Combinatorics and graph theory Books
MP-AMM American Mathematical Large Networks and Graph Limits
Book SynopsisTrade ReviewWritten by an eminent expert as the first monograph on this topic, this book can be recommended to anybody working on large networks and their applications in mathematics, computer science, social sciences, biology, statistical physics or chip design." - Zentralblatt Math"This is an amazing book: readable, deep, and lively. It sets out this emerging area, makes connections between old classical graph theory and graph limits, and charts the course of the future." - Persi Diaconis, Stanford University"It is always exciting when a mathematical theory turns out to be connected to a variety of other topics. This is the case with the recently developed subject of graph limits, which exhibits tight relations with a wide range of areas including statistical physics, analysis, algebra, extremal graph theory, and theoretical computer science. The book Large Networks and Graph Limits contains a comprehensive study of this active topic and an updated account of its present status. The author, Laszls Lovasz, initiated the subject, and together with his collaborators has contributed immensely to its development during the last decade. This is a beautiful volume written by an outstanding mathematician who is also an excellent expositor." - Noga Alon, Tel Aviv University, Israel"Modern combinatorics is by no means an isolated subject in mathematics, but has many rich and interesting connections to almost every area of mathematics and computer science. The research presented in Lovasz's book exemplifies this phenomenon by taking one of the most quintessentially combinatorial of objects--the finite graph--and through the process of taking limits of sequences of such graphs, reveals and clarifies connections to measure theory, analysis, statistical physics, metric geometry, spectral theory, property testing, algebraic geometry, and even Hilbert's tenth and seventeenth problems. Indeed, this book presents a wonderful opportunity for a student in combinatorics to explore other fields of mathematics, or conversely for experts in other areas of mathematics to become acquainted with some aspects of graph theory." - Terence Tao, University of California, Los Angeles, CA"László Lovász has written an admirable treatise on the exciting new theory of graph limits and graph homomorphisms, an area of great importance in the study of large networks. It is an authoritative, masterful text that reflects Lovász's position as the main architect of this rapidly developing theory. The book is a must for combinatorialists, network theorists, and theoretical computer scientists alike." - Bela Bollobas, Cambridge University, UKTable of Contents Preface Part 1. Large graphs: An informal introduction Very large networks Large graphs in mathematics and physics Part 2. The algebra of graph homomorphisms Notation and terminology Graph parameters and connection matrices Graph homomorphisms Graph algebras and homomorphism functions Part 3. Limits of dense graph sequences Kernels and graphons The cut distance Szemerédi partitions Sampling Convergence of dense graph sequences Convergence from the right On the structure of graphons The space of graphons Algorithms for large graphs and graphons Extremal theory of dense graphs Multigraphs and decorated graphs Part 4. Limits of bounded degree graphs Graphings Convergence of bounded degree graphs Right convergence of bounded degree graphs On the structure of graphings Algorithms for bounded degree graphs Part 5. Extensions: A brief survey Other combinatorial structures Appendix A Bibliography Author index Subject index Notation index
£78.30
MP-AMM American Mathematical Experimental Mathematics
Book SynopsisPresents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open. The hypotheses range from geometry and topology to combinatorics to algebra and number theory.Table of Contents Introduction The statistics of topology and algebra Combinatorial complexity and randomness Random permutations of Young diagrams of their cycles The geometry of Frobenius numbers for additive semigroups Bibliography
£43.16
Society for Industrial and Applied Mathematics Combinatorial Optimization Packing and Covering
Book SynopsisThis monograph presents new and elegant proofs of classical results and makes difficult results accessible. The integer programming models known as set packing and set covering have a wide range of applications. Sometimes, owing to the special structure of the constraint matrix, the natural linear programming relaxation yields an optimal solution that is integral, thus solving the problem. Sometimes, both the linear programming relaxation and its dual have integral optimal solutions. Under which conditions do such integrality conditions hold? This question is of both theoretical and practical interest. Min-max theorems, polyhedral combinatorics, and graph theory all come together in this rich area of discrete mathematics. This monograph presents several of these beautiful results as it introduces mathematicians to this active area of research.
£58.05
Analytics Press Show Me the Numbers
Book SynopsisTrade Review"Stephen Few is the master of creating simplicity and meaning through the clear visualization of data. Show Me the Numbers should be required reading for every businessperson, researcher, student, and teacher. A contemporary classic!" --Garr Reynolds, author, Presentation Zen and The Naked Presenter"Not just 'a' book on statistical graphics, it is 'the' book on statistical graphics. No other book has influenced my own view on the visual presentation of quantitative evidence as much as this. A true masterpiece." --Alberto Cairo, author, The Functional Art"If you are looking for practical, easy-to-follow guidelines for presenting numerical data, this is the best book there is. Stephen Few's examples are elegant, and his advice is right on the money." --Colin Ware, professor, University of New Hampshire, and author, Information Visualization: Perception for Design"A must-read for anyone developing reports or dashboards." --Cindi Howson, founder, BI Scorecard, and author, Successful Business Intelligence: Secrets to Making BI a Killer App"With calm clarity and well-crafted examples, Stephen Few explains how to make comprehensible and even compelling tables and graphs. In a world with petabytes of data, compact informative tables and graphs are more important than ever. Their quality is not measured in byte counts, but in insights, deep understandings, and confident decisions. Show Me the Numbers will raise expectations and guide data hackers to become information Rembrandts." --Ben Shneiderman, professor, University of Maryland, and coauthor, Readings in Information Visualization: Using Vision to Think"With this second edition, Show Me the Numbers has been transformed from a practical, engaging, and trustworthy guide for displaying numbers into the most comprehensive reference available for anyone who seeks to present data in enlightening ways, even to those with numberphobia." --Stacey Barr, performance measure specialist"Each concept builds upon the previous in a logical and easy-to-follow sequence, leading the reader steadily through the material, eager to see what is on the next page. In my work with health-care professionals, I list Show Me the Numbers as a must-have for my clients' reference libraries." --Katherine S. Rowell, founder, Katherine S. Rowell & Associates
£35.96
Cambridge University Press Coxeter Bialgebras
Book SynopsisThe goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.Table of ContentsIntroduction; 1. Coxeter groups and reflection arrangements; Part I. Coxeter Species: 2. Coxeter species and Coxeter bimonoids; 3. Basic theory of Coxeter bimonoids; 4. Examples of Coxeter bimonoids; 5. Coxeter operads; 6. Coxeter Lie monoids; 7. Structure theory of Coxeter bimonoids; Part II. Coxeter Spaces: 8. Coxeter spaces and Coxeter bialgebras; 9. Basic theory of Coxeter bialgebras; 10. Examples of Coxeter bialgebras; 11. Coxeter operad algebras; 12. Coxeter Lie algebras; 13. Structure theory of Coxeter bialgebras; Part III. Fock Functors: 14. Fock functors; 15. Coxeter bimonoids and Coxeter bialgebras; 16. Adjoints of Fock functors; 17. Structure theory under Fock functors; 18. Examples of Fock spaces; Appendix A. Category theory; References; List of Notations; List of Tables; List of Figures; List of Summaries; Author Index; Subject Index.
£123.50
Cambridge University Press Equivariant Cohomology in Algebraic Geometry
Book SynopsisIntended 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.Trade Review'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'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&M University'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 WashingtonTable of Contents1. 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.
