers and 1 tool paper presented in this book were carefully reviewed and selected from 19 submissions. The conference focuses on describing new unpublished contributions in the theory and applications of graph transformation as well as tool presentation papers that demonstrate main new features and functionalities of graph-based tools.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eTheoretical Advances.- Application Domains.- Tool Presentation.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415682195799,"sku":"9783031098420","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031098420.jpg?v=1730527770"},{"product_id":"algorithmic-aspects-in-information-and-management-16th-international-conference-aaim-2022-guangzhou-china-august-13-14-2022-proceedings-9783031160806","title":"Algorithmic Aspects in Information and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book constitutes the proceedings of the 16th International Conference on Algorithmic Aspects in Information and Management, AAIM 2022, which was held online during August 13-14, 2022. The conference was originally planned to take place in Guangzhou, China, but changed to a virtual event due to the COVID-19 pandemic.\u003cp\u003eThe 41 regular papers included in this book were carefully reviewed and selected from 59 submissions. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAn improvement of the bound on the odd chromatic number of 1-planar graphs.- AoI Minimizing of Wireless Rechargeable Sensor Network based on Trajectory Optimization of Laser-Charged UAV.- Monotone k-Submodular Knapsack Maximization: An Analysis of the Greedy+Singleton Algorithm.- The constrained parallel-machine scheduling problem with divisible processing times and penalties.- Energy-constrained Geometric Covering Problem.- Fast searching on $k$-combinable graphs.- Three Algorithms for Converting Control Flow Statements from Python to XD-M.- Class Ramsey numbers involving induced graphs.- An Approximation Algorithm for the Clustered Path Travelling Salesman Problem.- Hyperspectral Image Reconstruction for SD-CASSI systems based on Residual Attention Network.- Improved Approximation Algorithm for the Asymmetric Prize-Collecting TSP.- Injective edge coloring of power graphs and necklaces.- Guarantees for Maximization of $k$-Submodular Functions with a Knapsack and a Matroid Constraint.- Incremental SDN Deployment to Achieve Load Balance in ISP Networks.- Approximation scheme for single-machine rescheduling with job delay and rejection.- Defense of Scapegoating Attack in Network Tomography.- A Binary Search Double Greedy Algorithm for Non-monotone DR-submodular Maximization.- Streaming Adaptive Submodular Maximization.- Constrained Stochastic Submodular Maximization with State-Dependent Costs.- Online early work maximization problem on two hierarchical machines with  buffer or rearrangements.- Polynomial time algorithm for k-vertex-edge dominating problem in interval graphs.- Adaptive Competition-based Diversified-profit Maximization with Online Seed Allocation.- Collaborative Service Caching in Mobile Edge Nodes.- A Decentralized Auction Framework with Privacy Protection in Mobile Crowdsourcing.- On-line single machine scheduling with release dates and submodular rejection penalties.- Obnoxious Facility Location Games with Candidate Locations.- Profit Maximization for Multiple Products in Community-based Social Networks.- MCM: A Robust Map Matching Method by Tracking Multiple Road Candidates.- Security on Ethereum: Ponzi Scheme Detection in Smart Contract.- Cyclically orderable generalized Petersen graphs.- The r-dynamic chromatic number of planar graphs without special short cycles.- Distance Labeling of the Halved Folded $n$-Cube.- Signed network embedding based on muti-attention mechanism.- Balanced Graph Partitioning based on Mixed 0-1 Linear Programming and Iteration Vertex Relocation Algorithm.- Partial inverse min-max spanning tree problem under the weighted bottleneck Hamming distance.- Mixed Metric Dimension of Some Plane Graphs.- The Optimal Dynamic Rationing Policy in the Stock-Rationing Queue.- Pilot Pattern Design with Branch and Bound in PSA-OFDM System.- Bicriteria Algorithms for Maximizing the Difference Between Submodular Function and Linear Function under Noise.- On the Transversal Number of k-Uniform Connected Hypergraphs.- Total coloring of planar graphs without some adjacent cycles.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415690289495,"sku":"9783031160806","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031160806.jpg?v=1730527800"},{"product_id":"generating-functions-in-engineering-and-the-applied-sciences-9783031211454","title":"Generating Functions in Engineering and the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eGenerating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc.  This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems.  Specifically, the book discusses probability GFs (PGF),  moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs.  Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that readers who do not have prior knowledge of the topic can easily follow through the chapters and apply the lessons learned in their respective disciplines.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eTypes of Generating Functions.- Operations on Generating Functions.- Generating Functions in Statistics.- Applications of Generating Functions.- Bibliography.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415698055511,"sku":"9783031211454","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031211454.jpg?v=1730527824"},{"product_id":"integer-programming-and-combinatorial-optimization-24th-international-conference-ipco-2023-madison-wi-usa-june-21-23-2023-proceedings-9783031327254","title":"Integer Programming and Combinatorial","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21–23, 2023.\u003c\/p\u003e  \u003cp\u003eThe 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415709065559,"sku":"9783031327254","price":61.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031327254.jpg?v=1730527861"},{"product_id":"variable-neighborhood-search-9th-international-conference-icvns-2022-abu-dhabi-united-arab-emirates-october-25-28-2022-revised-selected-papers-9783031344992","title":"Variable Neighborhood Search: 9th International","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume constitutes the proceedings of the 9th International Conference on Variable Neighborhood Search, ICVNS 2023, held in Abu Dhabi, United Arab Emirates, in October 2022.\u003cp\u003eThe 11 full papers presented in this volume were carefully reviewed and selected from 29 submissions. The papers describe recent advances in methods and applications of variable neighborhood search.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eA metaheuristic approach for solving Monitor Placement Problem.- A VNS-based heuristic for the minimum number of resources under a perfect schedule.- BVNS for Overlapping Community Detection.- A Simulation-Based Variable Neighborhood Search Approach for Optimizing Cross-Training Policies.- Multi-Objective Variable Neighborhood Search for improving software modularity.- An Effective VNS for Delivery Districting.- BVNS for the Minimum Sitting Arrangement problem in a cycle.- Assigning Multi-Skill Confgurations to Multiple Servers with a Reduced VNS.- Multi-Round Infuence Maximization: A Variable Neighborhood Search Approach.- A VNS based heuristic for a 2D Open Dimension Problem.- BVNS for the bi-objective multi row equal facility layout problem.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415711392087,"sku":"9783031344992","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031344992.jpg?v=1730527870"},{"product_id":"frontiers-of-algorithmics-17th-international-joint-conference-ijtcs-faw-2023-macau-china-august-14-18-2023-proceedings-9783031393433","title":"Frontiers of Algorithmics: 17th International","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book constitutes the refereed proceedings of the 17th International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom (IJTCS-FAW 2023), consisting of the 17th International Conference on Frontier of Algorithmic Wisdom (FAW) and the 4th International Joint Conference on Theoretical Computer Science (IJTCS), held in Macau, China, during August 14–18, 2023.\u003c\/p\u003e\u003cp\u003eFAW started as the Frontiers of Algorithmic Workshop in 2007 at Lanzhou, China, and was held annually from 2007 to 2021 and published archival proceedings. IJTCS, the International joint theoretical Computer Science Conference, started in 2020, aimed to bring in presentations covering active topics in selected tracks in theoretical computer science.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eTo accommodate the diversified new research directions in theoretical computer science, FAW and IJTCS joined their forces together to organize an event for information exchange of new findings and work of enduring value in the field. \u003cbr\u003e The 21 full papers included in this book were carefully reviewed and selected from 34 submissions. They were organized in topical sections as follows: algorithmic game theory; algorithms and data structures; combinatorial optimization; and computational economics.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eUnderstanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial Auctions.- An Improved Analysis of the Greedy+Singleton Algorithm for k-Submodular Knapsack Maximization.- Generalized Sorting with Predictions Revisited.- Eliciting Truthful Reports with Partial Signals in Repeated Games.- On the NP-hardness of two scheduling problems under linear constraints.- On the Matching Number of k-Uniform Connected Hypergraphs with Maximum Degree.- Max-Min Greedy Matching Problem: Hardness for the Adversary and Fractional Variant.- Approximate Core Allocations for Edge Cover Games.- Random Approximation Algorithms for Monotone k-Submodular Function Maximization with Size Constraints.- Additive Approximation Algorithms for Sliding Puzzle.