Combinatorics and graph theory Books

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Book SynopsisThe theory of dynamical systems, or mappings, plays an important role in various disciplines of modern physics, including celestial mechanics and fluid mechanics. This comprehensive introduction to the general study of mappings has particular emphasis on their applications to the dynamics of the solar system. The book forms a bridge between continuous systems, which are suited to analytical developments and to discrete systems, which are suitable for numerical exploration. Featuring chapters based on lectures delivered at the School on Discrete Dynamical Systems (Aussois, France, February 1996) the book contains three parts - Numerical Tools and Modelling, Analytical Methods, and Examples of Application. It provides a single source of information that, until now, has been available only in widely dispersed journal articles.Table of Contents1. Part I: Modelling Mappings: An Aim and a Tool for the Study of Dynamical Systems 2. Spectra of Stretching Numbers and Helicity Angles 3. Diffusion and Transient Spectra in a 4-Dimensional Symplectic Mapping 4. Distribution of Periodic Orbits in 2-D Dynamical Systems 5. Symplectic Integrators 6. The Use of Mappings for Stability Problems in Beam Dynamics 7. Part II: Rigorous and Numerical Determination of Rotational Invariant Curves for the Standard Map 8. Interpolation of Discrete Hamiltonian Systems 9. Standard and Anomalous Diffusion in Dynamical Systems 10. Part III: Symplectic Maps and Their Use in Celestial Mechanics 11. Perturbation Theory for Volume Preserving Maps: Application to the Magnetic Field Lines in Plasma Physics

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Book SynopsisBiggs'' Discrete Mathematics has been a best-selling textbook since the first and revised editions were published in 1986 and 1990, respectively. This second edition has been developed in response to undergraduate course changes and changes in students'' needs. New to this edition are chapters on statements and proof, logical framework, and natural numbers and the integers, in addition to updated chapters from the previous edition. The new chapters are presented at a level suitable for mathematics and computer science students seeking a first approach to this broad and highly relevant topic. Each chapter contains newly developed tailored exercises, and miscellaneous exercises are presented throughout, providing the student with over 1000 individual tailored exercises. This edition is accompanied by a website www.oup.com/mathematics/discretemath containing hints and solutions to all exercises presented in the text, providing an invaluable resource for students and lecturers alike. The bTrade ReviewThis is a new edition of a successful textbook ... this revision is particularly welcome ... The text is written in a fluent but rigorous style and should appeal to sixthformers and undergraduates who are alienated by more formal presentations. There are plenty of approachable exercises, ranging from easy riders to establish technique to more challenging problems which introduce new ideas, and a bonus is that all the answers are available on a companion web-site. I can thoroughly recommend this text. * The Mathematical Gazette *A well known definition says that a textbook is a book such that everybody thinks he can write a better one. Biggs' Discrete Mathematics is an exception - not only for its wide range of topics and its clear organization but notably for its excellent style of explanation. * EMS *... the ideal choice for introductory courses to discrete mathematicians. * Zentralblatt MATH *Table of ContentsTHE LANGUAGE OF MATHEMATICS; TECHNIQUES; ALGORITHMS AND GRAPHS; ALGEBRAIC METHODS

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Book SynopsisMathematics of Tabletop Gamesprovides a bridge between mathematics and hobby tabletop gaming. Instead of focusing on games mathematicians play, such as nim and chomp, this book starts with the tabletop games played by avid gamers and hopes to address the question: which field of mathematics concerns itself with this situation?Readers interested in either mathematics or tabletop games will find this book an engaging way to begin exploring the other topic or the connection between the topics.Features Presents an entry-level exposition of interesting mathematical concepts that are not commonly taught outside of upper-level mathematics courses Acts as a resource for mathematics instructors who wish to provide new examples of standard mathematical concepts Features material that may help game designers and developers make design decisions about game mechanisms Provides working Python code that can be used to sol

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Book SynopsisAbout our author Richard A. Brualdi is Bascom Professor of Mathematics, Emeritus at the University of Wisconsin - Madison. He served as Chair of the Department of Mathematics from 1993-1999. His research interests lie in matrix theory and combinatorics/graph theory. Professor Brualdi is the author or co-author of 6 books, and has published extensively. He is one of the editors-in-chief of the journal Linear Algebra and its Applications and of the journal Electronic Journal of Combinatorics. He is a member of the American Mathematical Society, the Mathematical Association of America, the International Linear Algebra Society, and the Institute for Combinatorics and its Applications. He is also a Fellow of the Society for Industrial and Applied Mathematics.Table of Contents 1. What is Combinatorics? 2. The Pigeonhole Principle 3. Permutations and Combinations 4. Generating Permutations and Combinations 5. The Binomial Coefficients 6. The Inclusion-Exclusion Principle and Applications 7. Recurrence Relations and Generating Functions 8. Special Counting Sequences 9. Systems of Distinct Representatives 10. Combinatorial Designs 11. Introduction to Graph Theory 12. More on Graph Theory 13. Digraphs and Networks 14. Pólya Counting

