Combinatorics and Graph Theory eBooks

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The GCHQ Puzzle Book
By: GCHQ eBookWould GCHQ recruit you? Pit your wits against the people who cracked Enigma in the official puzzle book from Britain's secretive intelligence organisation . . .  Odd word out The themes in the following words are identical, but totally different! Which is the odd… More

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Algebraic Number Theory and Fermat's Last Theorem, Fourth Edition
By: Stewart, Ian eBookUpdated to reflect current research, Algebraic Number Theory and Fermat's Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematicsthe quest for a proof of Fermat's Last Theorem. The authors use this… More

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Introduction to Number Theory, 2nd Edition
By: Vazzana, Anthony eBookIntroduction to Number Theory is a classroomtested, studentfriendly 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,… More

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Algebraic Combinatorics
By: Chris Godsil eBookThis graduate level text is distinguished both by the range of topics and the novelty of the material it treatsmore than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It… More

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A Tour through Graph Theory
By: Karin R Saoub eBookA Tour Through Graph Theory introduces graph theory to students who are not mathematics majors. Rather than featuring formal mathematical proofs, the book focuses on explanations and logical reasoning. It also includes thoughtful discussions of historical problems and modern questions. The book… More

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Topics in Algebraic Graph Theory
eBookThe rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and… More

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Handbook of Graph Theory, Second Edition
By: Gross, Jonathan L. eBookIn the ten years since the publication of the bestselling 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… More

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Handbook of Graph Theory, Second Edition
eBookIn the ten years since the publication of the bestselling 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… More

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Algorithmic Graph Theory and Perfect Graphs
By: Martin Charles Golumbic eBookAlgorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving realworld problems. It remains a stepping… More

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Spectral Theory of Random Matrices
By: Girko, Vyacheslav L. eBookSpectral Theory of Random Matrices More

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Spectral Radius of Graphs
By: Dragan Stevanovic eBookSpectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer… More

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Computational Discrete Mathematics Combinatorics and Graph Theory with Mathematica Â®
By: Sriram Pemmaraju, Professor Steven Skiena eBookThis book was first published in 2003. Combinatorica, an extension to the popular computer algebra system MathematicaÂ®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the… More

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Combinatorics of Minuscule Representations
By: Professor R. M. Green eBookMinuscule representations occur in a variety of contexts in mathematics and physics. They are typically much easier to understand than representations in general, which means they give rise to relatively easy constructions of algebraic objects such as Lie algebras and Weyl groups. This book… More

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Uniform Central Limit Theorems
By: R. M. Dudley eBookIn this new edition of a classic work on empirical processes the author, an acknowledged expert, gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition, including the Bretagnolleâ Massart theorem giving constants in the Komlosâ … More

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Random Walks and Heat Kernels on Graphs
By: Martin T. Barlow eBookThis introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and… More

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Fibonacci and Catalan Numbers An Introduction
By: Ralph Grimaldi eBookDiscover the properties and realworld applications of the Fibonacci and the Catalan numbers With clear explanations and easytofollow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers. Beginning… More

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Introduction to Combinatorics
By: Martin J. Erickson eBookPraise for the First Edition â This excellent text should prove a useful accoutrement for any developing mathematics program . . . itâ s short, itâ s sweet, itâ s beautifully written.â â *The Mathematical Intelligencer* â Erickson has prepared an exemplary work . . . strongly recommended… More

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Combinatorial Reasoning An Introduction to the Art of Counting
By: Duane DeTemple, William Webb eBookWritten by two wellknown scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics. Focusing on modern techniques and applications, the book develops a variety of… More

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Distribution Modulo One and Diophantine Approximation
By: Professor Yann Bugeaud eBookThis book presents stateoftheart research on the distribution modulo one of sequences of integral powers of real numbers and related topics. Most of the results have never before appeared in one book and many of them were proved only during the last decade. Topics covered include the… More

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Topics in Topological Graph Theory
By: Jonathan L. Gross, Thomas W. Tucker eBookThe use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature.… More