- Differential Game Analysis for Cooperation Models in Automotive Supply Chain under Low-Carbon Emission Reduction Policies.- Adaptivity Gap for Influence Maximization with Linear Threshold Model on Trees.- Physically Verifying the First Nonzero Term in a Sequence: Physical ZKPs for ABC End View and Goishi Hiroi.- Mechanism Design in Fair Sequencing.- Red-Blue Rectangular Annulus Cover Problem.- Applying Johnson's Rule in Scheduling Multiple Parallel Two-Stage Flowshops.- The Fair k-Center with Outliers Problem: FPT and Polynomial Approximations.- Constrained Graph Searching on Trees.- EFX Allocations Exist for Binary Valuations.- Maximize Egalitarian Welfare for Cake Cutting.- Stackelberg Strategies on Epidemic Containment Games.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415715586391,"sku":"9783031393433","price":56.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031393433.jpg?v=1730527882"},{"product_id":"hypergroups-9783031394881","title":"Hypergroups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are developed along the lines of the structure theory of groups. The focus then turns to a number of concrete classes of hypergroups with small parameters, and continues with a closer look at the role of involutions (modeled after the definition of group-theoretic involutions) within the theory of hypergroups. Hypergroups generated by involutions lead to the exchange condition (a genuine generalization of the group-theoretic exchange condition), and this condition defines the so-called Coxeter hypergroups. Coxeter hypergroups can be treated in a similar way to Coxeter groups. On the other hand, their regular actions are mathematically equivalent to buildings (in the sense of Jacques Tits). A similar equivalence is discussed for twin buildings. The primary audience for the monograph will be researchers working in Algebra and\/or Algebraic Combinatorics, in particular on association schemes.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Basic Facts : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1\u003cp\u003e1.1 Neutral Elements and Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1\u003c\/p\u003e\u003cp\u003e1.2 Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3\u003c\/p\u003e\u003cp\u003e1.3 Complex Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6\u003c\/p\u003e\u003cp\u003e1.4 Thin Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9\u003c\/p\u003e\u003cp\u003e1.5 Groups and Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11\u003c\/p\u003e\u003cp\u003e1.6 Actions of Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13\u003c\/p\u003e\u003cp\u003e1.7 Hypergroups Admitting Regular Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18\u003c\/p\u003e\u003cp\u003e1.8 Association Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e2 Closed Subsets : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 27\u003c\/p\u003e\u003cp\u003e2.1 Basic Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27\u003c\/p\u003e\u003cp\u003e2.2 Dedekind Modularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32\u003c\/p\u003e\u003cp\u003e2.3 Generating Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33\u003c\/p\u003e\u003cp\u003e2.4 Commutators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37\u003c\/p\u003e\u003cp\u003e2.5 Conjugation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38\u003c\/p\u003e\u003cp\u003e2.6 The Thin Radical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41\u003c\/p\u003e\u003cp\u003e2.7 Foldings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e3 Elementary Structure Theory: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 47\u003c\/p\u003e\u003cp\u003e3.1 Centralizers and Normalizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47\u003c\/p\u003e\u003cp\u003e3.2 Su cient Conditions for Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52\u003c\/p\u003e\u003cp\u003e3.3 Strong Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55\u003c\/p\u003e\u003cp\u003e3.4 Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59\u003c\/p\u003e\u003cp\u003e3.5 Computations in Quotients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63\u003c\/p\u003e\u003cp\u003e3.6 Homomorphisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66\u003c\/p\u003e\u003cp\u003e3.7 The Homomorphism Theorem and the Isomorphism Theorems . . . . . . . . . . 71\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e4 Subnormality and Thin Residues : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 79\u003c\/p\u003e\u003cp\u003e4.1 Subnormal Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79\u003c\/p\u003e\u003cp\u003e4.2 Composition Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83\u003c\/p\u003e\u003cp\u003e4.3 The Thin Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88\u003c\/p\u003e\u003cp\u003e4.4 Thin Residues of Thin Residues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91\u003c\/p\u003e\u003cp\u003e4.5 Residually Thin Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94\u003c\/p\u003e\u003cp\u003e4.6 Finite Residually Thin Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97\u003c\/p\u003e\u003cp\u003e4.7 Solvable Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e5 Tight Hypergroups : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 107\u003c\/p\u003e\u003cp\u003e5.1 Tight Hypergroup Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107\u003c\/p\u003e\u003cp\u003e5.2 The Set S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111\u003c\/p\u003e\u003cp\u003e5.3 The Sets a b \\ Fc and Sa;b(Fc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113\u003c\/p\u003e\u003cp\u003e5.4 The Sets bf1b  \\ Fa and Sb;(f1;:::;fn)(Fa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117\u003c\/p\u003e\u003cp\u003e5.5 Structure Constants of Finite Tight Hypergroups . . . . . . . . . . . . . . . . . . . . . 