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Book SynopsisThis textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve differential equation models or directly simulate epidemics on networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike. Trade Review“The book adds to the knowledge of epidemic modeling on networks by providing a number of rigorous mathematical arguments and confirming the validity and optimal range of applicability of the epidemic models. It serves as a good reference guide for researchers and a comprehensive textbook for graduate students.” (Yilun Shang, Mathematical Reviews, November, 2017)“This is one of the first books to appear on modeling epidemics on networks. … This is a comprehensive and well-written text aimed at students with a serious interest in mathematical epidemiology. It is most appropriate for strong advanced undergraduates or graduate students with some background in differential equations, dynamical systems, probability and stochastic processes.” (William J. Satzer, MAA Reviews, September, 2017)Table of ContentsPreface.- ​Introduction to Networks and Diseases.- Exact Propagation Models: Top Down.- Exact Propagation Models: Bottom-Up.- Mean-Field Approximations for Heterogeneous Networks.- Percolation-Based Approaches for Disease Modelling.- Hierarchies of SIR Models.- Dynamic and Adaptive Networks.- Non-Markovian Epidemics.- PDE Limits for Large Networks.- Disease Spread in Networks with Large-scale structure.- Appendix: Stochastic Simulation.- Index.

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Book SynopsisThis text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study.The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck.The courses held were: Advanced homological algebra Introduction to the representation theory of algebras Auslander-Reiten theory for algebras of infinite representation type Cluster algebras arising from surfaces Cluster tilted algebras Cluster characters Introduction to K-theory Brauer graph algebras and applications to cluster algebras Table of ContentsIntroduction to the Representation Theory of Finite-Dimensional Algebras: The Functorial Approach (M. I. Platzeck).- Auslander–Reiten Theory for Finite-Dimensional Algebras (P. Malicki).- Cluster Algebras From Surfaces (R. Schiffler).- Cluster Characters (P.-G. Plamondon).- A Course on Cluster Tilted Algebras (I. Assem).- Brauer Graph Algebras (S. Schroll).

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Book SynopsisIn China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year.The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on methods of discrete extremization, such as inequality control, repeated extremum, partial adjustment, exploiting symmetry, polishing transform, space estimates, etc.Table of ContentsInequality Control; Repeated Extremum; Partial Adjustment; Exploiting Symmetry; Polishing Transform; Space Estimates; Block Estimates; Guesses and Contradiction; Global Estimates; Parameter Estimates; Counting in Two Ways; Shrinking the Encirclement; Considering Special Cases; Solutions to Exercises;

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Book SynopsisA textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.Trade Review"This book should be a must for all mathematicians who are involved in the training of Mathematical Olympiad teams, but it will also be a valuable source of problems for university courses." Mathematical ReviewsTable of ContentsPermutations and combinations; binomial coefficients and multinomial coefficients; the Pigeonhole principle and Ramsey numbers; the principle of inclusion and exclusion; generating functions; recurrence relations.

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Book SynopsisMultilayer networks has become a central topic in Network Science. The book presents a comprehensive account of this emerging field. Multilayer networks are formed by several networks and include social networks, financial markets, multi-modal transportation systems, infrastructures, molecular networks, and the brain.Table of ContentsPart I: Single and multilayer networks 1: Complex systems as multilayer networks Part II: Single networks 2: The structure of single networks 3: The dynamics on single networks Part III: Multilayer networks 4: Multilayer networks in nature, society and infrastructures 5: The mathematical definition 6: Basic structural properties 7: Structural correlations of multiplex networks 8: Communities 9: Centrality measures 10: Multilayer network models 11: Interdependent multilayer networks 12: Classical percolation, generalized percolation and cascades 13: Epidemic spreading 14: Diffusion 15: Synchronization, non-linear dynamics and control 16: Opinion dynamics and game theory Appendix A: The Barabasi Albert model: the master equation Appendix B: Entropy and null models of single networks Appendix C: Growing multiplex networks: the master equation Appendix D: Percolation of interdependent networks Appendix E: Directed percolation of interdependent networks Appendix F: Immunization strategies on multiplex networks Appendix G: Spectrum of the Supra-Laplacian Part I: Single and multilayer networks 1: Complex systems as multilayer networks Part II: Single networks 2: The structure of single networks 3: The dynamics on single networks Part III: Multilayer networks 4: Multilayer networks in nature, society and infrastuctures 5: The mathematical definition 6: Basic structural properties 7: Structural correlations of multiplex networks 8: Communities 9: Centrality measures 10: Multilayer network models 11: Interdependent multilayer networks 12: Classical percolation, generalized percolation and cascades 13: Epidemic spreading 14: Diffusion 15: Synchronization, non-linear dynamics and control 16: Opinion dynamics and game theory Appendix A: The Barabasi Albert model: the master equation Appendix B: Entropy and null models of single networks Appendix C: Growing multiplex networks: the master equation Appendix D: Percolation of interdependent networks Appendix E: Directed percolation of interdependent networks Appendix F: Immunization strategies on multiplex networks Appendix G: Spectrum of the Supra-Laplacian

