Discrete mathematics Books
Penguin Publishing Group Why Machines Learn
Book Synopsis
£18.99
McGraw-Hill Education Discrete Mathematics and Its Applications ISE
Book Synopsis
£53.09
Cambridge University Press An Invitation to Combinatorics
Book SynopsisActive 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.Trade Review'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'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'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'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'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'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, zbMATHTable of ContentsPreface; 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.
£37.04
Taylor & Francis Ltd Discrete Mathematics with Ducks
Book SynopsisDiscrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they've learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author's lively and friendly writing style is apTable of ContentsPreface for Instructors and Other TeachersPreface for Students and Other LearnersTheme: The Basics1 Counting and Proofs2 Sets and Logic3 Graphics and Functions4 Induction5 Algorithms with CiphersTheme I Supplement6 Binomial Coefficients and Pascal’s Triangle7 Balls and Boxes and PIE: Counting Techniques8 Recurrences9 Cutting Up Food: Counting and GeometryIII Theme: Graph Theory10 Trees11 Euler’s Formula and Applications12 Graph Traversals13 Graph ColoringTheme III Supplement: Problems on the Theme of Graph TheoryIV Other Material14 Probability and Expectation15 Fun with Cardinality16 Number Theory17 Computational ComplexityA Solutions to Check Yourself ProblemsB Solutions to Bonus Check-Yourself ProblemsC The Greek Alphabet and Some Uses for Some LettersD List of SymbolsBibliographyIndex
£37.99
Cambridge University Press Frameworks Tensegrities and Symmetry
Book SynopsisThis introduction to the theory of rigid structures explains how to analyze the performance of built and natural structures under loads, paying special attention to the simplifying role of symmetry. Written for researchers and graduate students in structural engineering and mathematics, and of interest to computer scientists and physicists.Trade Review'Rigidity theory mathematicians and structural engineers are like two branches of a tribe that separated long ago. In the intervening time, the language and knowledge of each group has evolved to where concepts no longer align and common terms no longer have common meanings. As a result, when they interact today, confusion reigns. Frameworks, Tensegrities and Symmetry is a guide that both groups can use to understand the other.' William F. Baker, Skidmore, Owings & Merrill'The authors promise 'an attempt to build a bridge between two cultures' and they have done a remarkable job of this unenviable task. Requiring only a minimum of mathematical and engineering prerequisites the book develops intuitively, and rigorously, the rigidity theory of both bar frameworks and tensegrity frameworks and applies this theory to analyse built structures. Two masters of the field have carefully designed the book to move seamlessly between the analysis and synthesis of specific structures and providing the general, generic and symmetric theories.' Anthony Nixon, Lancaster UniversityTable of Contents1. Introduction; Part I. The General Case: 2. Frameworks and Rigidity; 3. First-Order Analysis of Frameworks; 4. Tensegrities; 5. Energy Functions and the Stress Matrix; 6. Prestress Stability; 7. Generic Frameworks; 8. Finite Mechanisms; Part II. Symmetric Structures: 9. Groups and Representation Theory; 10. First-Order Symmetry Analysis; 11. Generating Stable Symmetric Tensegrities; A. Useful Theorems and Proofs.
£55.09
Association of Computing Machinery,U.S. Logic, Automata, and Computational Complexity:
Book SynopsisProfessor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for "his advancement of our understanding of the complexity of computation in a significant and profound way." This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook's synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook's ideas and their enduring impact on the research community. The book also contains biographical material, Cook's Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.
£42.46
Elsevier Science Publishing Co Inc Discrete Mathematics
Book SynopsisTrade Review"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 OpenTable of ContentsPart 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
£56.69
Elsevier Science Publishing Co Inc Differential Equations with Mathematica
Book SynopsisTable of Contents1. Preface 2. Introduction to Differential Equations 3. First-Order Ordinary Differential Equations 4. Applications of First-Order Ordinary Differential Equations 5. Higher-Order Differential Equations 6. Applications of Higher-Order Differential Equations 7. Systems of Ordinary Differential Equations 8. Applications of Systems of Ordinary Differential Equations 9. Laplace Transform Methods 10. Eigenvalue Problems and Fourier Series 11. Partial Differential Equations 12. Appendix: Getting Started 13. The Mathematica Menu 14. Bibliography 15. Index
£103.50
Oxford University Press Discrete Mathematics
Book SynopsisBiggs'' 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 bTrade ReviewThis 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 *A 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 *... the ideal choice for introductory courses to discrete mathematicians. * Zentralblatt MATH *Table of ContentsTHE LANGUAGE OF MATHEMATICS; TECHNIQUES; ALGORITHMS AND GRAPHS; ALGEBRAIC METHODS
£62.70
Oxford University Press Combinatorics
Book SynopsisHow 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.Trade ReviewClear 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 *Table of Contents1: 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
£9.49
Oxford University Press The Nature of Complex Networks
Book SynopsisThe 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.Trade ReviewThe 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 *Table of ContentsPreface 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
£89.00
Elsevier Science & Technology Machine Learning
Book Synopsis
£71.96
Elsevier Science Cognitive Intelligence with Neutrosophic
Book SynopsisTable of Contents1. Introduction to Neutrosophic Probability 2. Introduction to Neutrosophic Statistics 3. Applications Applications of Neutrosophic Statistics to Medicine Applications of Neutrosophic Statistics to Cognitive Data Applications of Neutrosophic Statistics to Bioinformatics
£103.50
Taylor & Francis Ltd Combinatorics of Permutations
Book SynopsisA CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, third edition continues to clearly show the usefulness of this subject for both students and researchers.The research in combinatorics of permutations has advanced rapidly since this book was published in a first edition. Now the third edition offers not only updated results, it remains the leading textbook for a course on the topic.Coverage is mostly enumerative, but there are algebraic, analytic, and topological parts as well, and applications.Since the publication of the second edition, there is tremendous progress in pattern avoidance (Chapters 4 and 5). There is also significant progress in the analytic combinatorics of permutations, which will be incorporated. A completely new technique from extremal comTable of ContentsForewardPreface to the First EditionPreface to the Second EditionPreface to the Third EditionAcknowledgementsIntroduction: No Way around It.1.In One Line and Close: Permutations as Linear Orders2.In One Line and Anywhere: Permutations as Linear Orders- Inversions3.In Many Circles: Permutations as Products of Cycles4.In Any Way but This: Pattern Avoidance—the Basics5.In This Way, but Nicely: Pattern Avoidance-Follow Up6.Mean and Insensitive: Random Permutations7.Permutations and the Rest: Algebraic Combinatorics of Permutations8.Get Them All: Algorithms and Permutations9.How Did We Get Here? Permutations as Genome RearrangementsDo Not Look Just Yet: Solutions to Odd-Numbered ExercisesReferencesList of Frequently Used NotationIndex
£105.00
Taylor & Francis Ltd Topics in Graph Theory
Book SynopsisThe interplay continues to grow between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences.Topics in Graph Theory is geared toward the more mathematically mature student. The first three chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level.The authors build upon material previously published in Graph Theory and Its Applications, Third Edition, by the same authors. That text covers material for both an underTable of Contents1. Foundations. 2. Isomorphisms and Symmetry. 3. Trees and Connectivity. 4. Planarity and Kuratowski’s Theorem. 5. Drawing Graphs and Maps. 6. Graph Colorings. 7. Measurement and Mappings. 8. Analytic Graph Theory. 9. Graph Colorings and Symmetry. 10. Algebraic Specification of Graphs. 11. Nonplanar Layouts.