£47.49
Taylor & Francis Ltd Occultism and the Origins of Psychoanalysis
Book SynopsisOccultism and the Origins of Psychoanalysis traces the origins of key psychoanalytic ideas back to their roots in hypnosis and the occult. Maria Pierri follows Freud’s early interest in ‘thought-transmission’, now known as telepathy. Trade Review"This book gives back to contemporary psychoanalysis the pleasure of exploring really little-known territories, fascinatingly restoring the connection between the past, present and "elsewhere" of communications between human beings, using the Freudian experience as its starting point, in order to reconsider in a reflective way the less visible, sometimes disorienting and mysterious levels of psychoanalytic practice. offers us an especially valuable reflection on the mysterious communicating paths which put individual and group unconsciouses in contact with each other, often bypassing in an apparently disconcerting manner the border controls." - Stefano Bolognini, past President of the IPA and the Italian Psychoanalytic Society"Following the thread of thought-transference, Maria Pierri goes through the events of the Freudian endeavour starting from its roots in hypnosis and occultism, through the dialogue with the masters, the pupils and the great female patients, the leading actresses of the cure. In his disquieting curiosity for telepathy, which he shared intimately with Ferenczi, Freud discovers that fortune-tellers, who do not know the future, can read the unconscious of their clients. But the "golden coin" of occultism, the generative mother-child communication, will be the great discovery of Ferenczi." - Luis J. Martin Cabré, Training analyst, past President Madrid Psychoanalytical Association."Today we know much about the polyphonic complex of contexts, experiences, relationships and ideas which made psychoanalysis possible and still nourish its current debates. We can be very grateful to Maria Pierri for bringing us up to date with the role and meaning of some little-known aspects of Freud’s life and work concerning occultism and the fascinating dialogue of the unconsciouses developed with Ferenczi: what the Author identifies as one of the matrices of the developments of contemporary psychoanalysis." - Marco Conci, MC, IPA Committee on the History of Psychoanalysis"This book gives back to contemporary psychoanalysis the pleasure of exploring really little-known territories, fascinatingly restoring the connection between the past, present and 'elsewhere' of communications between human beings, using the Freudian experience as its starting point, in order to reconsider in a reflective way the less visible, sometimes disorienting and mysterious levels of psychoanalytic practice. It offers us an especially valuable reflection on the mysterious communicating paths which put individual and group unconsciouses in contact with each other, often bypassing in an apparently disconcerting manner the border controls." - Stefano Bolognini, past president of the IPA and the Italian Psychoanalytic Society"Following the thread of thought-transference, Maria Pierri goes through the events of the Freudian endeavour starting from its roots in hypnosis and occultism, through the dialogue with the masters, the pupils and the great female patients, the leading actresses of the cure. In his disquieting curiosity for telepathy, which he shared intimately with Ferenczi, Freud discovers that fortune-tellers, who do not know the future, can read the unconscious of their clients. But the 'golden coin' of occultism, the generative mother-child communication, will be the great discovery of Ferenczi." - Luis J. Martin Cabré, training analyst, past president, Madrid Psychoanalytical Association"Today we know much about the polyphonic complex of contexts, experiences, relationships and ideas which made psychoanalysis possible and still nourish its current debates. We can be very grateful to Maria Pierri for bringing us up to date with the role and meaning of some little-known aspects of Freud’s life and work concerning occultism and the fascinating dialogue of the unconsciouses developed with Ferenczi: what the Author identifies as one of the matrices of the developments of contemporary psychoanalysis." - Marco Conci, MC, IPA Committee on the History of PsychoanalysisTable of ContentsIntroductionStefano BologniniPrologue: a result of character: the cocaine, this magical substance1. Vienna, Porta Orientis of the Unconscious The force of suggestion: the "wonderful somnambulists" HypnosisVienna, laboratory of modernity2. The Young FreudA passionate young researcher into natureFirst love Martha and Bertha: the languages of passion3. The Lesson of Jean Martin Charcot At the SalpêtrièreThe apparatus of language The magic of words4. The lesson of Josef Breuer and the "descent to the mothers"Studies on hysteriaA difficult separation: not all debts can be paidA foundation myth: a false pregnancy and a cure with a defect.5. Sigmund Freud’s lessonThe discovery of a false connection Irma’s throat and the feminine at the origin of psychoanalysis.Dream as desire 6. Fliess and the invention of psychoanalysis A secret correspondence My friend in BerlinFreud’s heart trouble7. The discovery of infantile sexualitySelf-analysis and the writing cure Cherchez la femme: the case of Emma Eckstein8. Original thought requires a ruptureThe "reader of thoughts" The accusation of plagiarism A future in the image of the past: predestination and superstition 9. Occultism made in the USASpiritualism Medium, media, and "mental telegraphy"First hypotheses about the unconscious10 Jung, spiritualism, and countertransference: the world of the deadJung, Poltergeist phenomena, and séances The arrival at Burghölzli First visit to ViennaEaster 1909: Jung’s spiritual complex and Sabina The dangerous fascination of the "beautiful Jewess"11. Ferenczi, the unclassifiableThe sultan and his "clairvoyant" A psychoanalyst "of a restless mind"Ferenczi and the hidden treasure of SpiritualismThe encounter with Freud: a postponed transferential appointment12. A journey to America Three men and an eventful, mutually analytic crossing: the outward journey… … and back again13. The Danaan gift The clairvoyant who reads Ferenczi’s mindThe patient who reads Ferenczi’s mindThe Palermo incident, or the interpretation of paranoiaThe psychic work of the clairvoyant: two unfulfilled prophecies14. An epistolary novelFerenczi and incestuous countertransferential storms: from mother to daughter What is still missing is the fatherly blessing: fatefulness and Oedipal coincidencesElma Pàlos, fragment of the analysis of a seduction The open wound in Ferenczi’s heart, a source of creativity 15. The Saturday goy: getting to know Dr Jones The Welsh liar Difficult beginnings Freud’s first pupil from BritainDr Jones’s stethoscope: rationalisation and censorship of excess countertransferenceA prescribed training analysis in Budapest 16. The intergenerational transmission of psychoanalysis Love and death: the three women of the three pupils"If you go to women, don't forget the whip"At school with Freud: the transmission of psychoanalysis17. The secret committeeThe transformations and the desertion of JungA missed meeting: the "Kreuzlingen gesture" The Committee: the Männerbund and the defence of the "Cause" (Die Sache)Totem and taboo: unconscious intelligence and intergenerational transmission of thought 18. 1913 - the year before the warThe last congress with JungA black tide of occultism The question of telepathyThe dialogues of the unconsciousEpilogue: a fortune-teller visits Freud in BerggasseCorrespondenceIndex
£29.99
CRC Press Introduction to Enumerative and Analytic
Book SynopsisThese award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The authorâs goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares.Updates to the Third Edition include: Quick Check exercises at the end of each section, which are typically easier than the regular exercises at the end of each chapter. A new section discussing the Lagrange Inversion Formula and its applications, strengthening the analytic flavor of the book. A
£80.74
Taylor & Francis Ltd Discrete Mathematics with Coding
Book SynopsisThis book, for a first undergraduate course in Discrete Mathematics, systematically exploits the relationship between discrete mathematics and computer programming. Unlike most discrete mathematics texts focusing on one of the other, the book explores the rich and important connection between these two disciplines and shows how each discipline reinforces and enhances the other.The mathematics in the book is self-contained, requiring only a good background in precalculus and some mathematical maturity. New mathematical topics are introduced as needed.The coding language used is VBA Excel. The language is easy to learn, has intuitive commands, and the reader can develop interesting programs from the outset. Additionally, the spreadsheet platform in Excel makes for convenient and transparent data input and output and provides a powerful venue for complex data manipulation. Manipulating data is greatly simpli?ed using spreadsheet features and visualizing the data can make Table of Contents1. Introduction. 2. VBA Operators. 3. Conditional Statements. 4. Loops, 5. Arrays. 6. String Functions. 7. Grids. 8. Recursion. 9. Charts and Graphs, 10. Random Numbers. 11. Linear Equations. 12. Linear Programming. 13. Matrix Algebra. 14. Determinants. 15. Propositional Logic. 16. Switching Circuits. 17. Gates and Logic Circuits. 18. Sets. 19. Counting. 20. Probability. 21. Random Variables. 22. Markov Chains. 23. Divisibility and Prime Numbers. 24. Congruence. 25. The Enigma Machine. 26. Large Numbers.
£87.39
CRC Press Introduction to Number Theory
Book SynopsisIntroduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbertâs tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Eulerâs theorem in RSA encryption, and quadratic residues in the construction of tournaments. Ideal for a one- or two-semester undergraduate-level course, this Second Edition: Features a more flexible structure that offers a greater range of options for course design Adds new sections on the representations of integ
£54.14
Cambridge University Press Finite Geometry and Combinatorial Applications 82 London Mathematical Society Student Texts Series Number 82
Book SynopsisThe projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to these geometries and their many applications to other areas of combinatorics. Coverage includes a detailed treatment of the forbidden subgraph problem from a geometrical point of view, and a chapter on maximum distance separable codes, which includes a proof that such codes over prime fields are short. The author also provides more than 100 exercises (complete with detailed solutions), which show the diversity of applications of finite fields and their geometries. Finite Geometry and Combinatorial Applications is ideal for anyone, from a third-year undergraduate to a researcher, who wishes to familiarise themselves with and gain an appreciation of finite geometry.Table of Contents1. Fields; 2. Vector spaces; 3. Forms; 4. Geometries; 5. Combinatorial applications; 6. The forbidden subgraph problem; 7. MDS codes; Appendix A. Solutions to the exercises; Appendix B. Additional proofs; Appendix C. Notes and references; References; Index.
£133.95
Cambridge University Press Networks of Networks in Biology
Book SynopsisBiological systems are extremely complex and have emergent properties that cannot be explained or even predicted by studying their individual parts in isolation. The reductionist approach, although successful in the early days of molecular biology, underestimates this complexity. As the amount of available data grows, so it will become increasingly important to be able to analyse and integrate these large data sets. This book introduces novel approaches and solutions to the Big Data problem in biomedicine, and presents new techniques in the field of graph theory for handling and processing multi-type large data sets. By discussing cutting-edge problems and techniques, researchers from a wide range of fields will be able to gain insights for exploiting big heterogonous data in the life sciences through the concept of ''network of networks''.Trade Review'… Networks of Networks in Biology should be of interest and a good introductory resource for molecular biologists, cell biologists, and biochemists, as well as bioinformaticians not yet acquainted with multilayer networks.' Ingo Brigandt, Quarterly Review of BiologyTable of ContentsPreface; Part I. Networks in Biology: 1. An Introduction to Biological Networks Nuria Planell, Xabier Martinez de Morentin and David Gomez-Cabrero; 2. Graph Theory Akram Dehnokhalaji and Nasim Nasrabadi; Part II. Network Analysis: 3. Structural Analysis of Biological Networks Narsis A. Kiani and Mikko Kivelä; 4. Networks From an Information-Theoretic and Algorithmic Complexity Perspective Hector Zenil and Narsis A. Kiani; 5. Integration and Feature Identification in Multi-layer Network using a Heat Diffusion Approach Gordon Ball and Jesper Tegnér; Part III. Multi-layer Networks: 6. Large Multiplex Networks Ginestra Bianconi; 7. Large Existing Tools for Analysis of Multilayer Networks Manlio De Domenico and Massimo Stella; 8. Large Dynamics on Multilayer Networks Manlio De Domenico and Massimo Stella; Part IV. Applications: 9. The Network of Networks Involved in Human Disease Celine Sin and Jörg Menche; 10. Towards a Multi-Layer Network Analysis of Disease: Challenges and Opportunities Through the Lens of Multiple Sclerosis Jesper Tegnér, Ingrid Kockum, Mika Gustafsson and David Gomez-Cabrero; 11. Microbiome: A Multi-Layer Network View Is Required Rodrigo Bacigalupe, Saeed Shoai and David Gomez-Cabrero; Part V. Conclusion : Concluding Remarks: Open Questions and Challenges Ginestra Bianconi, David Gomez-Cabrero, Jesper Tegnér and Narsis A. Kiani; Index.