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Book SynopsisPraise for the First EditionLuck, Logic, and White Lies teaches readers of all backgrounds about the insight mathematical knowledge can bring and is highly recommended reading among avid game players, both to better understand the game itself and to improve one's skills. Midwest Book ReviewThe best book I''ve found for someone new to game math is Luck, Logic and White Lies by Jörg Bewersdorff. It introduces the reader to a vast mathematical literature, and does so in an enormously clear manner. . . Alfred Wallace, Musings, Ramblings, and Things Left UnsaidThe aim is to introduce the mathematics that will allow analysis of the problem or game. This is done in gentle stages, from chapter to chapter, so as to reach as broad an audience as possible . . . Anyone who likes games and has a taste for analytical thinking will enjoy this book. Peter Fillmore, CMS NotesLuck, Logic, and Trade Review"The book presents mathematical explanation of problems related to playing games of chance, combinatorial and strategic games, with descriptions of their historical perspectives and recreational aspects. [. . .] The author notes that people play games investigating the unknown outcomes, in amusement and hope of winning in conditions of uncertainty caused by three possible mechanisms: chance, a large number of combinations of various moves, and different states of information among the individual players. Respectively, the games can be divided to three classes: games of chance (e.g., dice, cards, roulette) where the random processes dominate the players decisions; combinatorial games (chess, go) where the uncertainty rests on the multiplicity of possible moves; and strategic games (rock-paper-scissors) where the players’ uncertainty arises from imperfect information. Many games have mixed features (backgammon, poker, skat), and the degree of influence of the three main causes of uncertainty defines specifics of each game. The book introduces mathematical methods developed for description and solutions of games: the games of chance can be analyzed with the help of probability theory, the combinatorial games are considered by variety of methods used in particular problems, and the strategic games are studied by the game theory models for decision-making in the interactive optimizing economic processes. The book is organized in four parts containing 51 chapters on various topics.[. . .] All topics are illustrated by multiple figures and numerical tables. [. . .] It can be useful to instructors, students, and readers wishing to extend understanding of the games’ intrinsic features needed to improve ability to win in actual playing."- Stan Lipovetsky, Technometrics"As the title indicates, Bewersdorff’s book is intended to span the mathematics of games in general – not only games of chance but also including strategic and skill games. The author covers all the big categories of games – casino, tournament, and house or social games. In fact, the skill-strategic dimension of the games balanced with the chance-uncertainty dimension is the central element around which the author presents games as an important field of application of mathematics; he takes them as a good opportunity to advocate for the beauty and power of mathematics. To that point, the book is written so as to be both popular and scholarly, and these attributes are not at all inconsistent with each other for such a general topic, content, and style. [. . .] The book leaves the impression of its author’s being a skilled advocate of the unlimited power of mathematics, shown through the examples of games. Not only is mathematics able to describe the games and the way we play them, but it is entitled to address fundamental questions beyond the problem-solving aspects of games and gaming. It is mainly game theory and probability theory that grant mathematics such a virtue. [. . .] Although the chapters can mostly be read independent of each other, and the mathematical content is not systematized throughout the book, the mathematically-inclined reader can put things together to have an objective overview of one of the most interesting fields in application of mathematics – games – which themselves shaped the development of mathematics."– International Gambling Studies"The author provides a great deal of insight into a wide variety of games, all inspected from a mathematical point of view. He develops the prerequisites mathematically, so that someone with a good high-school background in mathematics and a willingness to learn will be able to build up the necessary tools for successful play. Moreover, the author’s arguments are often very detailed, so that even a novice can easily follow them. The numerous diagrams also help.I find Bewersdorff's writing to be clear and detailed. He has taken care in the presentation of the ideas. The book, the size of which has now grown to 568 pages, provides a great deal of information, and the reader can easily pick and choose topics of interest without having to absorb the entire treatise. The level of Mathematical skill needed, however, does vary greatly from chapter to chapter. When necessary, the reader can make use of previous chapters to develop the required background to proceed. To the prospective reader, good luck, and may your play be a winning one!"– The Mathematical IntelligencerThis book, successor to the first edition (2005) and translated from the 7th German edition, treats games of chance (“luck”), combinatorial games (“logic”), and games of strategy (bluff, or “white lies”). The first part develops succinctly the needed theory of probability and investigates the nature of randomness. The second part explores minimax optimization, Grundy values, Conway’s theory of games, and complexity theory. The third part is based on the fact that in a symmetric two-person zero-sum game, the players are guaranteed optimal mixed strategies; for some games, finding such strategies can be done by linear programming. This edition adds a fourth part that investigates measuring the proportion of skill in a game, with particular application to poker. The reader needs to be comfortable with algebra and summation signs, and infinite series make appearances; end-of-chapter notes and footnotes contribute further mathematical depth.– Mathematics Magazine, MAA"Exceptionally well written, organized and presented, Luck, Logic, and White Lies: The Mathematics of Games is a unique and unreservedly recommended addition to professional, community, college, and university library Game Theory & Mathematics collections."– Midwest Books Review"A great variety of games are analyzed in an accessible way. The treatment of blackjack, in particular, is superb."– Stewart Ethier, Professor Emeritus, University of Utah and author of The Doctrine of Chances: Probabilistic Aspects of Gambling "People play games for fun and for profit. To become better at a game, you need to study it. In Luck, Logic and White Lies, Jörg Bewersdorff takes you, almost imperceptibly, from the history of numerous concrete games to their mathematical analysis. This touches upon a wide range of techniques, not only in mathematics, but also in computing and psychology. If you get the hang of it, you can apply these techniques to other areas of life, such as business, economics, biology, and sociology."– Tom Verhoeff, Dept. Math & CS, Eindhoven University of TechnologyPraise for the First Edition"Luck, Logic, and White Lies teaches readers of all backgrounds about the insight mathematical knowledge can bring and is highly recommended reading among avid game players, both to better understand the game itself and to improve one's skills."– Midwest Book Review"The best book I've found for someone new to game math is Luck, Logic and White Lies by Jörg Bewersdorff. It introduces the reader to a vast mathematical literature, and does so in an enormously clear manner. . ."– Alfred Wallace, Musings, Ramblings, and Things Left Unsaid"The aim is to introduce the mathematics that will allow analysis of the problem or game. This is done in gentle stages, from chapter to chapter, so as to reach as broad an audience as possible [. . .] Anyone who likes games and has a taste for analytical thinking will enjoy this book."– Peter Fillmore, CMS NotesTable of ContentsI. Games of Chance. 1. Dice and Probability. 2. Waiting for a Double. 3. Tips on Playing the Lottery: More Equal Than Equal? 4. A Fair Division: But How? 5. The Red and the Black: The Law of Large Numbers. 6. Asymmetric Dice: Are They Worth Anything? 7. Probability and Geometry. 8. Chance and Mathematical Certainty: Are They Reconcilable? 9. In Quest of the Equiprobable. 10. Winning the Game: Probability and Value. 11. Which Die Is Best? 12. A Die Is Tested. 13. The Normal Distribution: A Race to the Finish! 14. And Not Only at Roulette: The Poisson Distribution. 15. When Formulas Become Too Complex: The Monte Carlo Method. 16. Markov Chains and the Game Monopoly. 17 Blackjack: A Las Vegas Fairy Tale. II. Combinatorial Games. 18. Which Move Is Best? 19. Chances of Winning and Symmetry. 20. A Game for Three. 21. Nim: The Easy Winner! 22. Lasker Nim: Winning Along a Secret Path. 23. Black-and-White Nim: To Each His (or Her) Own. 24. A Game with Dominoes: Have We Run Out of Space Yet? 25. Go: A Classical Game with a Modern Theory. 26. Misere Games: Loser Wins! 27. The Computer as Game Partner. 28. Can Winning Prospects Always Be Determined? 29. Games and Complexity: When Calculations Take Too Long. 30. A Good Memory and Luck: And Nothing Else? 31. Backgammon: To Double or Not to Double? 32. Mastermind: Playing It Safe. III. Strategic Games. 33. Rock–Paper–Scissors: The Enemy's Unknown Plan. 34. Minimax Versus Psychology: Even in Poker? 35. Bluffing in Poker: Can It Be Done Without Psychology? 36. Symmetric Games: Disadvantages Are Avoidable, but How? 37. Minimax and Linear Optimization: As Simple as Can Be. 38. Play It Again, Sam: Does Experience Make Us Wiser? 39. Le Her: Should I Exchange? 40. Deciding at Random: But How? 41. Optimal Play: Planning Efficiently. 42. Baccarat: Draw from a Five? 43. Three-Person Poker: Is It a Matter of Trust? 44 QUAAK! Child's Play? 45 Mastermind: Color Codes and Minimax. 46. A Car, Two Goats–and a Quizmaster. IV. Epilogue: Chance, Skill, and Symmetry. 47. A Player's Inuence and Its Limits. 48. Games of Chance and Games of Skill. 49. In Quest of a Measure. 50. Measuring the Proportion of Skill. 51. Poker: The Hotly Debated Issue.