£73.14
Springer New York Combinatorial Commutative Algebra
Book SynopsisRecent developments are covered Contains over 100 figures and 250 exercises Includes complete proofsTrade ReviewFrom the reviews: "The book under review constitutes a self-contained introduction to the use of combinatorial methods in commutative algebra. … Concrete calculations and examples are used to introduce and develop concepts. Numerous exercises provide the opportunity to work through the material and end of chapter notes comment on the history and development of the subject. The authors have provided us with a useful reference and an effective text book." (R. J. Shank, Zentralblatt MATH, Vol. 1090 (16), 2006)Table of ContentsMonomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.- Semigroup rings.- Multigraded polynomial rings.- Syzygies of lattice ideals.- Toric varieties.- Irreducible and injective resolutions.- Ehrhart polynomials.- Local cohomology.- Determinants.- Plücker coordinates.- Matrix Schubert varieties.- Antidiagonal initial ideals.- Minors in matrix products.- Hilbert schemes of points.
£61.74
Springer New York Convex Polytopes
Book Synopsis1 Notation and prerequisites.- 1.1 Algebra.- 1.2 Topology.- 1.3 Additional notes and comments.- 2 Convex sets.- 2.1 Definition and elementary properties.- 2.2 Support and separation.- 2.3 Convex hulls.- 2.4 Extreme and exposed points; faces and poonems.- 2.5 Unbounded convex sets.- 2.6 Polyhedral sets.- 2.7 Remarks.- 2.8 Additional notes and comments.- 3 Polytopes.- 3.1 Definition and fundamental properties.- 3.2 Combinatorial types of polytopes; complexes.- 3.3 Diagrams and Schlegel diagrams.- 3.4 Duality of polytopes.- 3.5 Remarks.- 3.6 Additional notes and comments.- 4 Examples.- 4.1 The d-simplex.- 4.2 Pyramids.- 4.3 Bipyramids.- 4.4 Prisms.- 4.5 Simplicial and simple polytopes.- 4.6 Cubical polytopes.- 4.7 Cyclic polytopes.- 4.8 Exercises.- 4.9 Additional notes and comments.- 5 Fundamental properties and constructions.- 5.1 Representations of polytopes as sections or projections.- 5.2 The inductive construction of polytopes.- 5.3 Lower semicontinuity of the functions fk(P).- 5.4 Gale-transforms and Gale-diagrams.- 5.5 Existence of combinatorial types.- 5.6 Additional notes and comments.- 6 Polytopes with few vertices.- 6.1 d-Polytopes with d + 2 vertices.- 6.2 d-Polytopes with d + 3 vertices.- 6.3 Gale diagrams of polytopes with few vertices.- 6.4 Centrally symmetric polytopes.- 6.5 Exercises.- 6.6 Remarks.- 6.7 Additional notes and comments.- 7 Neighborly polytopes.- 7.1 Definition and general properties.- 7.2 % MathType!MTEF!2!1!+-% feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadG% aGmUaaaeacaYOaiaiJigdaaeacaYOaiaiJikdaaaacbiGaiaiJ-rga% aiaawUfacaGLDbaaaaa!40CC!$$\left[ {\frac{1}{2}d} \right]$$-Neighborly d-polytopes.- 7.3 Exercises.- 7.4 Remarks.- 7.5 Additional notes and comments.- 8 Euler's relation.- 8.1 Euler's theorem.- 8.2 Proof of Euler's theorem.- 8.3 A generalization of Euler's relation.- 8.4 The Euler characteristic of complexes.- 8.5 Exercises.- 8.6 Remarks.- 8.7 Additional notes and comments.- 9 Analogues of Euler's relation.- 9.1 The incidence equation.- 9.2 The Dehn-Sommerville equations.- 9.3 Quasi-simplicial polytopes.- 9.4 Cubical polytopes.- 9.5 Solutions of the Dehn-Sommerville equations.- 9.6 The f-vectors of neighborly d-polytopes.- 9.7 Exercises.- 9.8 Remarks.- 9.9 Additional notes and comments.- 10 Extremal problems concerning numbers of faces.- 10.1 Upper bounds for fi, i ? 1, in terms of fo.- 10.2 Lower bounds for fi, i ? 1, in terms of fo.- 10.3 The sets f(P3) and f(PS3).- 10.4 The set fP4).- 10.5 Exercises.- 10.6 Additional notes and comments.- 11 Properties of boundary complexes.- 11.1 Skeletons of simplices contained in ?(P).- 11.2 A proof of the van Kampen-Flores theorem.- 11.3 d-Connectedness of the graphs of d-polytopes.- 11.4 Degree of total separability.- 11.5 d-Diagrams.- 11.6 Additional notes and comments.- 12 k-Equivalence of polytopes.- 12.1 k-Equivalence and ambiguity.- 12.2 Dimensional ambiguity.- 12.3 Strong and weak ambiguity.- 12.4 Additional notes and comments.- 13 3-Polytopes.- 13.1 Steinitz's theorem.- 13.2 Consequences and analogues of Steinitz's theorem.- 13.3 Eberhard's theorem.- 13.4 Additional results on 3-realizable sequences.- 13.5 3-Polytopes with circumspheres and circumcircles.- 13.6 Remarks.- 13.7 Additional notes and comments.- 14 Angle-sums relations; the Steiner point.- 14.1 Gram's relation for angle-sums.-14.2 Angle-sums relations for simplicial polytopes.- 14.3 The Steiner point of a polytope (by G. C. Shephard).- 14.4 Remarks.- 14.5 Additional notes and comments.- 15 Addition and decomposition of polytopes.- 15.1 Vector addition.- 15.2 Approximation of polytopes by vector sums.- 15.3 Blaschke addition.- 15.4 Remarks.- 15.5 Additional notes and comments.- 16 Diameters of polytopes (by Victor Klee).- 16.1 Extremal diameters of d-polytopes.- 16.2 The functions ? and ?b.- 16.3 Wv Paths.- 16.4 Additional notes and comments.- 17 Long paths and circuits on polytopes.- 17.1 Hamiltonian paths and circuits.- 17.2 Extremal path-lengths of polytopes.- 17.3 Heights of polytopes.- 17.4 Circuit codes.- 17.5 Additional notes and comments.- 18 Arrangements of hyperplanes.- 18.1 d-Arrangements.- 18.2 2-Arrangements.- 18.3 Generalizations.- 18.4 Additional notes and comments.- 19 Concluding remarks.- 19.1 Regular polytopes and related notions.