£47.49
Cambridge University Press Deep Learning on Graphs
Book SynopsisDeep learning on graphs has become one of the hottest topics in machine learning. The book consists of four parts to best accommodate our readers with diverse backgrounds and purposes of reading. Part 1 introduces basic concepts of graphs and deep learning; Part 2 discusses the most established methods from the basic to advanced settings; Part 3 presents the most typical applications including natural language processing, computer vision, data mining, biochemistry and healthcare; and Part 4 describes advances of methods and applications that tend to be important and promising for future research. The book is self-contained, making it accessible to a broader range of readers including (1) senior undergraduate and graduate students; (2) practitioners and project managers who want to adopt graph neural networks into their products and platforms; and (3) researchers without a computer science background who want to use graph neural networks to advance their disciplines.Trade Review'This timely book covers a combination of two active research areas in AI: deep learning and graphs. It serves the pressing need for researchers, practitioners, and students to learn these concepts and algorithms, and apply them in solving real-world problems. Both authors are world-leading experts in this emerging area.' Huan Liu, Arizona State University'Deep learning on graphs is an emerging and important area of research. This book by Yao Ma and Jiliang Tang covers not only the foundations, but also the frontiers and applications of graph deep learning. This is a must-read for anyone considering diving into this fascinating area.' Shuiwang Ji, Texas A&M University'The first textbook of Deep Learning on Graphs, with systematic, comprehensive and up-to-date coverage of graph neural networks, autoencoder on graphs, and their applications in natural language processing, computer vision, data mining, biochemistry and healthcare. A valuable book for anyone to learn this hot theme!' Jiawei Han, University of Illinois at Urbana-Champaign'This book systematically covers the foundations, methodologies, and applications of deep learning on graphs. Especially, it comprehensively introduces graph neural networks and their recent advances. This book is self-contained and nicely structured and thus suitable for readers with different purposes. I highly recommend those who want to conduct research in this area or deploy graph deep learning techniques in practice to read this book.' Charu Aggarwal, Distinguished Research Staff Member at IBM and recipient of the W. Wallace McDowell AwardTable of Contents1. Deep Learning on Graphs: An Introduction; 2. Foundation of Graphs; 3. Foundation of Deep Learning; 4. Graph Embedding; 5. Graph Neural Networks; 6. Robust Graph Neural Networks; 7. Scalable Graph Neural Networks; 8. Graph Neural Networks for Complex Graphs; 9. Beyond GNNs: More Deep Models for Graphs; 10. Graph Neural Networks in Natural Language Processing; 11. Graph Neural Networks in Computer Vision; 12. Graph Neural Networks in Data Mining; 13. Graph Neural Networks in Biochemistry and Healthcare; 14. Advanced Topics in Graph Neural Networks; 15. Advanced Applications in Graph Neural Networks.
£44.64
Cambridge University Press The Discrete Mathematical Charms of Paul Erdos
Book SynopsisPaul Erdos published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdos, along with his brilliant ways of working toward their answers. It includes young Erdos''s proof of Bertrand''s postulate, the Erdos-Szekeres Happy End Theorem, De Bruijn-Erdos theorem, Erdos-Rado delta-systems, Erdos-Ko-Rado theorem, Erdos-Stone theorem, the Erdos-Rényi-Sós Friendship Theorem, Erdos-Rényi random graphs, the Chvátal-Erdos theorem on Hamilton cycles, and other results of Erdos, as well as results related to his work, such as Ramsey''s theorem or Deza''s theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal aneTrade Review'Vašek Chvátal was born to write this one-of-a-kind book. Readers cannot help but be captivated by the evident love with which every page has been written. The human side of mathematics is intertwined beautifully with first-rate exposition of first-rate results.' Donald Knuth, Stanford University'This book is a treasure trove from so many viewpoints. It is a wonderful introduction and an alluring invitation to discrete mathematics - now a central field of mathematics identified mostly with the hero of this book. With lucid, carefully planned chapters on different topics it demonstrates the unique way in which Paul Erdős, one of the most prolific and influential mathematicians of the twentieth century, invented and approached problems. Sprinkled with historical and personal anecdotes and pictures, it opens a window to the unique personality of 'Uncle Paul'. And implicitly, it reveals the charming and candid way in which Vašek Chvátal, an authority in the field and a lifelong friend and collaborator of Erdős, likes to combine teaching and story-telling.' Avi Wigderson, IAS, Princeton'Paul Erdős is one of the founding fathers of modern combinatorics, whose ability to pose beautiful problems greatly determined the development of this field and influenced many other areas of mathematics. This book uses some basic questions, which intrigued Paul Erdős, to give a nice introduction to many topics in discrete mathematics. It contains a collection of beautiful results, covering such diverse subjects as discrete geometry, Ramsey theory, graph colorings, extremal problems for graphs and set systems and some others. It presents many elegant proofs and exposes the reader to various powerful combinatorial techniques.' Benjamin Sudakov, ETH Zurich'This is a brilliant book. It manages in one fell swoop to survey and develop a large part of combinatorial mathematics while at the same time chronicling the work of Paul Erdős. His contributions to different areas of mathematics are seen here to be part of a coherent whole. Chvátal's presentation is particularly appealing and accessible. The wonderful personal recollections add to the mathematical content to provide a portrait of Erdős' mind recognizable to those who knew him.' Bruce Rothschild, University of California, Los Angeles'Vašek Chvátal's book is a gem. Paul Erdős' favorite problems and best work are beautifully laid out. Readers unfamiliar with Erdős' work cannot fail to appreciate its power and elegance, and those who have seen bits and pieces will have the pleasure of seeing it thoughtfully and lovingly presented by a master. It's hard to imagine now, but there was a time when combinatorics was thought to be a jumble of results without depth or coherence. 'Uncle' Paul understood its heart and soul, and nowhere is this more evident than in Chvátal's wonderful compendium. This volume belongs on every math-lover's night-table!' Peter Winkler, Dartmouth College'Beautiful mathematics is presented with great care and clarity in Vašek Chvátal's book, complemented with well-written anecdotes and personal reminiscences about Paul Erdős. This combination makes the book a very enjoyable reading and a lively tribute to the memory of one of the most prolific mathematicians of all time. Studying discrete mathematics from this book is likely to give a great experience to students and established researchers alike.' Gábor Simonyi, Rényi Institute, Budapest'… Chvátal (emer., Concordia Univ.) has created a gem in this work and deserves congratulation … Highly recommended.' J. Johnson, Choice Magazine'This wonderfully written book is undoubtedly a significant contribution to the growing body of literature on the various developments in discrete mathematics over the last several decades. Still, to reduce it to only its mathematical dimension would be an act of injustice not only towards the book but also towards its author. The book is a powerful homage to Paul Erdos as one of the leading mathematicians of the twentieth century as well as a person who, with his unprecedented level of academic generosity and overall human kindness, was one of the pillars of the discrete mathematics community during his lifetime.' Veselin Jungic, MathSciNetTable of ContentsForeword; Preface; Acknowledgments; Introduction; 1. A glorious beginning – Bertrand's postulate; 2. Discrete geometry and spinoffs; 3. Ramsey's theorem; 4. Delta-systems; 5. Extremal set theory; 6. Van der Waerden's theorem; 7. Extremal graph theory; 8. The friendship theorem; 9. Chromatic number; 10. Thresholds of graph properties ; 11. Hamilton cycles; Appendix A. A few tricks of the trade; Appendix B. Definitions, terminology, notation; Appendix C. More on Erdős; References; Index.
£23.74
John Wiley & Sons Inc Graphs and Networks
Book SynopsisGraphs and Networks A unique blend of graph theory and network science for mathematicians and data science professionals alike. Featuring topics such as minors, connectomes, trees, distance, spectral graph theory, similarity, centrality, small-world networks, scale-free networks, graph algorithms, Eulerian circuits, Hamiltonian cycles, coloring, higher connectivity, planar graphs, flows, matchings, and coverings, Graphs and Networks contains modern applications for graph theorists and a host of useful theorems for network scientists. The book begins with applications to biology and the social and political sciences and gradually takes a more theoretical direction toward graph structure theory and combinatorial optimization. A background in linear algebra, probability, and statistics provides the proper frame of reference. Graphs and Networks also features: Applications to neuroscience, climate science, and the social and political sciencesA research outlook integrated directly into tTable of ContentsList of Figures iv Preface viii Chapter 1. From Königsberg to Connectomes 1 1.1. Introduction 1 1.2. Isomorphism 18 1.3. Minors and Constructions 25 Chapter 2. Fundamental Topics 39 2.1. Trees 39 2.2. Distance 44 2.3. Degree Sequences 52 2.4. Matrices 56 Chapter 3. Similarity and Centrality 70 3.1. Similarity Measures 70 3.2. Centrality Measures 74 3.3. Eigenvector and Katz Centrality 78 3.4. PageRank 84 Chapter 4. Types of Networks 91 4.1. Small-World Networks 91 4.2. Scale-Free Networks 95 4.3. Assortative Mixing 97 4.4. Covert Networks 102 Chapter 5. Graph Algorithms 107 5.1. Traversal Algorithms 107 5.2. Greedy Algorithms 113 5.3. Shortest Path Algorithms 118 Chapter 6. Structure, Coloring, Higher Connectivity 126 6.1. Eulerian Circuits 126 6.2. Hamiltonian Cycles 131 6.3. Coloring 136 6.4. Higher Connectivity 142 6.5. Menger's Theorem 148 Chapter 7. Planar Graphs 159 7.1. Properties of Planar Graphs 159 7.2. Euclid's Theorem on Regular Polyhedra 167 7.3. The Five Color Theorem 172 7.4. Invariants for Non-Planar Graphs 174 Chapter 8. Flows and Matchings 182 8.1. Flows in Networks 182 8.2. Stable Sets, Matchings, Coverings 188 8.3. Min-Max Theorems 192 8.4. Maximum Matching Algorithm 196 Appendix A. Linear Algebra 211 Appendix B. Probability and Statistics 215 Appendix C. Complexity of Algorithms 218 Appendix D. Stacks and Queues 222 Appendix. Bibliography 226
£77.36
Taylor & Francis Ltd Discrete Problems in Nature Inspired Algorithms
Book SynopsisThis book includes introduction of several algorithms which are exclusively for graph based problems, namely combinatorial optimization problems, path formation problems, etc. Each chapter includes the introduction of the basic traditional nature inspired algorithm and discussion of the modified version for discrete algorithms including problems pertaining to discussed algorithms. Trade Review"Each chapter includes detailed problem formulation, practical examples, flowcharts illustrating special algorithms, questions and solved exercises which reinforce important topics. Besides being very useful to those who are interested in discrete optimizations problems and applying various metaheuristics to them, involved reader can also benefit from the easy way it presents various ideas and approaches to problem solutions. It is written in a clean and easily understandable, but still highly scientific language and it is a beneficial reading for post-docs and researchers interested in metaheuristic approaches to graph-based discrete optimization problems."—Zentralblatt MATHTable of Contents1. Introduction to Optimization Problems 2. Particle Swarm Optimization 3. Genetic Algorithms 4. Ant Colony Optimization 5. Bat Algorithm 6. Cuckoo Search Algorithm 7. Artificial Bee Colony 8. Shuffled Frog Leap Algorithm 9. Brain Storm Swarm Optimization Algorithm 10. Intelligent Water Drop Algorithm 11. Egyptian Vulture Algorithm 12. Biogeography-Based Optimization 13. Invasive Weed Optimization 14. Glowworm Swarm Optimization 15. Bacteria Foraging Optimization Algorithm 16. Flower Pollination Algorithm