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Codes and Automata
By: Jean Berstel, Dominique Perrin, Christophe Reutenauer eBookThis major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book,… More

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Topics in Chromatic Graph Theory
eBookChromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks,… More

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ErdÅ sâ Koâ Rado Theorems: Algebraic Approaches
By: Christopher Godsil, Karen Meagher eBookAimed at graduate students and researchers, this fascinating text provides a comprehensive study of the ErdÅ sâ Koâ Rado Theorem, with a focus on algebraic methods. The authors begin by discussing wellknown proofs of the EKR bound for intersecting families. The natural generalization of the EKR… More

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Handbook of Discrete and Combinatorial Mathematics, Second Edition
eBookHandbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter… More

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Mathematics in Ancient Egypt A Contextual History
By: Annette Imhausen eBookMathematics in Ancient Egypt traces the development of Egyptian mathematics, from the end of the fourth millennium BCâ and the earliest hints of writing and number notationâ to the end of the pharaonic period in GrecoRoman times. Drawing from mathematical texts, architectural drawings,… More

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Introduction to Toric Varieties. (AM131)
By: Fulton, William eBookToric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and… More

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Handbook of Graph Drawing and Visualization
By: Tamassia, Roberto eBookGet an InDepth Understanding of Graph Drawing Techniques, Algorithms, Software, and Applications The Handbook of Graph Drawing and Visualization provides a broad, uptodate survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and… More

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Handbook of Financial Cryptography and Security
By: Rosenberg, Burton eBookThe Handbook of Financial Cryptography and Security elucidates the theory and techniques of cryptography and illustrates how to establish and maintain security under the framework of financial cryptography. It applies various cryptographic techniques to auctions, electronic voting, micropayment… More

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Algebraic Curves in Cryptography
By: Ling, San eBookThe reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a… More

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Handbook of Product Graphs, Second Edition
By: Hammack, Richard eBookHandbook of Product Graphs, Second Edition examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors.… More

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Pearls of Discrete Mathematics
By: Erickson, Martin eBookMethods Used to Solve Discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems,… More

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Combinatorial Scientific Computing
By: Naumann, Uwe eBookCombinatorial Scientific Computing explores the latest research on creating algorithms and software tools to solve key combinatorial problems on largescale highperformance computing architectures. It includes contributions from international researchers who are pioneers in designing software and… More

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Applied Algebra: Codes, Ciphers and Discrete Algorithms, Second Edition
By: Hardy, Darel W. eBookUsing mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior… More

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Graphs & Digraphs, Fifth Edition
By: Chartrand, Gary eBookContinuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents… More

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New Directions of Modern Cryptography
By: Cao, Zhenfu eBookModern cryptography has evolved dramatically since the 1970s. With the rise of new network architectures and services, the field encompasses much more than traditional communication where each side is of a single user. It also covers emerging communication where at least one side is of multiple… More

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Quantitative Graph Theory: Mathematical Foundations and Applications
By: Dehmer, Matthias eBookThe first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information… More

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Graphs & Digraphs, Sixth Edition
By: Chartrand, Gary eBookGraphs & Digraphs masterfully employs studentfriendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. Fully updated and thoughtfully reorganized to make reading and… More

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Spectral Theory of Random Matrices
By: Girko, Vyacheslav L. eBookSpectral Theory of Random Matrices More

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Hypergraphs Combinatorics of Finite Sets
By: C. Berge eBookGraph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional… More

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Combinatorics: A Very Short Introduction
By: Robin Wilson eBookHow many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of… More

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The Structure of Complex Networks Theory and Applications
By: Ernesto Estrada eBookThis book deals with the analysis of the structure of complex networks by combining results from graph theory, physics, and pattern recognition. The book is divided into two parts. 11 chapters are dedicated to the development of theoretical tools for the structural analysis of networks, and 7… More

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Graph Theory As I Have Known It
By: W. T. Tutte eBookThis book provides a unique and unusual introduction to graph theory by one of the founding fathers, and will be of interest to all researchers in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to… More