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Book SynopsisFocused on the mathematical foundations of social media analysis, Graph-Based Social Media Analysis provides a comprehensive introduction to the use of graph analysis in the study of social and digital media. It addresses an important scientific and technological challenge, namely the confluence of graph analysis and network theory with linear algebra, digital media, machine learning, big data analysis, and signal processing. Supplying an overview of graph-based social media analysis, the book provides readers with a clear understanding of social media structure. It uses graph theory, particularly the algebraic description and analysis of graphs, in social media studies.The book emphasizes the big data aspects of social and digital media. It presents various approaches to storing vast amounts of data online and retrieving that data in real-time. It demystifies complex social media phenomena, such as information diffusion, marketing and recommendationTable of ContentsGraphs in Social and Digital Media. Mathematical Preliminaries: Graphs and Matrices. Algebraic Graph Analysis. Web Search Based on Ranking. Label Propagation and Information Diffusion in Graphs. Graph-Based Pattern Classification and Dimensionality Reduction. Matrix and Tensor Factorization with Recommender System Applications. Multimedia Social Search Based on Hypergraph Learning. Graph Signal Processing in Social Media. Big Data Analytics for Social Networks. Semantic Model Adaptation for Evolving Big Social Data. Big Graph Storage, Processing and Visualization.

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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

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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.

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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

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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.

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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.

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Book SynopsisThis volume comprises 17 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The book is divided into 3 parts. The first part focuses on several domination-related concepts: broadcast domination, alliances, domatic numbers, dominator colorings, irredundance in graphs, private neighbor concepts, game domination, varieties of Roman domination and spectral graph theory. The second part covers domination in hypergraphs, chessboards, and digraphs and tournaments. The third part focuses on the development of algorithms and complexity of signed, minus and majority domination, power domination, and alliances in graphs. The third part also includes a chapter on self-stabilizing algorithms. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms.The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments and proof techniques used in the field. Table of Contents1. Glossary of Common Terms (Haynes).- Part 1. Related Parameters: 2. Broadcast Domination in Graphs (MacGillivray).- 3. Alliances and Related Domination Parameters (Haynes).- 4. Fractional Domatic, Idomatic and Total Domatic Numbers of a Graph (Goddard).- 5. Dominator and Total Dominator Colorings in Graphs (Henning).- 6. Irredundance (Mynhardt).- 7. The Private Neighbor Concept (McRae).- 8. An Introduction to Game Domination in Graphs (Henning).- 9. Domination and Spectral Graph Theory (Hoppen).- 10. Varieties of Roman Domination (Chellali).- Part 2. Domination in Selected Graph Families: 11. Domination and Total Domination in Hypergraphs (Yeo).- 12. Domination in Chessboards (Hedetniemi).- 13. Domination in Digraphs (Haynes).- Part 3. Algorithms and Complexity: 14. Algorithms and Complexity of Signed, Minus and Majority Domination (McRae).- 15. Algorithms and Complexity of Power Domination in Graphs (Mohan).- 16. Self-Stabilizing Domination Algorithms (Hedetniemi).- 17. Algorithms and Complexity of Alliances in Graphs (Hedetniemi)