£87.39
Taylor & Francis Ltd Analytic Combinatorics
Book Synopsis Analytic Combinatorics: A Multidimensional Approach is written in a reader-friendly fashion to better facilitate the understanding of the subject. Naturally, it is a firm introduction to the concept of analytic combinatorics and is a valuable tool to help readers better understand the structure and large-scale behavior of discrete objects. Primarily, the textbook is a gateway to the interactions between complex analysis and combinatorics. The study will lead readers through connections to number theory, algebraic geometry, probability and formal language theory. The textbook starts by discussing objects that can be enumerated using generating functions, such as tree classes and lattice walks. It also introduces multivariate generating functions including the topics of the kernel method, and diagonal constructions. The second part explains methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such aTable of ContentsA Primer on Combinatorical CalculusCombinatorical ParametersDerived and Transcendental ClassesGenerating Functions as Analytic ObjectsParallel TaxonomiesSingularities of Multvariable Rational FunctionsIntegration and Multivariable Coefficient AsymptoticsMultiple PointsPartitionsBibliographyGlossaryIndex
£80.74
Precalculus
Book SynopsisYear after year, PRECALCULUS: FUNCTIONS AND GRAPHS leads the way in helping students like you succeed in their Precalculus courses. Its clear explanations and examples and exercises featuring a variety of real-life applications make the content understandable and relatable. This 13th edition of Swokowski and Cole's bestselling text is consistently praised for being at just the right level for Precalculus students. Perhaps most important, this book effectively prepares readers for further courses in mathematics.Table of Contents1. TOPICS FROM ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Equations. Complex Numbers. Inequalities. 2. FUNCTIONS AND GRAPHS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Polynomial Functions of Degree Greater Than 2. Properties of Division. Zeros of Polynomials. Complex and Rational Zeros of Polynomials. Rational Functions. Variation. 4. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. 5. TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of the Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems. 6. ANALYTIC TRIGONOMETRY. Verifying Trigonometric Identities. Trigonometric Equations. The Additions and Subtraction of Formulas. Multiple-Angle Formulas. Product-To-Sum and Sum-To-Product Formulas. The Inverse Trigonometric Functions. 7. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Vectors. The Dot Product. Trigonometric Form for Complex Numbers. De Moivre���s Theorem and nth Roots of Complex Numbers. 8. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More Than Two Variables. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions. 9. SEQUENCES, SERIES, AND PROBABILITY. Infinite Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Permutations. Distinguishable Permutations and Combinations. Probability. 10. TOPICS FROM ANALYTICAL GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. 11. LIMITS OF FUNCTIONS. Introductions to Limits. Definition of a Limit. Techniques for Finding Limits. Limits Involving Infinity. Appendix I: Common Graphs and Their Equations. Appendix II: A Summary of Graph Transformations. Appendix III: Graphs of the Trigonometric Functions and Their Inverses. Appendix IV: Values of the Trigonometric Functions of Special Angles on a Unit Circle. Appendix V: Theorems on Limits.
£260.68
Taylor & Francis Ltd Combinatorial Pattern Matching Algorithms in
Book SynopsisEmphasizing the search for patterns within and between biological sequences, trees, and graphs, Combinatorial Pattern Matching Algorithms in Computational Biology Using Perl and R 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. The 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 strTrade ReviewI 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.—Anthony Labarre, SIGACT News, July 2012This text provides a solid foundation to the field. It will work as a practical handbook for pattern matching applications in computational biology. —Michael Goldberg, Computing Reviews, February 2010… 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. …—Ernesto D’Avanzo, Computing Reviews, February 2010… 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. …—Jannik Pewny, IACR Book Reviews, 2009…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.—Michael Levitt, Professor and Chair, Department of Structural Biology, Stanford University, California, USA…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.—From the Foreword, Alberto Apostolico, Professor, College of Computing, Georgia Tech, Atlanta, USAUnlocks 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.—Steven Skiena, Professor, Department of Computer Science, Stony Brook University, New York, USAI 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.—Anthony Labarre, SIGACT News, July 2012This text provides a solid foundation to the field. It will work as a practical handbook for pattern matching applications in computational biology. —Michael Goldberg, Computing Reviews, February 2010… 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. …—Ernesto D’Avanzo, Computing Reviews, February 2010… 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. …—Jannik Pewny, IACR Book Reviews, 2009…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.—Michael Levitt, Professor and Chair, Department of Structural Biology, Stanford University, California, USA…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.—From the Foreword, Alberto Apostolico, Professor, College of Computing, Georgia Tech, Atlanta, USAUnlocks 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.—Steven Skiena, Professor, Department of Computer Science, Stony Brook University, New York, USATable of ContentsIntroduction. 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.
£180.50
Barcharts, Inc Math Common Core For Kindergarten
Book SynopsisParents and teachers can use this laminated 6-page guide with their kindergartener to hit specific learning requirements of The Common Core State Standards for Mathematics. These expectations and skills are the stepping stones needed to succeed in school, college and the real world. Each guide in the series focuses on critical areas of the curriculum and features real-world problems, examples and illustrations, with parent and teacher guidance built in. Suggested uses: o Teacher/Parent â use as a quick way to review all of the standards for kindergarten, with or without guiding the student through the material o Student â you can spill anything you want on this and it will be ok, it's laminated so you can eat your lunch off it or use playdough on it
£6.00
Taylor & Francis Inc Physician Integration Alignment
Book SynopsisToday, with physician and hospital reimbursement being cut and tied to quality incentives, physicians and health plans are revisiting the concept of integration. Payers are demanding that the industry do more with less without sacrificing quality of care. As a result, physicians again find themselves integrating and aligning with hospitals that have the resources they lack or must develop together.Written by an acknowledged expert in the field of physician integration and managed care contracting, Physician Integration & Alignment: IPA, PHO, ACOs, and Beyond examines physician integration and alignment in the current healthcare market. It outlines the common characteristics of integrated groups and various organizational structures, and also explains how you can avoid making the same mistakes of the past. Filled with suggestions and ideas from successfully integrated practices, the book:Identifies industry drivers for the resurgence of intTable of Contents1994: The Initial Wave. Why Do It Again: The Drivers of the New Wave. Common Characteristics of Integrated Groups. Elements of Design for the New Integrated Networks. Avoiding the Mistakes of the Past. Antitrust and Other Regulatory Concerns. Options and More Options. A Checklist for the Design Process. Index
£68.39
Taylor & Francis Inc Handbook of Graph Theory
Book SynopsisIn the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second editionover 400 pages longer than its predecessorincorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation.With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick aTrade ReviewPraise for the First Edition:… a fine guide to various literatures, especially for topics like Ramsey theory … . Many first-rate mathematicians have contributed, making the exposition's quality high overall. …. Highly recommended.—CHOICE, January 2005, Vol. 42, No. 05Praise for the First Edition:… a fine guide to various literatures, especially for topics like Ramsey theory … . Many first-rate mathematicians have contributed, making the exposition's quality high overall. …. Highly recommended.—CHOICE, January 2005, Vol. 42, No. 05Table of ContentsIntroduction to Graphs. Graph Representation. Directed Graphs. Connectivity and Traversability. Colorings and Related Topics. Algebraic Graph Theory. Topological Graph Theory. Analytic Graph Theory. Graphical Measurement. Graphs in Computer Science. Networks and Flows. Communication Networks. Natural Science and Processes. Index.
£194.75
MP-AMM American Mathematical Asymptopia
Book SynopsisTrade ReviewThe style and the beauty make this book an excellent reading. Keep it on your coffee table or/and bed table and open it often, Asymptopia is a fascinating place." - Péter Hajnal, ACTA Sci. Math.Table of Contents An infinity of primes Stirling's formula Big Oh, little Oh and all that Integration in Asymptopia From integrals to sums Asymptotics of binomial coefficients (n k ) Unicyclic graphs Ramsey numbers Large deviations Primes Asymptotic geometry Algorithms Potpourri Really Big Numbers! Bibliography Index
£47.70
MP-AMM American Mathematical A Unified Approach to Structural Limits and Limits of Graphs with Bounded TreeDepth
Book SynopsisIntroduces a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases'' of a general theory.Table of Contents Introduction General theory Modelings for sparse structures Limits of graphs with bounded tree-depth Concluding remarks.
£67.50
MP-AMM American Mathematical Introduction to Analysis on Graphs
Book SynopsisExplores the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk on finite graphs.Table of Contents The Laplace operator on graphs Spectral properties of the Laplace operator Geometric bounds for the eigenvalues Eigenvalues on infinite graphs Estimates of the heat kernel The type problem Exercises Bibliography Index
£55.80
American Mathematical Society Graph Theory
Book SynopsisPresents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems intended to be used as homework assignments.Trade ReviewThis work could be the basis for a very nice one-semester ""transition"" course in which students evolve from users of theorems to creators of proofs. With their intuitive appeal and pictorial representations, graphs may be a better basis than analysis and limits for such a transtion."" - Choice
£59.40
American Mathematical Society DavenportZannier Polynomials and Dessins dEnfants
Book SynopsisThe polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.Table of Contents Introduction. Dessins d'enfants: From polynomials through Belyi functions to weighted trees. Existence theorem. Recapitulation and perspective. Classification of unitrees. Computation of Davenport-Zannier pairs for unitrees. Primitive monodromy groups of weighted trees. Trees with primitive monodromy groups. A zoo of examples and constructions. Diophantine invariants. Enumeration. What remains to be done. Bibliography. Index.