122\u003c\/p\u003e\u003cp\u003e5.6 Rings Arising from Certain Finite Tight Hypergroups . . . . . . . . . . . . . . . . . 126\u003c\/p\u003e\u003cp\u003e5.7 Finite Metathin Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128\u003c\/p\u003e\u003cp\u003e5.8 Finite Metathin Hypergroups with Restricted Thin Residue . . . . . . . . . . . . 132\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e6 Involutions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 137\u003c\/p\u003e\u003cp\u003e6.1 Basic Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138\u003c\/p\u003e\u003cp\u003e6.2 Cosets of Closed Subsets Generated by an Involution, I . . . . . . . . . . . . . . . . 142\u003c\/p\u003e\u003cp\u003e6.3 Cosets of Closed Subsets Generated by an Involution, II . . . . . . . . . . . . . . . 145\u003c\/p\u003e\u003cp\u003e6.4 Cosets of Closed Subsets Generated by an Involution, III . . . . . . . . . . . . . . . 147\u003c\/p\u003e\u003cp\u003e6.5 Length Functions De ned by Sets of Involutions . . . . . . . . . . . . . . . . . . . . . . 152\u003c\/p\u003e\u003cp\u003e6.6 Hypergroups Generated by Two Distinct Involutions . . . . . . . . . . . . . . . . . . 156\u003c\/p\u003e\u003cp\u003e6.7 Dichotomy and the Exchange Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161\u003c\/p\u003e\u003cp\u003e6.8 Projective Hypergroups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e7 Hypergroups with a Small Number of Elements : : : : : : : : : : : : : : : : : : : : : : 171\u003c\/p\u003e\u003cp\u003e7.1 Hypergroups of Cardinality at Most 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172\u003c\/p\u003e\u003cp\u003e7.2 Non-Symmetric Hypergroups of Cardinality 4 . . . . . . . . . . . . . . . . . . . . . . . . 179\u003c\/p\u003e\u003cp\u003e7.3 Hypergroups of Cardinality 6 with a Non-Normal Closed Subset, I . . . . . . 190\u003c\/p\u003e\u003cp\u003e7.4 Hypergroups of Cardinality 6 with a Non-Normal Closed Subset, II . . . . . . 202\u003c\/p\u003e\u003cp\u003e7.5 Non-Normal Closed Subsets Missing Four Elements . . . . . . . . . . . . . . . . . . . 215\u003c\/p\u003e\u003cp\u003e7.6 Non-Normal Closed Subsets Missing Four Elements and Thin Elements . . 221\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e8 Constrained Sets of Involutions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 223\u003c\/p\u003e\u003cp\u003e8.1 Basic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224\u003c\/p\u003e\u003cp\u003e8.2 Constrained Sets of Involutions and Cosets . . . . . . . . . . . . . . . . . . . . . . . . . . . 228\u003c\/p\u003e\u003cp\u003e8.3 Constrained Sets of Involutions and the Thin Radical . . . . . . . . . . . . . . . . . . 230\u003c\/p\u003e\u003cp\u003e8.4 Constrained Sets of Involutions and Dichotomy . . . . . . . . . . . . . . . . . . . . . . . 233\u003c\/p\u003e\u003cp\u003e8.5 Constrained Sets of Non-Thin Involutions and Dichotomy . . . . . . . . . . . . . . 239\u003c\/p\u003e\u003cp\u003e8.6 Constrained Sets of Involutions and Foldings . . . . . . . . . . . . . . . . . . . . . . . . . 244\u003c\/p\u003e\u003cp\u003e8.7 Dichotomic Constrained Sets of Involutions and Foldings . . . . . . . . . . . . . . . 248\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e9 Coxeter Sets of Involutions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 251\u003c\/p\u003e\u003cp\u003e9.1 General Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252\u003c\/p\u003e\u003cp\u003e9.2 The Sets V1(U) for Subsets U of Coxeter Sets V of Involutions . . . . . . . . . . 256\u003c\/p\u003e\u003cp\u003e9.3 The Sets V����1(U) for Subsets U of Coxeter Sets V of Involutions . . . . . . . . . 263\u003c\/p\u003e\u003cp\u003e9.4 Sets of Subsets of Coxeter Sets of Involutions . . . . . . . . . . . . . . . . . . . . . . . . . 265\u003c\/p\u003e\u003cp\u003e9.5 Spherical Coxeter Sets of Involutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268\u003c\/p\u003e\u003cp\u003e9.6 Subsets of Spherical Coxeter Sets of Involutions . . . . . . . . . . . . . . . . . . . . . . . 273\u003c\/p\u003e\u003cp\u003e9.7 Coxeter Sets of Involutions and Foldings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277\u003c\/p\u003e\u003cp\u003e9.8 Coxeter Sets of Involutions and Their Coxeter Numbers . . . . . . . . . . . . . . . . 280\u003c\/p\u003e\u003cp\u003e9.9 Coxeter Sets of Involutions and Type Preserving Bijections . . . . . . . . . . . . . 