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Book SynopsisThis book describes Python3 programming resources for implementing decision aiding algorithms in the context of a bipolar-valued outranking approach. These computing resources, made available under the name Digraph3, are useful in the field of Algorithmic Decision Theory and more specifically in outranking-based Multiple-Criteria Decision Aiding (MCDA). The first part of the book presents a set of tutorials introducing the Digraph3 collection of Python3 modules and its main objects, such as bipolar-valued digraphs and outranking digraphs. In eight methodological chapters, the second part illustrates multiple-criteria evaluation models and decision algorithms. These chapters are largely problem-oriented and demonstrate how to edit a new multiple-criteria performance tableau, how to build a best choice recommendation, how to compute the winner of an election and how to make rankings or ratings using incommensurable criteria. The book’s third part presents three real-world decision case studies, while the fourth part addresses more advanced topics, such as computing ordinal correlations between bipolar-valued outranking digraphs, computing kernels in bipolar-valued digraphs, testing for confidence or stability of outranking statements when facing uncertain or solely ordinal criteria significance weights, and tempering plurality tyranny effects in social choice problems. The fifth and last part is more specifically focused on working with undirected graphs, tree graphs and forests. The closing chapter explores comparability, split, interval and permutation graphs. The book is primarily intended for graduate students in management sciences, computational statistics and operations research. The chapters presenting algorithms for ranking multicriteria performance records will be of computational interest for designers of web recommender systems. Similarly, the relative and absolute quantile-rating algorithms, discussed and illustrated in several chapters, will be of practical interest to public and private performance auditors. Trade Review“The book … guides reader through each topic through sub-chapters and using links, even leading to the python.org interface for related content. From the moment reader download the Diagraph3 software, it helps reader understand with copyable code snippets and separate warning Note content. It guides reader through the operation of the algorithm through concrete, solved example.” (Rózsa Horváth–Bokor, zbMATH 1497.91004, 2022)Table of ContentsPart I: Introduction to the DIGRAPH3 Python Resources.- 1. Working with the DIGRAPH3 Python Resources.- 2. Working with Bipolar-Valued Digraphs.- 3. Working with Outranking Digraphs.- Part II: Evaluation Models and Decision Algorithms.- 4. Building a Best Choice Recommendation.- 5. How to Create a New Multiple-Criteria Performance Tableau.- 6. Generating Random Performance Tableaux.- 7. Who Wins the Election?.- 8. Ranking with Multiple Incommensurable Criteria.- 9. Rating by Sorting into Relative Performance Quantiles.- 10. Rating-by-Ranking with Learned Performance Quantile Norms.- 11. HPC Ranking of Big Performance Tableaux.- Part III: Evaluation and Decision Case Studies.- 12. Alice’s Best Choice: A Selection Case Study.- 13. The Best Academic Computer Science Depts: A Ranking Case Study.- 14. The Best Students, Where Do They Study? A Rating Case Study.- 15. Exercises.- Part IV: Advanced Topics.- 16. On Measuring the Fitness of a Multiple-Criteria Ranking.- 17. On Computing Digraph Kernels.- 18. On Confident Outrankings with Uncertain Criteria Significance Weights.- 19. Robustness Analysis of Outranking Digraphs.- 20. Tempering Plurality Tyranny Effects in Social Choice.- Part V: Working with Undirected Graphs.- 21. Bipolar-Valued Undirected Graphs.- 22. On Tree Graphs and Graph Forests.- 23. About Split, Comparability, Interval, and Permutation Graphs.

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Book SynopsisThis book details recent developments in the emerging area of plug-and-play (PnP) visual subgraph query interfaces (VQI). These PnP interfaces are grounded in the principles of human-computer interaction (HCI) and cognitive psychology to address long-standing limitations to bottom-up search capabilities in graph databases using traditional graph query languages, which often require domain experts and specialist programmers. This book explains how PnP interfaces go against the traditional mantra of VQI construction by taking a data-driven approach and giving end users the freedom to easily and quickly construct and maintain a VQI for any data sources without resorting to coding. The book walks readers through the intuitive PnP interface that uses templates where the underlying graph repository represents the socket and user-specified requirements represent the plug. Hence, a PnP interface enables an end user to change the socket (i.e., graph repository) or the plug (i.e., requirements) as necessary to automatically and effortlessly generate VQIs. The book argues that such a data-driven paradigm creates several benefits, including superior support for visual subgraph query construction, significant reduction in the manual cost of constructing and maintaining a VQI for any graph data source, and portability of the interface across diverse sources and querying applications. This book provides a comprehensive introduction to the notion of PnP interfaces, compares it to its classical manual counterpart, and reviews techniques for automatic construction and maintenance of these new interfaces. In synthesizing current research on plug-and-play visual subgraph query interface management, this book gives readers a snapshot of the state of the art in this topic as well as future research directions.Table of ContentsChapter 1 - The Future is Democratized Graphs.- Chapter 2 - Background.- Chapter 3 - The World of Visual Graph Query Interfaces: An Overview.- Chapter 4 - Plug-and-Play Visual Subgraph Query Interfaces.- Chapter 5 - The Building Block of PnP Interfaces: Canned Patterns.- Chapter 6 - Pattern Selection for Graph Databases.- Chapter 7 - Pattern Selection for Large Networks.- Chapter 8 - Maintenance of Patterns.- Chapter 9 - The Road Ahead.