£115.60
MP-AMM American Mathematical Conversational Problem Solving
Book SynopsisPresents a dialogue between a professor and eight students in a summer problem solving camp and allows for a conversational approach to the problems as well as some mathematical humour and a few non-mathematical digressions. The problems have been selected for their entertainment value, elegance, trickiness, and unexpectedness.Table of Contents The first day Polynomials Base mathematics A mysterious visitor Set theory Triangles Independence day Independence aftermath Amanda An aesthetical error Miraculous cancellation Probability theory Geometry Hodegepodge Self-referential mathematics All good things must come to an end Bibliography Index.
£39.56
MP-AMM American Mathematical The Unity of Combinatorics
Book SynopsisTopics covered include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable.Table of Contents Introduction Blocks, sequences, bow ties, and worms Combinatorial games Fibonacci, Pascal, and Catalan Catwalks, sandsteps, and Pascal pyramids Unique rook circuits Sums, colorings, squared squares, and packings Difference sets and combinatorial designs Geometric connections The groups $PSL(2,7)$ and $GL(3,2)$ and why they are isomorphic Incidence matrices, codes, and sphere packings Kirkman's Schoolgirls, fields, spreads, and hats $(7,3,1)$ and combinatorics $(7,3,1)$ and normed algebras $(7,3,1)$ and matroids Coin turning games and Mock Turtles The $(11,5,2)$ biplane, codes, designs, and groups Rick's Tricky Six Puzzle: More than meets the eye $S(5,8,24)$ The miracle octad generator Bibliography Index
£51.30
MP-AMM American Mathematical Inverse Problems and Zero Forcing for Graphs
Book SynopsisProvides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to a rich set of deep problems in that area as well as a breadth of ‘ancillary’ problems in related areas.Table of Contents Introduction to the inverse eigenvalue problem of a graph and zero forcing: Introduction to an motivation for the IEP-$G$ Zero forcing and maximum eigenvalue multiplicity Strong properties, theory, and consequences: Implicit function theorem and strong properties Consequences of the strong properties Theoretical underpinnings of the strong properties Further discussion of ancillary problems: Ordered multiplicity lists of a graph Rigid linkages Minimum number of district eigenvalues Zero forcing, propagation time, and throttling: Zero forcing, variants, and related parameters Propagation time and capture time Throttling Appendix A. Graph terminology and notation Bibliography Index
£98.10
MP-AMM American Mathematical An Introductory Course on Mathematical Game
Book SynopsisAn introductory and up-to-date course on game theory for mathematicians, economists and other scientists with a basic mathematical background. This self-contained book provides a formal description of classic game-theoretic concepts alongside rigorous proofs and illustrates the theory through abundant examples, applications, and exercises.Table of Contents Introduction to decision theory Strategic games Extensive games Games with incomplete information Fundamentals of cooperative games Applications of cooperative games Bibliography Notations Index Index of solution concepts Subject Index
£106.20
American Mathematical Society Topological and Ergodic Theory of Symbolic
Book SynopsisIntroduces symbolic dynamics from a perspective of topological dynamical systems. After introducing symbolic and topological dynamics, the core of the book consists of discussions of subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and the ergodic properties of these systems.Table of Contents First examples and general properties of subshifts Topological dynamics Subshifts of positive entropy Subshifts of zero entropy Further minimal Cantor systems Methods from ergodic theory Automata and linguistic complexity Miscellaneous background topics Solutions to exercises Bibliography Index
£67.45
American Mathematical Society Numbers and Figures
Book SynopsisOne of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking about several topics in elementary number theory and some of their connections to geometry, calculus, and real-life problems such as COVID-19 vaccines.Table of Contents Integer points, polygons, and polyhedra Simpson's paradox, Farey sequences, and Diophantine approximation A coin problem and generating functions Pythagorean triples and sums of squares Benford's law, uniform distribution and normal numbers Sums and integrals Index
£46.80
MP-AMM American Mathematical Combinatorics A Guided Tour
Book SynopsisCombinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Polya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.Trade ReviewThis is a well-written, reader-friendly, and self-contained undergraduate course on combinatorics, focusing on enumeration. The book includes plenty of exercises, and about half of them come with hints."" - M. Bona, Choice Magazine""The delineation of the topics is first rate-better than I have ever seen in any other book. ... CAGT has both good breadth and great presentation; it is in fact a new standard in presentation for combinatorics, essential as a resource for any instructor, including those teaching out of a different text. For the student: If you are just starting to build a library in combinatorics, this should be your first book."" - The UMAP Journal""... [This book] is an excellent candidate for a special topics course for mathematics majors; with the broad spectrum of applications that course can simultaneously be an advanced and a capstone course. This book would be an excellent selection for the textbook of such a course. ... This book is the best candidate for a textbook in combinatorics that I have encountered."" - Charles Ashbacher
£60.30
MP-AMM American Mathematical An Introductory Course on Mathematical Game
Book SynopsisPresents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field.Table of Contents Introduction to decision theory Strategic games Extensive games Games with incomplete information Fundamentals of cooperative games Applications of cooperative games Bibliography Notations Index Index of solution concepts Subject index.
£71.10
CRC Press Introduction to Number Theory
Book SynopsisIntroduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbertâs tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Eulerâs theorem in RSA encryption, and quadratic residues in the construction of tournaments. Ideal for a one- or two-semester undergraduate-level course, this Second Edition: Features a more flexible structure that offers a greater range of options for course design Adds new sections on the representations of integTrade ReviewPraise for the Previous Edition "The authors succeed in presenting the topics of number theory in a very easy and natural way, and the presence of interesting anecdotes, applications, and recent problems alongside the obvious mathematical rigor makes the book even more appealing. … a valid and flexible textbook for any undergraduate number theory course."—International Association for Cryptologic Research Book Reviews, May 2011 "… a welcome addition to the stable of elementary number theory works for all good undergraduate libraries."—J. McCleary, Vassar College, Poughkeepsie, New York, USA, from CHOICE, Vol. 46, No. 1, August 2009 "… a reader-friendly text. … provides all of the tools to achieve a solid foundation in number theory."—L’Enseignement Mathématique, Vol. 54, No. 2, 2008 The theory of numbers is a core subject of mathematics. The authors have written a solid update to the first edition (CH, Aug'09, 46-6857) of this classic topic. There is no shortage of introductions to number theory, and this book does not offer significantly different information. Nonetheless, the authors manage to give the subject a fresh, new feel. The writing style is simple, clear, and easy to follow for standard readers. The book contains all the essential topics of a first-semester course and enough advanced topics to fill a second. In particular, it includes several modern aspects of number theory, which are often ignored in other texts, such as the use of factoring in computer security, searching for large prime numbers, and connections to other branches of mathematics. Each section contains supplementary homework exercises of various difficulties, a crucial ingredient of any good textbook. Finally, much emphasis is placed on calculating with computers, a staple of modern number theory. Overall, this title should be considered by any student or professor seeking an excellent text on the subject. --A. Misseldine, Southern Utah University, Choice magazine 2016 Praise for the Previous Edition "The authors succeed in presenting the topics of number theory in a very easy and natural way, and the presence of interesting anecdotes, applications, and recent problems alongside the obvious mathematical rigor makes the book even more appealing. … a valid and flexible textbook for any undergraduate number theory course."—International Association for Cryptologic Research Book Reviews, May 2011 "… a welcome addition to the stable of elementary number theory works for all good undergraduate libraries."—J. McCleary, Vassar College, Poughkeepsie, New York, USA, from CHOICE, Vol. 46, No. 1, August 2009 "… a reader-friendly text. … provides all of the tools to achieve a solid foundation in number theory."—L’Enseignement Mathématique, Vol. 54, No. 2, 2008 The theory of numbers is a core subject of mathematics. The authors have written a solid update to the first edition (CH, Aug'09, 46-6857) of this classic topic. There is no shortage of introductions to number theory, and this book does not offer significantly different information. Nonetheless, the authors manage to give the subject a fresh, new feel. The writing style is simple, clear, and easy to follow for standard readers. The book contains all the essential topics of a first-semester course and enough advanced topics to fill a second. In particular, it includes several modern aspects of number theory, which are often ignored in other texts, such as the use of factoring in computer security, searching for large prime numbers, and connections to other branches of mathematics. Each section contains supplementary homework exercises of various difficulties, a crucial ingredient of any good textbook. Finally, much emphasis is placed on calculating with computers, a staple of modern number theory. Overall, this title should be considered by any student or professor seeking an excellent text on the subject. --A. Misseldine, Southern Utah University, Choice magazine 2016 Table of ContentsIntroduction. Divisibility. Greatest Common Divisor. Primes. Congruences. Special Congruences. Primitive Roots. Cryptography. Quadratic Residues. Applications of Quadratic Residues. Sums of Squares. Further Topics in Diophantine Equations. Continued Fractions. Continued Fraction Expansions of Quadratic Irrationals. Arithmetic Functions. Large Primes. Analytic Number Theory. Elliptic Curves.
£92.14
Taylor & Francis Inc Buildings and Schubert Schemes
Book SynopsisThe 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.Table of ContentsGrassmannians 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.
£175.75
Charlesbridge Publishing,U.S. Show and Tell! Great Graphs and Smart Charts: An
Book SynopsisA visual-learning expert races up the charts and graphs math success with kid-friendly content sure to help with homework.Want to find the most popular meal in the cafeteria? Compare town sports enrollments? Or maybe you just want to know who burps the most in your family! Learn what line graphs, bar graphs, pie charts, and pictographs are and how and when to use them to represent data. Each project shows how to build a chart or graph and ties it all together with a creative infographic that really puts the A in STEAM (Science, Technology, Engineering, ARTS, and Mathematics). Whether used as an introductory aid or to underscore previous knowledge, the book prepares today''s visually savvy children to succeed in school and life by analyzing the world around them.