- 19.2 k-Content of polytopes.- 19.3 Antipodality and related notions.- 19.4 Additional notes and comments.- Tables.- Addendum.- Errata for the 1967 edition.- Additional Bibliography.- Index of Terms.- Index of Symbols.Trade Review"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." (Peter McMullen, University College London) From the reviews of the second edition: "Branko Grünbaum’s book is a classical monograph on convex polytopes … . As was noted by many researchers, for many years the book provided a central reference for work in the field and inspired a whole generation of specialists in polytope theory. … Every chapter of the book is supplied with a section entitled ‘Additional notes and comments’ … these notes summarize the most important developments with respect to the topics treated by Grünbaum. … The new edition … is an excellent gift for all geometry lovers." (Alexander Zvonkin, Mathematical Reviews, 2004b)Table of Contents1 Notation and prerequisites.- 1.1 Algebra.- 1.2 Topology.- 1.3 Additional notes and comments.- 2 Convex sets.- 2.1 Definition and elementary properties.- 2.2 Support and separation.- 2.3 Convex hulls.- 2.4 Extreme and exposed points; faces and poonems.- 2.5 Unbounded convex sets.- 2.6 Polyhedral sets.- 2.7 Remarks.- 2.8 Additional notes and comments.- 3 Polytopes.- 3.1 Definition and fundamental properties.- 3.2 Combinatorial types of polytopes; complexes.- 3.3 Diagrams and Schlegel diagrams.- 3.4 Duality of polytopes.- 3.5 Remarks.- 3.6 Additional notes and comments.- 4 Examples.- 4.1 The d-simplex.- 4.2 Pyramids.- 4.3 Bipyramids.- 4.4 Prisms.- 4.5 Simplicial and simple polytopes.- 4.6 Cubical polytopes.- 4.7 Cyclic polytopes.- 4.8 Exercises.- 4.9 Additional notes and comments.- 5 Fundamental properties and constructions.- 5.1 Representations of polytopes as sections or projections.- 5.2 The inductive construction of polytopes.- 5.3 Lower semicontinuity of the functions fk(P).- 5.4 Gale-transforms and Gale-diagrams.- 5.5 Existence of combinatorial types.- 5.6 Additional notes and comments.- 6 Polytopes with few vertices.- 6.1 d-Polytopes with d + 2 vertices.- 6.2 d-Polytopes with d + 3 vertices.- 6.3 Gale diagrams of polytopes with few vertices.- 6.4 Centrally symmetric polytopes.- 6.5 Exercises.- 6.6 Remarks.- 6.7 Additional notes and comments.- 7 Neighborly polytopes.- 7.1 Definition and general properties.- 7.2 % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaadG % aGmUaaaeacaYOaiaiJigdaaeacaYOaiaiJikdaaaacbiGaiaiJ-rga % aiaawUfacaGLDbaaaaa!40CC! $$ \left[ {\frac{1} {2}d} \right] $$-Neighborly d-polytopes.- 7.3 Exercises.- 7.4 Remarks.- 7.5 Additional notes and comments.- 8 Euler’s relation.- 8.1 Euler’s theorem.- 8.2 Proof of Euler’s theorem.- 8.3 A generalization of Euler’s relation.- 8.4 The Euler characteristic of complexes.- 8.5 Exercises.- 8.6 Remarks.- 8.7 Additional notes and comments.- 9 Analogues of Euler’s relation.- 9.1 The incidence equation.- 9.2 The Dehn-Sommerville equations.- 9.3 Quasi-simplicial polytopes.- 9.4 Cubical polytopes.- 9.5 Solutions of the Dehn-Sommerville equations.- 9.6 The f-vectors of neighborly d-polytopes.- 9.7 Exercises.- 9.8 Remarks.- 9.9 Additional notes and comments.- 10 Extremal problems concerning numbers of faces.- 10.1 Upper bounds for fi, i ? 1, in terms of fo.- 10.2 Lower bounds for fi, i ? 1, in terms of fo.- 10.3 The sets f(P3) and f(PS3).- 10.4 The set fP4).- 10.5 Exercises.- 10.6 Additional notes and comments.- 11 Properties of boundary complexes.- 11.1 Skeletons of simplices contained in ?(P).- 11.2 A proof of the van Kampen-Flores theorem.- 11.3 d-Connectedness of the graphs of d-polytopes.- 11.4 Degree of total separability.- 11.5 d-Diagrams.- 11.6 Additional notes and comments.- 12 k-Equivalence of polytopes.- 12.1 k-Equivalence and ambiguity.- 12.2 Dimensional ambiguity.- 12.3 Strong and weak ambiguity.- 12.4 Additional notes and comments.- 13 3-Polytopes.- 13.1 Steinitz’s theorem.- 13.2 Consequences and analogues of Steinitz’s theorem.- 13.3 Eberhard’s theorem.- 13.4 Additional results on 3-realizable sequences.- 13.5 3-Polytopes with circumspheres and circumcircles.- 13.6 Remarks.- 13.7 Additional notes and comments.- 14 Angle-sums relations; the Steiner point.- 14.1 Gram’s relation for angle-sums.- 14.2 Angle-sums relations for simplicial polytopes.- 14.3 The Steiner point of a polytope (by G. C. Shephard).- 14.4 Remarks.- 14.5 Additional notes and comments.- 15 Addition and decomposition of polytopes.- 15.1 Vector addition.- 15.2 Approximation of polytopes by vector sums.- 15.3 Blaschke addition.- 15.4 Remarks.- 15.5 Additional notes and comments.- 16 Diameters of polytopes (by Victor Klee).- 16.1 Extremal diameters of d-polytopes.- 16.2 The functions ? and ?b.- 16.3 Wv Paths.- 16.4 Additional notes and comments.- 17 Long paths and circuits on polytopes.- 17.1 Hamiltonian paths and circuits.- 17.2 Extremal path-lengths of polytopes.- 17.3 Heights of polytopes.- 17.4 Circuit codes.- 17.5 Additional notes and comments.- 18 Arrangements of hyperplanes.- 18.1 d-Arrangements.- 18.2 2-Arrangements.- 18.3 Generalizations.- 18.4 Additional notes and comments.- 19 Concluding remarks.- 19.1 Regular polytopes and related notions.- 19.2 k-Content of polytopes.- 19.3 Antipodality and related notions.- 19.4 Additional notes and comments.- Tables.- Addendum.- Errata for the 1967 edition.- Additional Bibliography.- Index of Terms.- Index of Symbols.