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Elementary Number Theory, Group Theory and Ramanujan Graphs
By: Davidoff, Giuliana eBookThis text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering.… More

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The Mathematics of Logic
By: Kaye,Richard W. eBookThis undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for firstorder logic. Looking at a series of interesting systems, increasing in complexity,… More

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Introduction to Lattices and Order
By: B. A. Davey, H. A. Priestley eBookThis new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints… More

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Solutions Manual to accompany Combinatorial Reasoning: An Introduction to the Art of Counting
By: Duane DeTemple, William Webb eBookThis is a solutions manual to accompanyÂ Combinatorial Reasoning: An Introduction to the Art of Counting Written by wellknown scholars in the field, Combinatorial Reasoning: An Introduction to the Art of CountingÂ introduces combinatorics alongside modern techniques, showcases the… More

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Simulation for Applied Graph Theory Using Visual C++
By: Shaharuddin Salleh, Zuraida Abal Abas eBookThe tool for visualization is Microsoft Visual C++. This popular software has the standard C++ combined with the Microsoft Foundation Classes (MFC) libraries for Windows visualization. This book explains how to create a graph interactively, solve problems in graph theory with minimum number of C++… More

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Surveys in Combinatorics 2015
eBookThis volume contains nine survey articles based on the invited lectures given at the 25th British Combinatorial Conference, held at the University of Warwick in July 2015. This biennial conference is a wellestablished international event, with speakers from around the world. The volume provides an… More

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Introduction to Random Graphs
By: Alan Frieze, MichaÅ KaroÅ ski eBookFrom social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this… More

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Permutation Groups and Cartesian Decompositions
By: Cheryl E. Praeger, Csaba Schneider eBookPermutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nanâ Scott theory are presented not only for… More

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Additive Combinatorics A Menu of Research Problems
By: Bela Bajnok eBookAdditive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from… More

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An Invitation to the RogersRamanujan Identities
By: Andrew V. Sills eBookThe RogersRamanujan identities are a pair of infinite seriesâ infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator… More

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Matrix Inequalities for Iterative Systems
By: Hanjo Taubig eBookThe book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positivesemidefinite, as well as… More

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Introduction to Abstract Algebra
By: Smith, Jonathan D.H. eBookTaking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from… More

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Combinatorics of Permutations, Second Edition
By: Bona, Miklos eBookA Unified Account of Permutations in Modern Combinatorics A 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a onesemester course, Combinatorics of Permutations,… More

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Combinatorics of Set Partitions
By: Mansour, Toufik eBookFocusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Designed for students and researchers in discrete mathematics, the book is a… More

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Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs
By: Molitierno, Jason J. eBookOn the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs. Applications of… More

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Discrete Mathematics and Applications, Second Edition
By: Kevin Ferland eBookThis book is intended for a onesemester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book. Part one focuses on how to write proofs,… More

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Introduction to Combinatorics, Second Edition
By: Walter D. Wallis, John C. George eBookWhat Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be… More

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Bent Functions Results and Applications to Cryptography
By: Natalia Tokareva eBookBent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. As these maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding… More

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Discrete Geometry
By: Bezdek, Andras eBookCelebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society… More

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Quantum Groups
By: Street,Ross eBookAlgebra has moved well beyond the topics discussed in standard undergraduate texts on Â¬Ã«modern algebraÂ¬Ã. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the… More

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Matroids: A Geometric Introduction
By: Gary Gordon, Jennifer McNulty eBookMatroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician… More

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Elliptic Functions
By: J. V. Armitage, W. F. Eberlein eBookIn its first six chapters this 2006 text seeks to present the basic ideas and properties of the Jacobi elliptic functions as an historical essay, an attempt to answer the fascinating question: 'what would the treatment of elliptic functions have been like if Abel had developed the ideas, rather… More

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Descriptive Complexity, Canonisation, and Definable Graph Structure Theory
By: Martin Grohe eBookDescriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book… More