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Book SynopsisThe first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are.New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises — more than a hundred in total — which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.

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Book SynopsisThis book focuses on combinatorial problems in mathematical competitions. It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions. Some enlightening and novel examples and exercises are well chosen in this book.With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems. Their mathematical culture and ability will be improved remarkably after reading this book.Table of ContentsCounting Principles and Counting Formulas; Pigeonhole Principles and Mean Value Principles; Generating Functions; Recurrence Sequence of Numbers; Classification and Method of Fractional Steps; Corresponding Method; Counting in Two Ways; Recurrence Method; Coloring Method and Evaluation Method; Proof by Contradiction and Extreme Principle; Locally Adjusted Method; Constructive Method; Combinatorial Counting Problems; Existence Problems and the Proof of Inequalities in Combinatorial Problems; Combinatorial Extremum Problems.

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Book SynopsisThis is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them.The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity.The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading.The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.

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Book SynopsisThe solutions to each problem are written from a first principles approach, which would further augment the understanding of the important and recurring concepts in each chapter. Moreover, the solutions are written in a relatively self-contained manner, with very little knowledge of undergraduate mathematics assumed. In that regard, the solutions manual appeals to a wide range of readers, from secondary school and junior college students, undergraduates, to teachers and professors.

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Book SynopsisDiscrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they've learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author's lively and friendly writing style is apTable of ContentsPreface for Instructors and Other TeachersPreface for Students and Other LearnersTheme: The Basics1 Counting and Proofs2 Sets and Logic3 Graphics and Functions4 Induction5 Algorithms with CiphersTheme I Supplement6 Binomial Coefficients and Pascal’s Triangle7 Balls and Boxes and PIE: Counting Techniques8 Recurrences9 Cutting Up Food: Counting and GeometryIII Theme: Graph Theory10 Trees11 Euler’s Formula and Applications12 Graph Traversals13 Graph ColoringTheme III Supplement: Problems on the Theme of Graph TheoryIV Other Material14 Probability and Expectation15 Fun with Cardinality16 Number Theory17 Computational ComplexityA Solutions to Check Yourself ProblemsB Solutions to Bonus Check-Yourself ProblemsC The Greek Alphabet and Some Uses for Some LettersD List of SymbolsBibliographyIndex

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Book SynopsisThis book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes.As well as exploring the basic mathematical background of finite fields and elliptic curves, Guide to Pairing-Based Cryptography offers an overview of the most recent developments in optimizations for pairing implementation. Each chapter includes a presentation of the problem it discusses, the mathematical formulation, a discussion of implementation issues, solutions accompanied by code or pseudocode, several numerical results, and references to further reading and notes. Intended as a self-contained handbook, this book is an invaluable resource for computer scientists, applied mathematicians and security professionals interested in cryptography.Table of ContentsIntroduction. Mathematical Background. Pairings. Pairing-Friendly Elliptic Curves. Miller's Algorithm. Arithmetic of Finite Fields. Final Exponentiation. Algorithms. Software Implementation. Hardware Implementation.

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Book SynopsisIncluding many algorithms described in simple terms, this book stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter.Trade Review"Cameron covers an impressive amount of material in a relatively small space...an outstanding supplement to other texts..." M. Henle, Choice"...used as a text at the senior or graduate level and is an excellent reference....The range of topics is very good." The UMAP JournalTable of ContentsPreface; 1. What is combinatorics?; 2. On numbers and counting; 3. Subsets, partitions, permutations; 4. Recurrence relations and generating functions; 5. The principle of inclusion and exclusion; 6. Latin squares and SDRs; 7. Extremal set theory; 8. Steiner triple theory; 9. Finite geometry; 10. Ramsey's theorem; 11. Graphs; 12. Posets, lattices and matroids; 13. More on partitions and permutations; 14. Automorphism groups and permutation groups; 15. Enumeration under group action; 16. Designs; 17. Error-correcting codes; 18. Graph colourings; 19. The infinite; 20. Where to from here?; Answers to selected exercises; Bibliography; Index.

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Book SynopsisCombinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. This classic volume is the first to attempt to present a thorough treatment of this theory.Trade Review' … a thorough treatment of the theory of combinatorics.' Monatshefte für Mathematik'Since the first edition almost fifteen years ago, a new generation of young mathematicians has grown up on reading this book and solving the problems at the end of each chapter, thus deepening the understanding of the results read, analyzing special cases and proving additional results. Furthermore, this monograph is an excellent reference book for those working in this area of mathematics.' Acta Sci. Math.'This is an excellent book, essential for anybody working in the field. Although written by several authors, who constitute the collective author M. Lothaire, the book makes a surprisingly compact impression. As already mentioned, it has all prerequisites for an important reference tool.' EMSTable of Contents1. Words D. Perrin; 2. Square free words and idempotent semigroups J. Berstel and C. Reutenauer; 3. Van der Waerden's theorem J. E. Pin; 4. Repetitive mappings and morphisms G. Pirillo; 5. Factorizations of free monoids D. Perrin; 6. Subwords J. Sakarovitch and I. Simon; 7. Unavoidable irregularities in words M. P. Schützenberger; 8. The critical factorization theorem Choffrut; 9. Equations in words; 10. Rearrangements of words D. Foata; 11. Words and trees R. Cori.