£56.99
Springer-Verlag New York Inc. Problems in Analytic Number Theory
Book SynopsisProblems.- 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.Trade ReviewM.R. MurtyProblems in Analytic Number Theory"The reviewer strongly approves of the problem-based approach to learning, and recommends this book to any student of analytic number theory."—MATHEMATICAL REVIEWSFrom the reviews of the second edition:“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)"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)Table of ContentsProblems.- 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.
£44.99
Springer New York Combinatorial Computational Biology of RNA Pseudoknots and Neutral Networks
Book SynopsisIn this monograph, new combinatorial and computational approaches in the study of RNA structures are presented which enhance both mathematics and computational biology.Trade ReviewFrom the reviews:“This book is devoted to the study of the structure of combinatorial models of the ribonucleic acid (RNA). … This book can serve as an introduction to the study of combinatorial computational biology as well as a reference of known results and state of the art in this topic.” (Ludovit Niepel, Zentralblatt MATH, Vol. 1207, 2011)Table of ContentsIntroduction.- Secondary Structures, Pseudoknot RNA and Beyond.- Folding Sequences into Structures.- Evolution of RNA Sequences.- Methods.- References.- Index.
£49.49
Springer New York Algebraic Graph Theory
Book SynopsisThis book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.Trade ReviewC. Godsil and G.F. Royle Algebraic Graph Theory "A welcome addition to the literature . . . beautifully written and wide-ranging in its coverage."—MATHEMATICAL REVIEWS "An accessible introduction to the research literature and to important open questions in modern algebraic graph theory"—L'ENSEIGNEMENT MATHEMATIQUETable of Contents* Graphs * Groups * Transitive Graphs * Arc-Transitive Graphs * Generalized Polygons and Moore Graphs * Homomorphisms * Kneser Graphs * Matrix Theory * Interlacing * Strongly Regular Graphs * Two-Graphs * Line Graphs and Eigenvalues * The Laplacian of a Graph * Cuts and Flows * The Rank Polynomial * Knots * Knots and Eulerian Cycles * Glossary of Symbols * Index
£36.99
Springer Binary Quadratic Forms Classical Theory and Modern Computations
Book Synopsis1 Elementary Concepts.- 2 Reduction of Positive Definite Forms.- 3 Indefinite Forms.- 3.1 Reduction, Cycles.- 3.2 Automorphs, Pell's Equation.- 3.3 Continued Fractions and Indefinite Forms.- 4 The Class Group.- 4.1 Representation and Genera.- 4.2 Composition Algorithms.- 4.3 Generic Characters Revisited.- 4.4 Representation of Integers.- 5 Miscellaneous Facts.- 5.1 Class Number Computations.- 5.2 Extreme Cases and Asymptotic Results.- 6 Quadratic Number Fields.- 6.1 Basic Algebraic Definitions.- 6.2 Algebraic Numbers and Quadratic Fields.- 6.3 Ideals in Quadratic Fields.- 6.4 Binary Quadratic Forms and Classes of Ideals.- 6.5 History.- 7 Composition of Forms.- 7.1 Nonfundamental Discriminants.- 7.2 The General Problem of Composition.- 7.3 Composition in Different Orders.- 8 Miscellaneous Facts II.- 8.1 The Cohen-Lenstra Heuristics.- 8.2 Decomposing Class Groups.- 8.3 Specifying Subgroups of Class Groups.- 9 The 2-Sylow Subgroup.- 9.1 Classical Results on the Pell Equation.- 9.2 ModernRTable of Contents1 Elementary Concepts.- 2 Reduction of Positive Definite Forms.- 3 Indefinite Forms.- 3.1 Reduction, Cycles.- 3.2 Automorphs, Pell’s Equation.- 3.3 Continued Fractions and Indefinite Forms.- 4 The Class Group.- 4.1 Representation and Genera.- 4.2 Composition Algorithms.- 4.3 Generic Characters Revisited.- 4.4 Representation of Integers.- 5 Miscellaneous Facts.- 5.1 Class Number Computations.- 5.2 Extreme Cases and Asymptotic Results.- 6 Quadratic Number Fields.- 6.1 Basic Algebraic Definitions.- 6.2 Algebraic Numbers and Quadratic Fields.- 6.3 Ideals in Quadratic Fields.- 6.4 Binary Quadratic Forms and Classes of Ideals.- 6.5 History.- 7 Composition of Forms.- 7.1 Nonfundamental Discriminants.- 7.2 The General Problem of Composition.- 7.3 Composition in Different Orders.- 8 Miscellaneous Facts II.- 8.1 The Cohen-Lenstra Heuristics.- 8.2 Decomposing Class Groups.- 8.3 Specifying Subgroups of Class Groups.- 8.3.1 Congruence Conditions.- 8.3.2 Exact and Exotic Groups.- 9 The 2-Sylow Subgroup.- 9.1 Classical Results on the Pell Equation.- 9.2 Modern Results.- 9.3 Reciprocity Laws.- 9.4 Special References for Chapter 9.- 10 Factoring with Binary Quadratic Forms.- 10.1 Classical Methods.- 10.2 SQUFOF.- 10.3 CLASNO.- 10.4 SPAR.- 10.4.1 Pollard p — 1.- 10.4.2 SPAR.- 10.5 CFRAC.- 10.6 A General Analysis.- Appendix 1:Tables, Negative Discriminants.- Appendix 2:Tables, Positive Discriminants.