286\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e10 Regular Actions of (Twin) Coxeter Hypergroups: : : : : : : : : : : : : : : : : : : : : 293\u003c\/p\u003e\u003cp\u003e10.1 Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293\u003c\/p\u003e\u003cp\u003e10.2 Twin Buildings, I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298\u003c\/p\u003e\u003cp\u003e10.3 Twin Buildings, II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301\u003c\/p\u003e\u003cp\u003e10.4 Regular Actions of Coxeter Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305\u003c\/p\u003e\u003cp\u003e10.5 Regular Actions of Twin Coxeter Hypergroups . . . . . . . . . . . . . . . . . . . . . . . . 315\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eReferences : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 333\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415715651927,"sku":"9783031394881","price":89.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031394881.jpg?v=1730527882"},{"product_id":"graph-theoretic-concepts-in-computer-science-49th-international-workshop-wg-2023-fribourg-switzerland-june-28-30-2023-revised-selected-papers-9783031433795","title":"Graph-Theoretic Concepts in Computer Science:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume constitutes the thoroughly refereed proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023.\u003cbr\u003e The 33 full papers presented in this volume were carefully reviewed and selected from a total of 116 submissions. The WG 2022 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science, or by extracting new graph theoretic problems from applications.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eProportionally Fair Matching with Multiple Groups.- Reconstructing Graphs from Connected Triples.- Parameterized Complexity of Vertex Splitting to Pathwidth at most 1.- Odd Chromatic Number of Graph Classes.- Deciding the Erdos-P osa property in 3-connected digraphs.- New Width Parameters for Independent Set: One-sided-mim-width and Neighbor-depth.- Computational Complexity of Covering Colored Mixed Multigraphswith Degree Partition Equivalence Classes of Size at Most Two.- Cutting Barnette graphs perfectly is hard.- Metric dimension parameterized by treewidth in chordal graphs.- Efficient Constructions for the Gyori-Lovasz Theorem on Almost Chordal Graphs.- Generating faster algorithms for d-Path Vertex Cover.- A new width parameter of graphs based on edge cuts: -edge-crossing width.- Snakes and Ladders: a Treewidth Story.- Parameterized Results on Acyclic Matchings with Implications for Related Problems.- P-matchings Parameterized by Treewidth.- Algorithms and hardness for Metric Dimension on digraphs.- Degreewidth : a New Parameter for Solving Problems on Tournaments.- Approximating Bin Packing with Con ict Graphs via Maximization Techniques.- i-Metric Graphs: Radius, Diameter and all Eccentricities.- Maximum edge colouring problem on graphs that exclude a xed minor.- Bounds on Functionality and Symmetric Di erence { Two Intriguing Graph Parameters.- Cops and Robbers on Multi-layer Graphs.- Parameterized Complexity of Broadcasting in Graphs.- Turan's Theorem Through Algorithmic Lens.- On the Frank number and nowhere-zero ows on graphs.- On the minimum number of arcs in 4-dicritical oriented graphs.- Tight Algorithms for Connectivity Problems Parameterized byModular-Treewidth.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415721910615,"sku":"9783031433795","price":61.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031433795.jpg?v=1730527896"},{"product_id":"reshaping-convex-polyhedra-9783031475108","title":"Reshaping Convex Polyhedra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e^ the= study= of= convex= polyhedra= in= ordinary= space= is= a= central= piece= classical= and= modern= geometry= that= has= had= significant= impact= on= many= areas= mathematics= also= computer= science.= present= book= project= by= joseph= o'rourke= costin= vîlcu= brings= together= two= important= strands= subject= = combinatorics= polyhedra,= intrinsic= underlying= surface.= this= leads= to= remarkable= interplay= concepts= come= life= wide= range= very= attractive= topics= concerning= polyhedra.= gets= message= across= thetheory= although= with= roots,= still= much= alive= today= continues= be= inspiration= basis= lot= current= research= activity.= work= presented= manuscript= interesting= applications= discrete= computational= geometry,= as= well= other= mathematics.= treated= detail= include= unfolding= onto= surfaces,= continuous= flattening= convexity= theory= minimal= length= enclosing= polygons.= along= way,= open= problems= suitable= for= graduate= students= are= raised,=","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415728202071,"sku":"9783031475108","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031475108.jpg?v=1730527912"}],"url":"https:\/\/bookcurl.com\/collections\/discrete-mathematics.oembed?page=7","provider":"Book Curl","version":"1.0","type":"link"}