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Forbidden Configurations in Discrete Geometry
By: David Eppstein eBookThis book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations,… More

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Combinatorics An Introduction
By: Theodore G. Faticoni eBookBridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking Combinatorics: An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents casebycase methods for… More

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Paradigms of Combinatorial Optimization Problems and New Approaches
eBookCombinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management.Â The three volumes of the Combinatorial Optimization series aim to cover a wide rangeÂ of topics in this area.… More

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Applications of Combinatorial Optimization
eBookCombinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management.Â The three volumes of the Combinatorial Optimization series aim to cover a wide rangeÂ of topics in this area.… More

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Basic Phylogenetic Combinatorics
By: Andreas Dress, Katharina T. Huber, Jacobus Koolen, Vincent Moulton, Andreas Spillner eBookPhylogenetic combinatorics is a branch of discrete applied mathematics concerned with the combinatorial description and analysis of phylogenetic trees and related mathematical structures such as phylogenetic networks and tight spans. Based on a natural conceptual framework, the book focuses on the… More

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A Course in Combinatorics
By: J. H. van Lint, R. M. Wilson eBookThis is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes,… More

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Additive Combinatorics
By: Terence Tao, Van H. Vu eBookAdditive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduatelevel 2006 text will… More

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Groups, Graphs and Random Walks
eBookAn accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings… More

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Crossing Numbers of Graphs
By: Marcus Schaefer eBookCrossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and… More

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Graph Searching Games and Probabilistic Methods
By: Anthony Bonato, Pawel Pralat eBookGraph Searching Games and Probabilistic Methods is the first book that focuses on the intersection of graph searching games and probabilistic methods. The book explores various applications of these powerful mathematical tools to games and processes such as Cops and Robbers, Zombie and Survivors,… More

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Graphs, Algorithms, and Optimization
By: William Kocay, Donald L. Kreher eBookGraph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NPCompleteness and polynomial reduction. A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on… More

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Weyl Group Multiple Dirichlet Series Type A Combinatorial Theory (AM175)
By: Ben Brubaker, Daniel Bump, Solomon Friedberg eBookWeyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet… More

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Across the Board The Mathematics of Chessboard Problems
By: John J. Watkins eBookAcross the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itselfthat simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination… More

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The Fascinating World of Graph Theory
By: Arthur Benjamin, Gary Chartrand, Ping Zhang eBookGraph theory goes back several centuries and revolves around the study of graphsâ mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in… More

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Combinatorics of Train Tracks. (AM125)
By: Penner, R. C. eBookMeasured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in twoand threedimensional topology, geometry, and dynamical systems. This book presents a selfcontained and comprehensive treatment of the rich… More

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Handbook of Combinatorial Designs, Second Edition
By: Colbourn, Charles J. eBookContinuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions,… More

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Mathematics in Games, Sports, and Gambling:  The Games People Play
By: Gould, Ronald J. eBookWith an emphasis on mathematical thinking and problem solving, Mathematics in Games, Sports, and Gambling  The Games People Play shows how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. It draws on numerous examples,… More

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Combinatorics of Spreads and Parallelisms
By: Johnson, Norman eBookCombinatorics of Spreads and Parallelisms covers all known finite and infinite parallelisms as well as the planes comprising them. It also presents a complete analysis of general spreads and partitions of vector spaces that provide groups enabling the construction of subgeometry partitions of… More

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Introduction to Abstract Algebra, Second Edition
By: Smith, Jonathan D. H. eBookIntroduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups.… More

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Combinatorial Methods with Computer Applications
By: Gross, Jonathan L. eBookCombinatorial Methods with Computer Applications provides indepth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete… More

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Mathematical Underpinnings of Analytics Theory and Applications
By: Peter Grindrod eBookAnalytics is the application of mathematical and statistical concepts to large data sets so as to distil insights that offer the owner some options for action and competitive advantage or value. This makes it the most desirable and valuable part of big data science. Driven by the increased data… More