£123.49
Elsevier Science Industrial Network Security
Book Synopsis
£62.06
Elsevier Science Securing NextGeneration Connected Healthcare
Book Synopsis
£124.20
Elsevier Science Intelligent FractalBased Image Analysis
Book Synopsis
£110.70
Elsevier Science Discrete Mathematics With Logic
Book SynopsisTable of Contents1: Discreteness 2: Basic set theory 3: Working with finite sets 4: Formal logic 5: Induction 6: Set structures 7: Elementary number theory 8: Codes and cyphers 9: Graphs and trees
£76.90
Elsevier Science An Introduction to Discrete Mathematics
Book Synopsis
£73.79
John Wiley & Sons Inc Evolutionary Optimization Algorithms
Book SynopsisA clear and lucid bottom-up approach to the basic principles of evolutionary algorithms Evolutionary 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. This 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. Evolutionary Optimization Algorithms: Provides 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 Gives a careful treatment of recently developed EAs?including opposition-based learning, artiTable of ContentsAcknowledgments xxi Acronyms xxiii List of Algorithms xxvii Part I: Introduction to Evolutionary Optimization 1 Introduction 1 2 Optimization 11 Part II: Classic Evolutionary Algorithms 3 Generic Algorithms 35 4 Mathematical Models of Genetic Algorithms 63 5 Evolutionary Programming 95 6 Evolution Strategies 117 7 Genetic Programming 141 8 Evolutionary Algorithms Variations 179 Part III: More Recent Evolutionary Algorithms 9 Simulated Annealing 223 10 Ant Colony Optimization 241 11 Particle Swarm Optimization 265 12 Differential Evolution 293 13 Estimation of Distribution Algorithms 313 14 Biogeography-Based Optimization 351 15 Cultural Algorithms 377 16 Opposition-Based Learning 397 17 Other Evolutionary Algorithms 421 Part IV: Special Type of Optimization Problems 18 Combinatorial Optimization 449 19 Constrained Optimization 481 20 Multi-Objective Optimization 517 21 Expensive, Noisy and Dynamic Fitness Functions 563 Appendices A Some Practical Advice 607 B The No Free Lunch Theorem and Performance Testing 613 C Benchmark Optimization Functions 641 References 685 Topic Index 727
£99.86
Cambridge University Press Zeta Functions of Graphs A Stroll through the Garden 128 Cambridge Studies in Advanced Mathematics Series Number 128
Book SynopsisThis stimulating introduction to zeta (and related) functions of graphs develops the fruitful analogy between combinatorics and number theory - for example, the Riemann hypothesis for graphs - making connections with quantum chaos, random matrix theory, and computer science. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.Trade Review'The book is very appealing through its informal style and the variety of topics covered and may be considered the standard reference book in this field.' Zentralblatt MATHTable of ContentsList of illustrations; Preface; Part I. A Quick Look at Various Zeta Functions: 1. Riemann's zeta function and other zetas from number theory; 2. Ihara's zeta function; 3. Selberg's zeta function; 4. Ruelle's zeta function; 5. Chaos; Part II. Ihara's Zeta Function and the Graph Theory Prime Number Theorem: 6. Ihara zeta function of a weighted graph; 7. Regular graphs, location of poles of zeta, functional equations; 8. Irregular graphs: what is the RH?; 9. Discussion of regular Ramanujan graphs; 10. The graph theory prime number theorem; Part III. Edge and Path Zeta Functions: 11. The edge zeta function; 12. Path zeta functions; Part IV. Finite Unramified Galois Coverings of Connected Graphs: 13. Finite unramified coverings and Galois groups; 14. Fundamental theorem of Galois theory; 15. Behavior of primes in coverings; 16. Frobenius automorphisms; 17. How to construct intermediate coverings using the Frobenius automorphism; 18. Artin L-functions; 19. Edge Artin L-functions; 20. Path Artin L-functions; 21. Non-isomorphic regular graphs without loops or multiedges having the same Ihara zeta function; 22. The Chebotarev Density Theorem; 23. Siegel poles; Part V. Last Look at the Garden: 24. An application to error-correcting codes; 25. Explicit formulas; 26. Again chaos; 27. Final research problems; References; Index.
£62.99
Cambridge University Press Representation Theory of the Symmetric Groups The OkounkovVershik Approach Character Formulas and Partition Algebras 121 Cambridge Studies in Advanced Mathematics Series Number 121
Book SynopsisThe representation theory of the symmetric groups is a classical topic that has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained introduction comprises classical and modern topics, including an exhaustive exposition of the new Okounkov–Vershik approach.Trade Review"This beautifully written new book is a welcome addition... It is almost entirely self-contained, only assuming some basic group theory and linear algebra, yet it takes one to the forefront of recent advances in the area. It would be entirely suitable for a single semester or year-long graduate course, as it is replete with examples and exercises of varying difficulty. I suspect it will also find its way on to the shelf as a valuable reference work for researchers in the field, as it is an excellent complement to books of Kleshchev, Sagan, James, and James and Kerber." David John Hemmer, Mathematical ReviewsTable of ContentsPreface; 1. Representation theory of finite groups; 2. The theory of Gelfand–Tsetlin bases; 3. The Okounkov–Vershik approach; 4. Symmetric functions; 5. Content evaluation and character theory; 6. The Littlewood–Richardson rule; 7. Finite dimensional *-algebras; 8. Schur–Weyl dualities and the partition algebra; Bibliography; Index.
£87.99
Cambridge University Press Homotopy Theory of Higher Categories From Segal Categories to nCategories and Beyond 19 New Mathematical Monographs Series Number 19
Book SynopsisThe study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern technTable of ContentsPrologue; Acknowledgements; Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. The need for weak composition; 5. Simplicial approaches; 6. Operadic approaches; 7. Weak enrichment over a Cartesian model category: an introduction; Part II. Categorical Preliminaries: 8. Some category theory; 9. Model categories; 10. Cartesian model categories; 11. Direct left Bousfield localization; Part III. Generators and Relations: 12. Precategories; 13. Algebraic theories in model categories; 14. Weak equivalences; 15. Cofibrations; 16. Calculus of generators and relations; 17. Generators and relations for Segal categories; Part IV. The Model Structure: 18. Sequentially free precategories; 19. Products; 20. Intervals; 21. The model category of M-enriched precategories; 22. Iterated higher categories; Part V. Higher Category Theory: 23. Higher categorical techniques; 24. Limits of weak enriched categories; 25. Stabilization; Epilogue; References; Index.