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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.

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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

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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

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Book SynopsisScientific visualization has always been an integral part of discovery, starting first with simplified drawings of the pre-Enlightenment and progressing to present day. Mathematical formalism often supersedes visual methods, but their use is at the core of the mental process. As historical examples, a spatial description of flow led to electromagnetic theory, and without visualization of crystals, structural chemistry would not exist. With the advent of computer graphics technology, visualization has become a driving force in modern computing. A Concise Introduction to Scientific Visualization – Past, Present, and Future serves as a primer to visualization without assuming prior knowledge. It discusses both the history of visualization in scientific endeavour, and how scientific visualization is currently shaping the progress of science as a multi-disciplinary domain. Table of ContentsPreface.- Early Visual Models.- Illustration and Analysis.- Scientific Visualization in the 19th Century.- A Convergence with Computer Science.- Recent Developments.- The Future.- Bibliography

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Book SynopsisChapter(s) “Chapter Name or No.” is/are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.Table of ContentsA stochastic algorithm for non-monotone DR-submodular maximziation over a convex set.- Flow shop scheduling problems with transportation constraints revisited.- LotterySampling: A Randomized Algorithm for the Heavy Hitters and Top-k Problems in Data Streams.- Approximation Algorithms for the Min-Max Mixed Rural Postmen Cover Problem and Its Variants.- Large k-gons in a 1.5D Terrain.- Nondeterministic Auxiliary Depth-Bounded Storage Automata and Semi-Unbounded Fan-in Cascading Circuits (Extended Abstract).-Analysis of Approximate sorting in I/O model.-Two Generalizations of Proper Coloring: Hardness and Approximability.-Approximation Algorithms for Capacitated Assignment with Budget Constraints and Applications in Transportation Systems.-On the Complexity of Minimum Maximal Acyclic Matchings.-Online non-monotone DR-submodular maximization: 1/4 approximation ratio and sublinear regret.-Fair Division with Minimal Withheld Information in Social Networks.- Facility Location Games with Ordinal Preferences.-Fully Dynamic $k$-Center Clustering with Outliers.-Refutation of Spectral Graph Theory Conjectures with Monte Carlo Search.-Online one-sided smooth function maximization.-Revisiting Maximum Satisfiability and Related Problems in Data Streams.-Turing Machines with Two-level Memory: A Deep Look into the Input/Output Complexity.- A quantum version of Pollard's Rho of which Shor's Algorithm is a particular case.-Single machine scheduling with rejection to minimize the $k$-th power of the makespan.- Escape from the Room.- Algorithms for hard-constraint point processes via discretization.-Space Limited Graph Algorithms on Big Data Counting Cycles on Planar Graphs in Subexponential Time.-Semi-strict chordal digraphs.- Reallocation Problems with Minimum Completion Time.-The bound coverage problem by aligned disks in L1 metric.-Facility Location Games with Group Externalities.- Some New Results on Gallai Theorem and Perfect Matching for k-Uniform Hypergraphs.- Refined Computational Complexities of Hospitals/Residents Problem with Regional Caps.- Customizable Hub Labeling: Properties and Algorithms Linear-Time Algorithm for Paired-Domination on Distance-Hereditary Graphs.-Bounding the Number of Eulerian Tours in Undirected Graphs.- A Probabilistic Model Revealing Shortcomings in Lua's Hybrid Tables.- A 4-Space Bounded.- Approximation Algorithm \\for Online Bin Packing Problem.-Generalized Sweeping Line Spanners.- Rooting Gene Trees via Phylogenetic Networks.- An evolving network model from clique extension.- Online semi-matching problem with two heterogeneous sensors in a metric space.- Two-Stage BP Maximization under $p$-matroid Constraint.- The Hamiltonian Path Graph is Connected for Simple $s,t$ Paths in Rectangular Grid Graphs.- An $O(n^3)$-Time Algorithm for the Min-Gap.- Unit-Length Job Scheduling Problem.- Approximation Schemes for k-Facility Location.- Improved Deterministic Algorithms for Non-monotone Submodular Maximization.- Distributed Dominating Sets in Interval Graphs.- Optimal Window Queries on Line Segments using the Trapezoidal Search DAG.- On Rotation Distance, Transpositions and Rank Bounded Trees.- Hitting Geometric Objects Online via Points in $\mathbb{Z}^d$.- Capacitated Facility Location with Outliers/Penalties Improved Separated Red Blue Center Clustering.- Proper colorability of segment intersection graphs.

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Book SynopsisThis textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.Table of ContentsPreface.- List of Algorithms.- List of Bibliographical Notes.- Part 1. Topics in network optimisation.- 1. An introduction to graphs.- 2. Graph connectedness.- 3. Algorithmic complexity.- 4. Optimal paths.- 5. Trees.- 6. Location problems.- 7. Maximum flow networks.- 8. Minimum-cost network flows.- Part 2. Topics in classical graph theory.- 9. Matchings.- 10. Eulerian graphs.- 11. Hamiltonian graphs.- 12. Graph connectivity.- 13. Planarity.- 14. Graph colouring.- 15. Oriented graphs. Part 3. Topics in modern graph theory.- 16. Domination in graphs.- 17. Ramsey Theory.- 18. Extremal graph theory.- 19. Graph enumeration.- 20. The probabilistic method.- Index.