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AgentBased Modeling and Network Dynamics
By: Akira Namatame, ShuHeng Chen eBookWhile the significance of networks in various human behavior and activities has a history as long as human's existence, network awareness is a recent scientific phenomenon. The neologism network science is just one or two decades old. Nevertheless, with this limited time, network thinking has… More

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Combinatorics: Ancient & Modern
eBookWho first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a wellstudied and vibrant area of research, with books and scholarly articles… More

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How to Prove It
By: Velleman, Daniel J. eBookMany students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and… More

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Combinatorics Topics, Techniques, Algorithms
By: Peter J. Cameron eBookCombinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at secondyear undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which… More

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Analytic Combinatorics
By: Philippe Flajolet, Robert Sedgewick eBookAnalytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability… More

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Enumerative Combinatorics: Volume 1
By: Richard P. Stanley eBookRichard Stanley's twovolume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting… More

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The CauchySchwarz Master Class An Introduction to the Art of Mathematical Inequalities
By: J. Michael Steele eBookThis lively, problemoriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the CauchySchwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are… More

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Finite Geometry and Combinatorial Applications
By: Simeon Ball eBookThe 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… More

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Dynamics and Analytic Number Theory
eBookWritten by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in… More

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Error Correcting Codes A Mathematical Introduction
By: D J. Baylis eBookAssuming little previous mathematical knowledge, Error Correcting Codes provides a sound introduction to key areas of the subject. Topics have been chosen for their importance and practical significance, which Baylis demonstrates in a rigorous but gentle mathematical style.Coverage includes optimal… More

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Handbook of Discrete and Computational Geometry, Third Edition
eBookThe Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use… More

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GameTheoretical Models in Biology
By: Broom, Mark eBookCovering the major topics of evolutionary game theory, GameTheoretical Models in Biology presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In… More

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Commutation Relations, Normal Ordering, and Stirling Numbers
By: Mansour, Toufik eBookCommutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV â VU =… More

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New Directions of Modern Cryptography
By: Zhenfu Cao eBookModern cryptography has evolved dramatically since the 1970s. With the rise of new network architectures and services, the field encompasses much more than traditional communication where each side is of a single user. It also covers emerging communication where at least one side is of multiple… More

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Computational Number Theory
By: Das, Abhijit eBookDeveloped from the author's popular graduatelevel course, Computational Number Theory presents a complete treatment of numbertheoretic algorithms. Avoiding advanced algebra, this selfcontained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also… More

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Introduction to Coding Theory, Second Edition
By: Jurgen Bierbrauer eBookThis book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary… More

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Combinatorics, Second Edition
By: Nicholas Loehr eBookCombinatorics, Second Edition is a wellrounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up onetoone correspondences between two sets of… More

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Group Theoretic Cryptography
By: GonzÃ¡lez Vasco, Maria Isabel eBookGroup theoretic problems have propelled scientific achievements across a wide range of fields, including mathematics, physics, chemistry, and the life sciences. Many cryptographic constructions exploit the computational hardness of group theoretical problems, and the area is viewed as a potential… More

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Threshold Graphs and Related Topics
By: N.V.R. Mahadev, U.N. Peled eBookThreshold graphs have a beautiful structure and possess many important mathematical properties. They have applications in many areas including computer science and psychology. Over the last 20 years the interest in threshold graphs has increased significantly, and the subject continues to attract… More

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Combinatorics of Symmetric Designs
By: Ionin, Yury J. eBookThe aim of this book is to provide a unified exposition of the theory of symmetric designs with emphasis on recent developments. The authors cover the combinatorial aspects of the theory giving particular attention to the construction of symmetric designs and related objects. The last five chapters… More

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Topics in Structural Graph Theory
By: Ortrud R. Oellermann eBookThe rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms… More

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Surveys in Combinatorics 2013
eBookThis volume contains nine survey articles based on the invited lectures given at the 24th British Combinatorial Conference, held at Royal Holloway, University of London in July 2013. This biennial conference is a wellestablished international event, with speakers from around the world. The volume… More