£15.29
Taylor & Francis Inc Handbook of Graph Drawing and Visualization
Book SynopsisGet an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and ApplicationsThe Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, science, and engineering. Each chapter is self-contained and includes extensive references.The first several chapters of the book deal with fundamental topological and geometric concepts and techniques used in graph drawing, such as planarity testing and embedding, crossings and planarization, symmetric drawings, and proximity drawings. The following chapters present a large collection of algorithms for constructing drawings of graphs, including tree, planar straight-line, planar orthogonal and polyline, spine and radial, circular, rectangular, hierarchical, and three-dimensional drawings as well as labeling algorithms, simultaneous embeddings, and force-directed methods. The book then introduces the GraphML language for representing graphs and their drawings and describes three software systems for constructing drawings of graphs: OGDF, GDToolkit, and PIGALE. The final chapters illustrate the use of graph drawing methods in visualization applications for biological networks, computer security, data analytics, education, computer networks, and social networks.Edited by a pioneer in graph drawing and with contributions from leaders in the graph drawing research community, this handbook shows how graph drawing and visualization can be applied in the physical, life, and social sciences. Whether you are a mathematics researcher, IT practitioner, or software developer, the book will help you understand graph drawing methods and graph visualization systems, use graph drawing techniques in your research, and incorporate graph drawing solutions in your products.Trade Review"In the topological and geometric foundations to graph drawing, this collection goes beyond defining planarity or even minimizing edge crossings, discussing also spine, radial, circular, tree, and rectangular drawing definitions and algorithms. There is much content on formally defining and approaching such subjective and even aesthetic areas as legibility in name placement and labeling, as well as maximizing pleasing symmetries and other methods related to edge lengths and linearity that research has shown to impart information to humans effectively. Many chapters touch on history and open problems in this well-arranged compendium weighted toward content ripe for practical implementation."—Tom Schulte, MAA Reviews, February 2014"This handbook fills an important need. It is an impressive compendium of research in the booming field of graph drawing and visualization: algorithms, layout strategies, and software for diverse problem domains. It’s great to have all these resources in one place, showing the vibrant activity in graph drawing and visualization. The book lays a foundation for the next generation of research breakthroughs. Whether you drill down or go wide, you’ll learn something useful. You’ll see how effectively designed network visualizations can produce powerful insights in many fields."—Prof. Ben Shneiderman, University of Maryland"This handbook is the most comprehensive reference on graph drawing I have ever seen. It is an indispensable aid to programmers, engineers, students, teachers, and researchers who create or use algorithms and systems for visualizing networks and abstract graphs. It covers the theory and practice in core topics and related areas, such as labeling, programming frameworks, and applications in network analysis. It’s an amazing compendium of almost everything known about practical graph drawing."—Stephen North, Executive Director and Co-Founder of graphviz.org"After two decades of annual graph drawing conferences, the field is sufficiently developed to warrant this nearly 900-page Handbook. All constituencies are well-served. New researchers can become quickly oriented to the field through the opening foundational chapters. Practitioners can find algorithms to suit their needs in the heart of the handbook: ten chapters on a wealth of algorithms, usefully organized into intuitive categories: from planar algorithms to three-dimensional drawings, passing through the natural restrictions—radial, rectangular, circular, polyline—and from hierarchical to force-directed.Many algorithms are now incorporated into graph-drawing software packages, and all the major packages are described in chapters by their developers. The key application areas are surveyed, some to be expected—biological networks, social networks, cartography—and some less obvious but no less active, e.g., education and computer security. All chapters are authored by the leaders of the field and edited into a pleasing common style.The field of graph drawing remains dynamic, as testified by the many open problems collected in the chapters, from turning Mani’s theorem into an algorithm for 3-connected planar graphs, to deciding whether every degree-6 graph has a 2-bend orthogonal drawing in 3D. It is an achievement to so thoroughly cover the range from theory to algorithms to software to applications, and I expect the Handbook to serve as the key resource for researchers in the field."—Joseph O’Rourke, Smith CollegeTable of ContentsPlanarity Testing and Embedding. Crossings and Planarization. Symmetric Graph Drawing. Proximity Drawings. Tree Drawing Algorithms. Planar Straight-Line Drawing Algorithms. Planar Orthogonal and Polyline Drawing Algorithms. Spine and Radial Drawings. Circular Drawing Algorithms. Rectangular Drawing Algorithms. Simultaneous Embedding of Planar Graphs. Force-Directed Drawing Algorithms. Hierarchical Drawing Algorithms. Three-Dimensional Drawings. Labeling Algorithms. Graph Markup Language (GraphML). The Open Graph Drawing Framework (OGDF). GDToolkit. PIGALE. Biological Networks. Computer Security. Graph Drawing for Data Analytics. Graph Drawing and Cartography. Graph Drawing in Education. Computer Networks. Social Networks. Index.
£194.75
Merchant Books Principia Mathematica - Volume Two
£27.97
Merchant Books Principia Mathematica - Volume Three
£24.42
Watchmaker Publishing Philosophiae Naturalis Principia Mathematica (Latin Edition)
£25.39
Society for Industrial & Applied Mathematics,U.S. An Introduction to Compressed Sensing
Book SynopsisCompressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing.An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate.The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.
£78.20
ISTE Ltd and John Wiley & Sons Inc Graphs and Networks: Multilevel Modeling
Book SynopsisA transport network is typically a network of roads, streets, pipes, aqueducts, power lines, or nearly any structure that permits either vehicular movement or the flow of some commodity. Transport network analysis, a field of transport engineering that typically employs the use of graph theory, is used to determine the flow of vehicles, commodities, or people through these networks. It may combine different modes of transport - for example, walking and driving - to model multi-modal journeys. This edition is completely updated and contains two new chapters covering spatial analysis and urban management through graph theory simulation. Highly practical, the simulation approach allows readers to solve classic problems, such as placement of high-speed roads, the capacity of a network, pollution emission control, and more.
£170.95
ISTE Ltd and John Wiley & Sons Inc Mathematics for Informatics and Computer Science
Book SynopsisHow many ways do exist to mix different ingredients, how many chances to win a gambling game, how many possible paths going from one place to another in a network ? To this kind of questions Mathematics applied to computer gives a stimulating and exhaustive answer. This text, presented in three parts (Combinatorics, Probability, Graphs) addresses all those who wish to acquire basic or advanced knowledge in combinatorial theories. It is actually also used as a textbook. Basic and advanced theoretical elements are presented through simple applications like the Sudoku game, search engine algorithm and other easy to grasp applications. Through the progression from simple to complex, the teacher acquires knowledge of the state of the art of combinatorial theory. The non conventional simultaneous presentation of algorithms, programs and theory permits a powerful mixture of theory and practice. All in all, the originality of this approach gives a refreshing view on combinatorial theory.Trade Review"On the other hand if you are looking for an approach to combinatorics that is routed in applications and with lots of exercises then this is the book for you. Yes, dare I say it, it's fun." (I Programmer, 21 January 2011)Table of ContentsGeneral Introduction xxiii Chapter 1. Some Historical Elements 1 PART 1. COMBINATORICS 17 Part 1. Introduction 19 Chapter 2. Arrangements and Combinations 21 Chapter 3. Enumerations in Alphabetical Order 43 Chapter 4. Enumeration by Tree Structures 63 Chapter 5. Languages, Generating Functions and Recurrences 85 Chapter 6. Routes in a Square Grid 105 Chapter 7. Arrangements and Combinations with Repetitions 119 Chapter 8. Sieve Formula 137 Chapter 9. Mountain Ranges or Parenthesis Words: Catalan Numbers 165 Chapter 10. Other Mountain Ranges 197 Chapter 11. Some Applications of Catalan Numbers and Parenthesis Words 215 Chapter 12. Burnside’s Formula 227 Chapter 13. Matrices and