£76.99
Cambridge University Press Graph Structure and Monadic SecondOrder Logic A LanguageTheoretic Approach 138 Encyclopedia of Mathematics and its Applications Series Number 138
Book SynopsisThe study of graph structure has advanced with great strides. This book unifies and synthesizes research over the last 25 years, detailing both theory and application. It will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.Trade Review'In its huge breadth and depth the authors manage to provide a comprehensive study of monadic second-order logic on graphs covering almost all aspects of the theory that can be presented from a language theoretical or algebraic point of view. There is currently no other textbook or any other source that matches the range of materials covered in this book. As such it is a fantastic resource for those who to study this area [and] will undoubtedly turn into the standard reference for this area.' Stephan Kreutzer, Mathematical ReviewsTable of ContentsForeword Maurice Nivat; Introduction; 1. Overview; 2. Graph algebras and widths of graphs; 3. Equational and recognizable sets in many-sorted algebras; 4. Equational and recognizable sets of graphs; 5. Monadic second-order logic; 6. Algorithmic applications; 7. Monadic second-order transductions; 8. Transductions of terms and words; 9. Relational structures; Conclusion and open problems; References; Index of notation; Index.
£160.55
Penguin Publishing Group Why Machines Learn
£15.19
Princeton University Press Math Bytes
Book SynopsisHow can reposting on Twitter kill a movie's opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson's method for disproving Fermat's Last Theorem? This title deals with these questions.Trade ReviewOne of Choice's Outstanding Academic Titles for 2014 "[Math Bytes] manages to fulfill its aim of providing a 'tasty byte of math and computing' while following a clear, concise, and to-the-point format... [P]rovides interesting insights to some of the complex, highly sophisticated algorithms that lie behind some of our most widely used technological resources."--Rachael Skyner, Science "The author's humanistic, sincere enjoyment of communicating his selections permeates and I think defines the book... The choice of topics and exposition details make the book entertainingly relevant."--Alexander Bogomolny, Cut the Knot "Math Bytes is fun and full of puzzles and brainteasers in a mashup of mathematics, social media, and pop culture referencing Beyonce, Google, and Twitter among others... This reviewer is simply a fool for math puzzles (though some readers might stop at simply a fool). Math Bytes scratches that itch quite nicely."--Robert Schaefer, New York Journal of Books "Printed on glossy paper and filled with colourful photographs, illustrations and diagrams on nearly every page, this book discusses mathematical ideas that can help us make sense of the digital world. The author's offbeat viewpoint comes from a truly unusual background; he studied mime with the legendary Marcel Marceau whilst pursuing his doctorate in applied maths."--Devorah Bennu, GrrlScientist, The Guardian "Tim Chartier, a professor of mathematics at Davidson College, has put together a delightful book of recreational mathematics. His presentation of a large array of topics is accompanied by excellent graphics, many in color... In sum, a fun book."--Philip J. Davis, SIAM News "The mathematical topics are interesting and informative; if you teach at the college level, you are likely to find some interesting fodder for your courses here. You also may, as I did, learn some new things yourself... This book, which is filled with photos, drawings, and anecdotes, is a treasure trove of amusing mathematical vignettes. It makes for very pleasant summer reading."--Mark Hunacek, MAA Reviews "The reader is constantly challenged to think about it or answer certain questions and to solve some problems (some solutions are provided at the end). Most of all, it's such a lovely little booklet that does not give you the time to get bored with. The average chapter length, including the many illustrations, is only 10 pages. Just enough to catch your interest and get bitten by the mathematics."--A. Bultheel, European Mathematical Society "For readers who love math, computing and puzzles, Math Bytes will be a welcome gift."--George Erdosh, San Francisco Book Review "[L]ively and entertaining book... All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pace--a bit and a byte at a time."--Zentralblatt MATH "A mathematical Pandora's box released is perhaps the best way to describe this book. It overflows with ideas, flitting from one fascinating topic to the next, often without an apparent connection. The range is impressive... Everyone should find a 'math byte' of interest in this book, and perhaps end up finding other topics of interest as well."--Choice "I definitely learnt a few new things and was entertained as I did so. Furthermore, anything that spreads the message that mathematics is both interesting and useful has to be a good thing, so I wish this book success."--Rob Ashmore, Mathematics Today "A fun collection of mathematical applications that has something for everyone, even mathphobes."--Anne Quinn, National Council of Teachers of MathematicsTable of ContentsPreface ix 1Your First Byte 1 2Deceiving Arithmetic 5 3Two by Two 11 4Infinite Detail 21 5Plot the Course 32 6Doodling into a Labyrinth 42 7Obama-cize Yourself 54 8Painting with M&Ms 61 9Distorting Reality 73 10A Pretty Mathematical Face 86 11March MATHness 98 12Ranking a Googol of Bits 105 13A Byte to Go 124 14Up to the Challenge 125 Bibliography 131 Index 133 Image Credits 135
£18.00
Princeton University Press Essential Discrete Mathematics for Computer
Book SynopsisTrade Review"I want to share with everybody my enjoyment of this excellent textbook."---Narciso Marti-Oliet, European Math Society"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."---London Mathematical Society, Glenn Hawe
£60.00
Pluto Press Marxian Economics
Book SynopsisA rare opportunity to delve into Japanese Marxist economicsTrade Review'The contribution of Japanese writers to the study of Marxist Political Economy remains underestimated in the Anglophone world … Among the important achievements of Japanese writers is the capacity to shed original light not only on the ‘pure economics’ of Marx’s thinking but on his Political Economy in the broadest sense. Hiroshi Onishi’s book is an invaluable addition to the canon which the late Makoto Itoh helped establish. It serves both as a textbook and as a historical introduction to the entire development of modern capitalist society from its pre-capitalist origins to the present day from a Historical Materialist perspective, which all scholars and researchers will welcome. An indispensable read.' -- Alan Freeman, University of ManitobaTable of ContentsPreface 1. Human Being in Marxian Materialism: Human Beings, Nature, and Relations of Production 2. Capitalism as a Commodity Producing Society: Quantitative Character of Capitalistic Production, and Capital as Self-valorizing Value 3. Capitalism as the Industrial Society: Qualitative Character of Capitalistic Production, and Capital as Self-Valorizing Value 4. The Growth and Death of Capitalism: Accumulation Theory, A New Quality Created by Quantity 5. The Distribution of Produced Surplus Value among Industries and to Non-Productive Sectors 6. Pre-Capitalistic Economic Formations Addendum I: Decentralized Market Model of the Marxian Optimal Growth Theory Addendum II: Class-Dynamics Incorporated in the Marxian Optimal Growth Model Addendum III: A Conversion of the Analytical Marxist Model to Labor Hire Model to Express the Historical Trend of Firm Size Disparity Mathematical Appendix: How to Solve Dynamic Optimization Problems
£22.49
Springer Us 3D Audio Using Loudspeakers 444 The Springer International Series in Engineering and Computer Science
Book Synopsis3-D Audio Using Loudspeakers is concerned with 3-D audio systems implemented using a pair of conventional loudspeakers. 3-D Audio Using Loudspeakers discusses the theory, implementation, and testing of a head-tracked loudspeaker 3-D audio system.Table of ContentsPreface. 1. Introduction. 2. Background. 3. Theory and Implementation. 4. Physical Validation. 5. Psychophysical Validation. 6. Discussion. A: Inverting FIR Filters. References. Index.