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Concepts of Combinatorial Optimization
eBookCombinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management.Â The three volumes of the Combinatorial Optimization series aim to cover a wide rangeÂ of topics in this area.… More

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Enumerative Combinatorics: Volume 2
By: Richard P. Stanley, Sergey Fomin eBookThis second volume of a twovolume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, Dfinite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions… More

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A Double Hall Algebra Approach to Affine Quantum Schurâ Weyl Theory
By: Bangming Deng, Jie Du, Qiang Fu eBookThe theory of Schurâ Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine qSchur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schurâ Weyl theory. To begin,… More

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Analysis of Boolean Functions
By: Ryan O'Donnell eBookBoolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their… More

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Guide to PairingBased Cryptography
eBookThis book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identitybased cryptography and the simplification of existing protocols like signature schemes. As well as exploring the basic mathematical background of finite fields… More

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Big Data of Complex Networks
eBookBig Data of Complex Networks presents and explains the methods from the study of big data that can be used in analysing massive structural data sets, including both very large networks and sets of graphs. As well as applying statistical analysis techniques like sampling and bootstrapping in an… More

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Inequalities for Graph Eigenvalues
By: Zoran StaniÄ eBookWritten for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with finite simple graphs: the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, Seidel matrix,… More

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Topics in Graph Automorphisms and Reconstruction
By: Josef Lauri, Raffaele Scapellato eBookThis indepth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and pseudosimilarity.… More

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Quadratics
By: Richard A. Mollin eBookThe first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in addition to providing deeper applications of the… More

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Graph Theoretic Methods in Multiagent Networks
By: Mehran Mesbahi, Magnus Egerstedt eBookThis accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum… More

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Descent in Buildings (AM190)
By: Bernhard MÃŒhlherr, Holger Petersson, Richard Weiss eBookDescent in Buildings begins with the resolution of a major open question about the local structure of BruhatTits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving… More

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Combinatorial Group Theory and Topology. (AM111)
By: Gersten, S. M. eBookGroup theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge,… More

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TemperleyLieb Recoupling Theory and Invariants of 3Manifolds (AM134)
By: Kauffman, Louis H. eBookThis book offers a selfcontained account of the 3manifold invariants arising from the original Jones polynomial. These are the WittenReshetikhinTuraev and the TuraevViro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic TemperleyLieb algebra,… More

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Fundamental Number Theory with Applications, Second Edition
By: Mollin, Richard A. eBookAn update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easytofollow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes… More

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Advanced Number Theory with Applications
By: Mollin, Richard A. eBookExploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page… More

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Applied Combinatorics, Second Edition
By: Roberts, Fred eBookNow with solutions to selected problems, Applied Combinatorics, Second Edition presents the tools of combinatorics from an applied point of view. This bestselling textbook offers numerous references to the literature of combinatorics and its applications that enable readers to delve more deeply… More

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Algebraic Number Theory, Second Edition
By: Mollin, Richard A. eBookBringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. This edition focuses on integral domains, ideals, and unique factorization in the first… More

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Near Rings, Fuzzy Ideals, and Graph Theory
By: Satyanarayana, Bhavanari eBookNear Rings, Fuzzy Ideals, and Graph Theory explores the relationship between near rings and fuzzy sets and between near rings and graph theory. It covers topics from recent literature along with several characterizations. After introducing all of the necessary fundamentals of algebraic systems, the… More

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Introduction to Modern Cryptography, Second Edition
By: Katz, Jonathan eBookCryptography is ubiquitous and plays a key role in ensuring data secrecy and integrity as well as in securing computer systems more broadly. Introduction to Modern Cryptography provides a rigorous yet accessible treatment of this fascinating subject. The authors introduce the core principles of… More

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An Introduction to Number Theory with Cryptography
By: Kraft, James S. eBookNumber theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction… More

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Graphs, Algorithms, and Optimization, Second Edition
By: William Kocay, Donald L. Kreher eBookThe second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view.… More

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Mathematical Foundations of Public Key Cryptography
By: Wang, Xiaoyun eBookIn Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and… More