Circulation on a Graph 253 Chapter 14. Parts and Partitions of a Set 275 Chapter 15. Partitions of a Number 289 Chapter 16. Flags 305 Chapter 17. Walls and Stacks 315 Chapter 18. Tiling of Rectangular Surfaces using Simple Shapes 331 Chapter 19. Permutations 345 PART 2. PROBABILITY 387 Part 2. Introduction 389 Chapter 20. Reminders about Discrete Probabilities 395 Chapter 21. Chance and the Computer 427 Chapter 22. Discrete and Continuous 447 Chapter 23. Generating Function Associated with a Discrete Random Variable in a Game 469 Chapter 24. Graphs and Matrices for Dealing with Probability Problems 497 Chapter 25. Repeated Games of Heads or Tails 509 Chapter 26. Random Routes on a Graph 535 Chapter 27. Repetitive Draws until the Outcome of a Certain Pattern 565 Chapter 28. Probability Exercises 597 PART 3. GRAPHS 637 Part 3. Introduction 639 Chapter 29. Graphs and Routes 643 Chapter 30. Explorations in Graphs 661 Chapter 31. Trees with Numbered Nodes, Cayley’s Theorem and Prüfer Code 705 Chapter 32. Binary Trees 723 Chapter 33. Weighted Graphs: Shortest Paths and Minimum Spanning Tree 737 Chapter 34. Eulerian Paths and Cycles, Spanning Trees of a Graph 759 Chapter 35. Enumeration of Spanning Trees of an Undirected Graph 779 Chapter 36. Enumeration of Eulerian Paths in Undirected Graphs 799 Chapter 37. Hamiltonian Paths and Circuits 835 APPENDICES 867 Appendix 1. Matrices 869 Appendix 2. Determinants and Route Combinatorics 885 Bibliography 907 Index 911
£132.00
ISTE Ltd and John Wiley & Sons Inc Graph Partitioning
Book SynopsisGraph partitioning is a theoretical subject with applications in many areas, principally: numerical analysis, programs mapping onto parallel architectures, image segmentation, VLSI design. During the last 40 years, the literature has strongly increased and big improvements have been made. This book brings together the knowledge accumulated during many years to extract both theoretical foundations of graph partitioning and its main applications.Table of ContentsIntroduction xiii Charles-Edmond Bichot, Patrick Siarry Chapter 1. General Introduction to Graph Partitioning 1 Charles-Edmond Bichot 1.1. Partitioning 1 1.2. Mathematical notions 2 1.3. Graphs 4 1.4. Formal description of the graph partitioning problem 8 1.5. Objective functions for graph partitioning 11 1.6. Constrained graph partitioning 13 1.7. Unconstrained graph partitioning 14 1.8. Differences between constrained and unconstrained partitioning 16 1.9. From bisection to k-partitioning: the recursive bisection method 17 1.10. NP-hardness of graph partitioning optimization problems 19 1.11. Conclusion 22 1.12. Bibliography 22 Part 1: Graph Partitioning for Numerical Analysis 27 Chapter 2. A Partitioning Requiring Rapidity and Quality: The Multilevel Method and Partitions Refinement Algorithms 29 Charles-Edmond Bichot 2.1. Introduction 29 2.2. Principles of the multilevel method 30 2.3. Graph coarsening 33 2.4. Partitioning of the coarsened graph 37 2.5. Uncoarsening and partitions refinement 40 2.6. The spectral method 52 2.7. Conclusion 59 2.8. Bibliography 60 Chapter 3. Hypergraph Partitioning 65 Cédric Chevalier 3.1. Definitions and metrics 65 3.2. Connections between graphs, hypergraphs, and matrices 67 3.3. Algorithms for hypergraph partitioning 68 3.4. Purpose 72 3.5. Conclusion 77 3.6. Software references 78 3.7. Bibliography 78 Chapter 4. Parallelization of Graph Partitioning 81 François Pellegrini 4.1. Introduction 81 4.2. Distributed data structures 84 4.3. Parallelization of the coarsening phase 87 4.4. Folding 93 4.5. Centralization 95 4.6. Parallelization of the refinement phase 96 4.7. Experimental results 107 4.8. Conclusion 111 4.9. Bibliography 111 Chapter 5. Static Mapping of Process Graphs 115 François Pellegrini 5.1. Introduction 115 5.2. Static mapping models 116 5.3. Exact algorithms 121 5.4. Approximation algorithms 123 5.5. Conclusion 133 5.6. Bibliography 134 Part 2: Optimization Methods for Graph Partitioning 137 Chapter 6. Local Metaheuristics and Graph Partitioning 139 Charles-Edmond Bichot 6.1. General introduction to metaheuristics 140 6.2. Simulated annealing 141 6.3. Iterated local search 149 6.4. Other local search metaheuristics 158 6.5. Conclusion 159 6.6. Bibliography 159 Chapter 7. Population-based Metaheuristics, Fusion-Fission and Graph Partitioning Optimization 163 Charles-Edmond Bichot 7.1. Ant colony algorithms 163 7.2. Evolutionary algorithms 165 7.3. The fusion-fission method 182 7.4. Conclusion 195 7.5. Acknowledgments 196 7.6. Bibliography 196 Chapter 8. Partitioning Mobile Networks into Tariff Zones 201 Mustapha Oughdi, Sid Lamrous, Alexandre Caminada 8.1. Introduction 201 8.2. Spatial division of the network 208 8.3. Experimental results 220 8.4. Conclusion 222 8.5. Bibliography 223 Chapter 9. Air Traffic Control Graph Partitioning Application 225 Charles-Edmond Bichot, Nicolas Durand 9.1. Introduction 225 9.2. The problem of dividing up the airspace 227 9.3. Modeling the problem 231 9.4. Airspace partitioning: towards a new optimization metaheuristic 237 9.5. Division of the central European airspace 240 9.6. Conclusion 246 9.7. Acknowledgments 247 9.8. Bibliography 247 Part 3: Other Approaches to Graph Partitioning 249 Chapter 10. Application of Graph Partitioning to Image Segmentation 251 Amir Nakib, Laurent Najman, Hugues Talbot, Patrick Siarry 10.1. Introduction 251 10.2. The image viewed in graph form 251 10.3. Principle of image segmentation using graphs 254 10.4. Image segmentation via maximum flows 257 10.5. Unification of segmentation methods via graph theory 265 10.6. Conclusions and perspectives 269 10.7. Bibliography 271 Chapter 11. Distances in Graph Partitioning 275 Alain Guénoche 11.1. Introduction 275 11.2. The Dice distance 276 11.3. Pons-Latapy distance 281 11.4. A partitioning method for distance arrays 283 11.5. A simulation protocol 286 11.6. Conclusions 292 11.7. Acknowledgments 293 11.8. Bibliography 293 Chapter 12. Detection of Disjoint or Overlapping Communities in Networks 297 Jean-Baptiste Angelelli, Alain Guénoche, Laurence Reboul 12.1. Introduction 297 12.2. Modularity of partitions and coverings 299 12.3. Partitioning method 301 12.4. Overlapping partitioning methods 307 12.5. Conclusion 311 12.6. Acknowledgments 312 12.7. Bibliography 312 Chapter 13. Multilevel Local Optimization of Modularity 315 Thomas Aynaud, Vincent D. Blondel, Jean-Loup Guillaume and Renaud Lambiotte 13.1. Introduction 315 13.2. Basics of modularity 317 13.3. Modularity optimization 319 13.4. Validation on empirical and artificial graphs 327 13.5. Discussion 333 13.6. Conclusion 341 13.7. Acknowledgments 342 13.8. Bibliography 342 Appendix. The Main Tools and Test Benches for Graph Partitioning 347 Charles-Edmond Bichot A.1. Tools for constrained graph partitioning optimization 348 A.2. Tools for unconstrained graph partitioning optimization 350 A.3. Graph partitioning test benches 351 A.4. Bibliography 354 Glossary 357 List of Authors 361 Index 365
£132.00
ISTE Ltd and John Wiley & Sons Inc Advanced Graph Theory and Combinatorics
Book SynopsisAdvanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.Table of ContentsForeword ix Introduction xi Chapter 1. A First Encounter with Graphs 1 1.1. A few definitions 1 1.1.1. Directed graphs 1 1.1.2. Unoriented graphs 9 1.2. Paths and connected components 14 1.2.1. Connected components 16 1.2.2. Stronger notions of connectivity 18 1.3. Eulerian graphs 23 1.4. Defining Hamiltonian graphs 25 1.5. Distance and shortest path 27 1.6. A few applications 30 1.7. Comments 35 1.8. Exercises 37 Chapter 2. A Glimpse at Complexity Theory 43 2.1. Some complexity classes 43 2.2. Polynomial reductions 46 2.3. More hard problems in graph theory 49 Chapter 3. Hamiltonian Graphs 53 3.1. A necessary condition 53 3.2. A theorem of Dirac 55 3.3. A theorem of Ore and the closure of a graph 56 3.4. Chvátal’s condition on degrees 59 3.5. Partition of Kn into Hamiltonian circuits 62 3.6. De Bruijn graphs and magic tricks 65 3.7. Exercises 68 Chapter 4. Topological Sort and Graph Traversals 69 4.1. Trees 69 4.2. Acyclic graphs 79 4.3. Exercises 82 Chapter 5. Building New Graphs from Old Ones 85 5.1. Some natural transformations 85 5.2. Products 90 5.3. Quotients 92 5.4. Counting spanning trees 93 5.5. Unraveling 94 5.6. Exercises 96 Chapter 6. Planar Graphs 99 6.1. Formal definitions 99 6.2. Euler’s formula 104 6.3. Steinitz’ theorem 109 6.4. About the four-color theorem 113 6.5. The five-color theorem 115 6.6. From Kuratowski’s theorem to minors 120 6.7. Exercises 123 Chapter 7. Colorings 127 7.1. Homomorphisms of graphs 127 7.2. A digression: isomorphisms and labeled vertices 131 7.3. Link with colorings 134 7.4. Chromatic number and chromatic polynomial 136 7.5. Ramsey numbers 140 7.6. Exercises 147 Chapter 8. Algebraic Graph Theory 151 8.1. Prerequisites 151 8.2. Adjacency matrix 154 8.3. Playing with linear recurrences 160 8.4. Interpretation of the coefficients 168 8.5. A theorem of Hoffman 169 8.6. Counting directed spanning trees 172 8.7. Comments 177 8.8. Exercises 178 Chapter 9. Perron–Frobenius Theory 183 9.1. Primitive graphs and Perron’s theorem 183 9.2. Irreducible graphs 188 9.3. Applications 190 9.4. Asymptotic properties 195 9.4.1. Canonical form 196 9.4.2. Graphs with primitive components 197 9.4.3. Structure of connected graphs 206 9.4.4. Period and the Perron–Frobenius theorem 214 9.4.5. Concluding examples 218 9.5. The case of polynomial growth 224 9.6. Exercises 231 Chapter 10. Google’s Page Rank 233 10.1. Defining the Google matrix 238 10.2. Harvesting the primitivity of the Google matrix 241 10.3. Computation 246 10.4. Probabilistic interpretation 246 10.5. Dependence on the parameter α 247 10.6. Comments 248 Bibliography 249 Index 263