£123.49
Scarecrow Press Foundations of Diatonic Theory
Book SynopsisFoundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals is an introductory, undergraduate-level textbook that provides an easy entry point into the challenging field of diatonic set theory, a division of music theory that applies the techniques of discrete mathematics to the properties of diatonic scales. After introducing mathematical concepts that relate directly to music theory, the text concentrates on these mathematical relationships, firmly establishing a link between introductory pedagogy and recent scholarship in music theory. It then relates concepts in diatonic set theory directly to the study of music fundamentals through pedagogical exercises and instructions. Ideal for introductory music majors, the book requires only a general knowledge of mathematics, and the exercises are provided with solutions and detailed explanations. With its basic description of musical elements, this textbook is suitable for courses in music fundamentals, music theoTrade ReviewNot only does Foundations of Diatonic Theory accomplish its stated goals, but it does so in such a masterful way, and with such a refreshing approach, that after reading it, any course on music fundamentals, music and mathematics, or diatonic set theory taught without its perspective would feel incomplete. * GAMUT: Online Journal of the Music Theory Society of the Mid-Atlantic *Because of its innovative approach, Foundations of Diatonic Theory will come as a breath of fresh air for those who decide to incorporate it into fundamentals courses. It would also provide courses on music and mathematics, and on diatonic set theory, with a way of getting into the material that encourages students to think critically—a most desirable quality in a text, as critical thinking should be demanded of the student by any graduate or upper-division undergraduate course. If Johnson’s Montessori-style approach is contagious among the next generation of textbook authors, the benefits to theory students and instructors alike could be enormous. * GAMUT: Online Journal of the Music Theory Society of the Mid-Atlantic *Table of ContentsPart 1 Preface Part 2 Introduction Chapter 3 1. Spatial Relations and Musical Structures Chapter 4 2. Interval Patterns and Musical Structures Chapter 5 3. Triads and Seventh Chords and Their Structures Part 6 Conclusion Part 7 For Further Study Part 8 Notes Part 9 Sources Cited Part 10 Index
£56.05
MP-AMM American Mathematical Jerusalem Combinatorics 93
Book SynopsisContains twenty-two papers presented at the International Conference in Combinatorics, held in Jerusalem in May 1993. This title describes developments in algebraic combinatorics, enumeration, graph and hypergraph theory, combinatorial geometry, and geometry of polytopes and arrangements.Table of ContentsOn $h$-vectors and symmetry by R. M. Adin Combinatorial aspects of the Poincare polynomial associated with a reflection group by H. Barcelo and A. Goupil Partial unimodality for $f$-vectors of simplicial polytopes and spheres by A. Bjorner Polyominoes and polygons by M. Bousquet-Melou Log-concave and unimodal sequences in algebra, combinatorics, and geometry: An update by F. Brenti A fine classification of closed planar sets according to their non-seeing property by Z. Deutsch On the skeleton of the dual cut polytope by A. Deza and M. Deza A High-school Algebra, "formal calculus," proof of the Bieberbach conjecture [after L. Weinstein] by S. B. Ekhad and D. Zeilberger Node firing games on graphs by K. Eriksson Combinatorial presentation of the structure constants of the center of the group algebra of $ {\mathfrak S}_n$ by A. Goupil Abstract rigidity in $m$-space by J. E. Graver, B. Servatius, and H. Servatius A meshing technique for de Bruijn tori by G. Hurlbert and G. Isaak A structural decomposition for hypergraphs by P. Jeavons, D. Cohen, and M. Gyssens Hypercube embedding of distances with few values by M. Laurent On Borsuk's problem by A. Nilli Zonotopal tilings and the Bohne-Dress theorem by J. Richter-Gebert and G. M. Ziegler Plane trees and algebraic numbers by G. Shabat and A. Zvonkin Applications of the Hopf trace formula to computing homology representations by S. Sundaram Stabbing oriented convex polygons in randomized $O(n^2)$ time by S. Teller and M. Hohmeyer On the finitization of Eckhoff's conjecture by H. Tverberg New cases of the colored Tverberg theorem by S. T. Vrecica and R. T. Zivaljevic Shellability in the lattice of subgroups of a finite group by V. Welker.
£109.25
MP-AMM American Mathematical Grobner Bases and Convex Polytopes
Book SynopsisDeals with the interplay of computational commutative algebra and the theory of convex polytopes. This title centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties.Table of ContentsGrobner basics The state polytope Variation of term orders Toric ideals Enumeration, sampling and integer programming Primitive partition identities Universal Grobner bases Regular triangulations The second hypersimplex $\mathcal A$-graded algebras Canonical subalgebra bases Generators, Betti numbers and localizations Toric varieties in algebraic geometry Some specific Grobner bases Bibliography Index.
£55.80
MP-AMM American Mathematical Stable Marriage and Its Relation to Other
Book SynopsisUses the theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms.Trade ReviewThis short book will provide extremely enjoyable reading to anyone with an interest in discrete mathematics and algorithm design. Mathematical Reviews Anyone would enjoy reading this book. If one had to learn French first, it would be worth the effort. Computing ReviewsTable of ContentsIntroduction, definitions, and examples Existence of a stable matching: the fundamental algorithm Principle of deferred decisions: coupon collecting Theoretical developments: application to the shortest path Searching a table by hashing; mean behavior of thefundamental algorithm Implementing the fundamental algorithm Research problems Annotated bibliography Appendix A. Later developments Appendix B. Solutions to exercises Index.
£24.65
MP-AMM American Mathematical Extremal Graph Theory with Emphasis on Probabili
Book SynopsisProblems in extremal graph theory have traditionally been tackled by ingenious methods which made use of the structure of extremal graphs. Based on the NSF-CBMS Regional Conference on Graph Theory held at Emory University in June, 1984, this book focuses on a trend towards probabilistic methods.Table of ContentsSubdivisions Contractions Small graphs of large girth Large graphs of small diameter Cycles in dense graphs The evolution of random graphs The size Ramsey number of a path Weakly saturated graphs List colourings.
£25.95
MP-AMM American Mathematical Groups Languages and Geometry
Book SynopsisContains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Geometric Group Theory and Computer Science held at Mount Holyoke College (South Hadley, MA). This work features articles about insights from computer experiments, applications of formal language theory, decision problems, and complexity problems.Table of ContentsOpen problems in combinatorial group theory by G. Baumslag, A. G. Myasnikov, and V. Shpilrain The bar problem-A simple tiling problem which is $NP$-complete on the Euclidean tessellation by squares but which is polynomial time on the hyperbolic tessellations by $4g$-gons, $g \geq 2$ by D. Beauquier, D. E. Muller, and P. E. Schupp When are centralizers of finite subgroups of $Out(F_n)$ finite? by D. L. Boutin Computing angles in hyperbolic groups by Z. Grunschlag On effective decidability of the homeomorphism problem for non-compact surfaces by O. Ly Some presentations of the trivial group by C. F. Miller III and P. E. Schupp A language theoretic analysis of combings by S. Rees.
£97.20
MP-AMM American Mathematical Combinatorial Games
Book SynopsisContrasts combinatorial games, which have complete information and no chance moves, with those of classical game theory. This book introduces a theory of numbers, including infinitesimals and transfinite numbers, which has emerged as a special case of the theory of games. It also describes impartial games.Table of ContentsWhat is a game? by R. K. Guy Numbers and games by J. H. Conway Impartial games by R. K. Guy More ways of combining games by J. H. Conway Introductory overview of mathematical go endgames by E. R. Berlekamp Games and codes by V. Pless Complexity of games by A. S. Fraenkel..., Welter's game, Sylver coinage, dots-and-boxes,... by R. J. Nowakowski Unsolved problems in combinatorial games by R. K. Guy Selected bibliography on combinatorial games and some related material by A. S. Fraenkel.
£99.90
MP-AMM American Mathematical Kvant Selecta Volume 1
Book SynopsisThere is a tradition in Russia that holds that mathematics can be both challenging and fun. One fine outgrowth of that tradition is the magazine, ""Kvant"", which has been enjoyed by many of the best students since its founding in 1970. This book presents a collection of articles from ""Kvant"".Table of ContentsTwo games with matchsticks by I. M. Yaglom Economics and linear inequalities by A. B. Katok Economics and linear inequalities (Continuation) by A. B. Katok Switching networks by R. V. Freivald Who will go to Rio? by G. M. Adel'son-Vel'skii, I. N. Bernshtein, and M. L. Gerver From the life of units by A. L. Toom Nonrepeating sequences by G. A. Gurevich Words with restrictions by A. M. Stepin and A. T. Tagi-Zade Planar switching circuits by S. Ovchinnikov Classification algorithms by P. Bleher and M. Kel'bert How to detect a counterfeit coin by G. Shestopal The generalized problem of counterfeit coins by M. Mamikon Truthtellers, liars, and deceivers by P. Bleher Solvable and unsolvable algorithmic problems by V. A. Uspenskii and A. L. Semenov Best bet for simpletons by P. A. Pevzner.
£52.20
American Mathematical Society Coloring Mixed Hypergraphs
Book SynopsisThe theory of graph coloring has existed for more than 150 years. This book states that in the case of hypergraphs, there exist problems on both the minimum and the maximum number of colors. This feature pervades the theory, methods, algorithms, and applications of mixed hypergraph coloring.Table of ContentsIntroduction The lower chromatic number of a hypergraph Mixed hypergraphs and the upper chromatic number Uncolorable mixed hypergraphs Uniquely colorable mixed hypergraphs $\mathcal{C}$-perfect mixed hypergraphs Gaps in the chromatic spectrum Interval mixed hypergraphs Pseudo-chordal mixed hypergraphs Circular mixed hypergraphs Planar mixed hypergraphs Coloring block designs as mixed hypergraphs Modelling with mixed hypergraphs Bibliography List of figures Index.
£57.95
MP-AMM American Mathematical Lectures on Generating Functions
Book SynopsisIntroduces readers to the language of generating functions, which is the main language of enumerative combinatorics. This book starts with definitions, simple properties, and many examples of generating functions. It discusses topics such as formal grammars, generating functions in several variables, and the exclusion-inclusion principle.Table of ContentsFormal power series and generating functions. Operations with formal power series. Elementary generating functions Generating functions for well-known sequences Unambiguous formal grammars. The Lagrange theorem Analytic properties of functions represented as power series and their asymptotics of their coefficients Generating functions of several variables Partitions and decompositions Dirichlet generating functions and the inclusion-exclusion principle Enumeration of embedded graphs Final and bibliographical remarks Bibliography Index.
£44.81
MP-AMM American Mathematical Trends in Optimization
Book SynopsisPresents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint Mathematics Meetings in Phoenix (AZ). This book describes Lovasz's fundamental algorithm for producing a short vector in a lattice by basis reduction.Table of ContentsLattice basis reduction in optimization: Selected topics by K. Aardal Polyhedral methods in discrete optimization by A. Atamturk Graphs and combinatorial optimization by G. Cornuejols Integer programming duality by J. B. Lasserre The design and analysis of approximation algorithms: Facility location as a case study by D. B. Shmoys Algebraic recipes for integer programming by B. Sturmfels Nonlinear and semidefinite programming by S. J. Wright Index.
£98.10
MP-AMM American Mathematical Complex Graphs and Networks
Book SynopsisBased on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, this work presents fresh perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate the information age.Table of ContentsGraph theory in the information age Old and new concentration inequalities A generative model--the preferential attachment scheme Duplication models for biological networks Random graphs with given expected degrees The rise of the giant component Average distance and the diameter Eigenvalues of the adjacency matrix of $G(\mathbf{w})$ The semi-circle law for $G(\mathbf{w})$ Coupling on-line and off-line analyses of random graphs The configuration model for power law graphs The small world phenomenon in hybrid graphs Bibliography Index.
£49.50