£125.06
ISTE Ltd and John Wiley & Sons Inc Probabilistic Combinatorial Optimization on
Book SynopsisThis title provides a comprehensive survey over the subject of probabilistic combinatorial optimization, discussing probabilistic versions of some of the most paradigmatic combinatorial problems on graphs, such as the maximum independent set, the minimum vertex covering, the longest path and the minimum coloring. Those who possess a sound knowledge of the subject mater will find the title of great interest, but those who have only some mathematical familiarity and knowledge about complexity and approximation theory will also find it an accessible and informative read.Table of ContentsPreface 11 Chapter 1. A Short Insight into Probabilistic Combinatorial Optimization 15 1.1. Motivations and applications 15 1.2. A formalism for probabilistic combinatorial optimization 19 1.3. The main methodological issues dealing with probabilistic combinatorial optimization 24 1.3.1. Complexity issues 24 1.3.1.1. Membership in NPO is not always obvious 24 1.3.1.2. Complexity of deterministic vs. complexity of probabilistic optimization problems 24 1.3.2. Solution issues 26 1.3.2.1. Characterization of optimal a priori solutions 26 1.3.2.2. Polynomial subcases 28 1.3.2.3. Exact solutions and polynomial approximation issues 29 1.4. Miscellaneous and bibliographic notes 31 FIRST PART. PROBABILISTIC GRAPH-PROBLEMS 35 Chapter 2. The Probabilistic Maximum Independent Set 37 2.1. The modification strategies and a preliminary result 39 2.1.1. Strategy M1 39 2.1.2. Strategies M2 and M3 39 2.1.3. Strategy M4 41 2.1.4. Strategy M5 41 2.1.5. A general mathematical formulation for the five functionals 42 2.2. PROBABILISTIC MAX INDEPENDENT SET1 44 2.2.1. Computing optimal a priori solutions 44 2.2.2. Approximating optimal solutions 45 2.2.3. Dealing with bipartite graphs 46 2.3. PROBABILISTIC MAX INDEPENDENT SET2 and 3 47 2.3.1. Expressions for E(G, S, M2) and E(G, S, M3) 47 2.3.2. An upper bound for the complexity of E(G, S, M2) 48 2.3.3. Bounds for E(G, S, M2) 49 2.3.4. Approximating optimal solutions 51 2.3.4.1. Using argmax{_vi∈S pi} as an a priori solution 51 2.3.4.2. Using approximations of MAX INDEPENDENT SET 53 2.3.5. Dealing with bipartite graphs 53 2.4. PROBABILISTIC MAX INDEPENDENT SET4 55 2.4.1. An expression for E(G, S, M4) 55 2.4.2. Using S∗ or argmax{_vi∈S pi} as an a priori solution 56 2.4.3. Dealing with bipartite graphs 57 2.5. PROBABILISTIC MAX INDEPENDENT SET5 58 2.5.1. In general graphs 58 2.5.2. In bipartite graphs 60 2.6. Summary of the results 61 2.7. Methodological questions 63 2.7.1. Maximizing a criterion associated with gain 65 2.7.1.1. The minimum gain criterion 65 2.7.1.2. The maximum gain criterion 66 2.7.2. Minimizing a criterion associated with regret 68 2.7.2.1. The maximum regret criterion 68 2.7.3. Optimizing expectation 70 2.8. Proofs of the results 71 2.8.1. Proof of Proposition 2.1 71 2.8.2. Proof of Theorem 2.6 74 2.8.3. Proof of Proposition 2.3 77 2.8.4. Proof of Theorem 2.13 78 Chapter 3. The Probabilistic Minimum Vertex Cover 81 3.1. The strategies M1, M2 and M3 and a general preliminary result 82 3.1.1. Specification of M1, M2 and M3 82 3.1.1.1. Strategy M1 82 3.1.1.2. Strategy M2 83 3.1.1.3. Strategy M3 83 3.1.2. A first expression for the functionals 84 3.2. PROBABILISTIC MIN VERTEX COVER1 84 3.3. PROBABILISTIC MIN VERTEX COVER2 86 3.4. PROBABILISTIC MIN VERTEX COVER3 87 3.4.1. Building E(G, C, M3) 87 3.4.2. Bounds for E(G, C, M3) 88 3.5. Some methodological questions 89 3.6. Proofs of the results 91 3.6.1. Proof of Theorem 3.3 91 3.6.2. On the the bounds obtained in Theorem 3.3 93 Chapter 4. The Probabilistic Longest Path 99 4.1. Probabilistic longest path in terms of vertices 100 4.2. Probabilistic longest path in terms of arcs 102 4.2.1. An interesting algebraic expression 104 4.2.2. Metric PROBABILISTIC ARC WEIGHTED LONGEST PATH 105 4.3. Why the strategies used are pertinent 109 4.4. Proofs of the results 110 4.4.1. Proof of Theorem 4.1 110 4.4.2. Proof of Theorem 4.2 112 4.4.3. An algebraic proof for Theorem 4.3 114 4.4.4. Proof of Lemma 4.1 116 4.4.5. Proof of Lemma 4.2 117 4.4.6. Proof of Theorem 4.4 117 Chapter 5. Probabilistic Minimum Coloring 125 5.1. The functional E(G,C) 127 5.2. Basic properties of probabilistic coloring 131 5.2.1. Properties under non-identical vertex-probabilities 131 5.2.2. Properties under identical vertex-probabilities 131 5.3. PROBABILISTIC MIN COLORING in general graphs 132 5.3.1. The complexity of probabilistic coloring 132 5.3.2. Approximation 132 5.3.2.1. The main result 132 5.3.2.2. Further approximation results 137 5.4. PROBABILISTIC MIN COLORING in bipartite graphs 139 5.4.1. A basic property 139 5.4.2. General bipartite graphs 141 5.4.3. Bipartite complements of bipartite matchings 147 5.4.4. Trees 151 5.4.5. Cycles 154 5.5. Complements of bipartite graphs 155 5.6. Split graphs 156 5.6.1. The complexity of PROBABILISTIC MIN COLORING 156 5.6.2. Approximation results 159 5.7. Determining the best k-coloring in k-colorable graphs 164 5.7.1. Bipartite graphs 164 5.7.1.1. PROBABILISTIC MIN 3-COLORING 164 5.7.1.2. PROBABILISTIC MIN k-COLORING fork > 3 168 5.7.1.3. Bipartite complements of bipartite matchings 171 5.7.2. The complements of bipartite graphs 171 5.7.3. Approximation in particular classes of graphs 174 5.8. Comments and open problems 175 5.9. Proofs of the different results 178 5.9.1. Proof of [5.5] 178 5.9.2. Proof of [5.4] 179 5.9.3. Proof of Property 5.1 180 5.9.4. Proof of Proposition 5.2 181 5.9.5. Proof of Lemma 5.11 183 SECOND PART. STRUCTURAL RESULTS 185 Chapter 6. Classification of Probabilistic Graph-problems 187 6.1. When MS is feasible 187 6.1.1. The a priori solution is a subset of the initial vertex-set 188 6.1.2. The a priori solution is a collection of subsets of the initial vertex-set 191 6.1.3. The a priori solution is a subset of the initial edge-set 193 6.2. When application of MS itself does not lead to feasible solutions 198 6.2.1. The functional associated with MSC 198 6.2.2. Applications 199 6.2.2.1. The a priori solution is a cycle 200 6.2.2.2. The a priori solution is a tree 201 6.3. Some comments 205 6.4. Proof of Theorem 6.4 206 Chapter 7. A Compendium of Probabilistic NPO Problems on Graphs 211 7.1. Covering and partitioning 214 7.1.1. MIN VERTEX COVER 214 7.1.2. MIN COLORING 214 7.1.3. MAX ACHROMATIC NUMBER 215 7.1.4. MIN DOMINATING SET 215 7.1.5. MAX DOMATIC PARTITION 216 7.1.6. MIN EDGE-DOMINATING SET 216 7.1.7. MIN INDEPENDENT DOMINATING SET 217 7.1.8. MIN CHROMATIC SUM 217 7.1.9. MIN EDGE COLORING 218 7.1.10. MIN FEEDBACK VERTEX-SET 219 7.1.11. MIN FEEDBACK ARC-SET 220 7.1.12. MAX MATCHING 220 7.1.13. MIN MAXIMAL MATCHING 220 7.1.14. MAX TRIANGLE PACKING 220 7.1.15. MAX H-MATCHING 221 7.1.16. MIN PARTITION INTO CLIQUES 222 7.1.17. MIN CLIQUE COVER 222 7.1.18. MIN k-CAPACITED TREE PARTITION 222 7.1.19. MAX BALANCED CONNECTED PARTITION 223 7.1.20. MIN COMPLETE BIPARTITE SUBGRAPH COVER 223 7.1.21. MIN VERTEX-DISJOINT CYCLE COVER 223 7.1.22. MIN CUT COVER 224 7.2. Subgraphs and supergraphs 224 7.2.1. MAX INDEPENDENT SET 224 7.2.2. MAX CLIQUE 224 7.2.3. MAX INDEPENDENT SEQUENCE 225 7.2.4. MAX INDUCED SUBGRAPH WITH PROPERTY π 225 7.2.5. MIN VERTEX DELETION TO OBTAIN SUBGRAPH WITH PROPERTY π 225 7.2.6. MIN EDGE DELETION TO OBTAIN SUBGRAPH WITH PROPERTY π 226 7.2.7. MAX CONNECTED SUBGRAPH WITH PROPERTY π 226 7.2.8. MIN VERTEX DELETION TO OBTAIN CONNECTED SUBGRAPH WITH PROPERTY π 226 7.2.9. MAX DEGREE-BOUNDED CONNECTED SUBGRAPH 226 7.2.10. MAX PLANAR SUBGRAPH 227 7.2.11. MIN EDGE DELETION k-PARTITION 227 7.2.12. MAX k-COLORABLE SUBGRAPH 227 7.2.13. MAX SUBFOREST 228 7.2.14. MAX EDGE SUBGRAPH or DENSE k-SUBGRAPH 228 7.2.15. MIN EDGE K-SPANNER 228 7.2.16. MAX k-COLORABLE INDUCED SUBGRAPH 229 7.2.17. MIN EQUIVALENT DIGRAPH 229 7.2.18. MIN CHORDAL GRAPH COMPLETION 229 7.3. Iso- and other morphisms 229 7.3.1. MAX COMMON SUBGRAPH 229 7.3.2. MAX COMMON INDUCED SUBGRAPH 230 7.3.3. MAX COMMON EMBEDDED SUBTREE 230 7.3.4. MIN GRAPH TRANSFORMATION 230 7.4. Cuts and connectivity 231 7.4.1. MAX CUT 231 7.4.2. MAX DIRECTED CUT 231 7.4.3. MIN CROSSING NUMBER 231 7.4.4. MAX k-CUT 232 7.4.5. MIN k-CUT 233 7.4.6. MIN NETWORK INHIBITION ON PLANAR GRAPHS 233 7.4.7. MIN VERTEX k-CUT 234 7.4.8. MIN MULTI-WAY CUT 234 7.4.9. MIN MULTI-CUT 234 7.4.10. MIN RATIO-CUT 235 7.4.11. MIN b-BALANCED CUT 236 7.4.12. MIN b-VERTEX SEPARATOR 236 7.4.13. MIN QUOTIENT CUT 236 7.4.14. MIN k-VERTEX CONNECTED SUBGRAPH 236 7.4.15. MIN k-EDGE CONNECTED SUBGRAPH 237 7.4.16. MIN BICONNECTIVITY AUGMENTATION 237 7.4.17. MIN STRONG CONNECTIVITY AUGMENTATION 237 7.4.18. MIN BOUNDED DIAMETER AUGMENTATION 237 Appendix A. Mathematical Preliminaries 239 A.1. Sets, relations and functions 239 A.2. Basic concepts from graph-theory 242 A.3. Elements from discrete probabilities 246 Appendix B. Elements of the Complexity and the Approximation Theory 249 B.1. Problem, algorithm, complexity 249 B.2. Some notorious complexity classes 250 B.3. Reductions and NP-completeness 251 B.4. Approximation of NP-hard problems 252 Bibliography 255 Index 261
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