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Book SynopsisMagic tricks can be easy to perform and have an interesting mathematical foundation. In this rich, colourfully illustrated volume, Ehrhard Behrends presents around 30 card tricks and number games that are easy to learn, with no prior knowledge required. This is maths as you've never experienced it before: entertaining and fun!Table of Contents You can count on it Let's mix it up! Optimally packaged information: Coding Chance makes magic Appendix References.

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Book SynopsisTrade Review"Visualizing Music provides a rich visual overview of the discipline of music theory while offering practical suggestions for scholars."—Timothy Koozin, Moores School of Music, University of HoustonTable of ContentsPrefaceAcknowledgmentsAccessing Audiovisual MaterialsIntroductionPart 1: Preliminaries1. Leveraging the Power of the Brain2. The Role of Metaphor3. Multivariate Images4. Telling a Story5. Facilitating Comparison6. Information Layers7. Information Integration8. Making Every Part of an Image Count9. Presenting Tabular Data10. Small Multiples11. Using Color12. Additional General Principles13. Case Study: Western NotationPart 2: Musical Spaces14. Pitch Spaces15. Collections, Scales, and Modes16. The Circle of Fifths17. The Tonnetz18. Atonal Spaces19. Symmetrical Pitch Structures20. Tonal Hierarchy, Tendency, Progression21. The Overtone SeriesPart 3: Musical Time22. Basic Durations23. Unmeasured Musical Time24. Musically Measured Musical Time25. Externally Measured Musical Time (Performance Timing)26. ProportionPart 4: Pitch, Texture, Timbre, Form27. Textual Representations of Pitch28. Piano Roll Notation29. Alternate Notational Systems30. Tuning and Temperament31. Microtuning32. Timbre33. Texture34. Voice Leading35. Schematic and Procedural Representations36. Formal Models37. Pitch-Class Set Tables38. Instrument Ranges39. TranslationsPart 5: Music Analysis40. Lutosławksi's Jeux Venitiens41. Annotating Musical Scores42. Thematic Analysis43. Contour Analysis44. Tonal Plans45. Symmetry in Music Analysis46. Rhythmic Analysis47. Formal Analysis48. Hierarchy in Music49. Serialism50. Corpus Studies51. Musical Chronologies, Influences, and Styles52. AnimationPart 6: Visualization in the Professional Realm53. Conference Handouts54. Presentation Slide Shows55. Conference Posters56. Print Publication57. The Essential Visualization ToolboxEpilogueBibliographyIndex

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Book SynopsisTable of ContentsAutomated theorem proving: a quarter century review by D. W. Loveland Citation to Hao Wang Computer theorem proving and artificial intelligence by H. Wang Citation to Lawrence Wos and Steven Winker Open questions solved with the assistance of AURA by L. Wos and S. Winker Some automatic proofs in analysis by W. W. Bledsoe Proof-checking, theorem-proving, and program verification by R. S. Boyer and J. S. Moore A mechanical proof of the turing completeness of pure LISP by R. S. Boyer and J. S. Moore Automating higher-order logic by P. B. Andrews, D. A. Miller, E. L. Cohen, and F. Pfenning Abelian group unification algorithms for elementary terms by D. Lankford, G. Butler, and B. Brady Combining satisfiability procedures by equality sharing by G. Nelson On the decision problem and the mechanization of theorem-proving in elementary geometry by W. Wen-Tsun Some recent advances in mechanical theorem-proving of geometries by W. Wen-Tsun Proving elementary geometry theorems using Wu's algorithm by S.-C. Chou Automated theory formation in mathematics by D. B. Lenat Student use of an interactive theorem prover by J. McDonald and P. Suppes.

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Book SynopsisEnumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years'' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the RedfieldPólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.Trade Review'It's indeed a very good introduction to enumerative combinatorics and has all the trappings of a pedagogically sound enterprise, in the old-fashioned sense: exercises, good explanations (not too terse, but certainly not too wordy), and mathematically serious (nothing namby-pamby here). It's an excellent book.' Michael Berg, MAA Reviews'Cameron's Notes on Counting is a clever introductory book on enumerative combinatorics … Overall, the text is well-written with a friendly tone and an aesthetic organization, and each chapter contains an ample number of quality exercises. Summing Up: Recommended.' A. Misseldine, CHOICETable of Contents1. Introduction; 2. Formal power series; 3. Subsets, partitions and permutations; 4. Recurrence relations; 5. The permanent; 6. q-analogues; 7. Group actions and cycle index; 8. Mobius inversion; 9. The Tutte polynomial; 10. Species; 11. Analytic methods: a first look; 12. Further topics; 13. Bibliography and further directions; Index.

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Book SynopsisWick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the HudsonParthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by WallstromRota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a ''field calculus'' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, DysonSchwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathemaTrade Review'This book offers an excellent account of the probabilistic aspects of quantum theory, focused on the interplay between quantum field theory and quantum stochastic calculus. The text is highly accessible thanks to the careful choice of topics and the systematic use of elegant combinatorial and algebraic methods. This makes the book suitable for graduate level teaching and self-study. I highly recommend it as a timely addition to the classical literature on quantum probability.' Madalin Guta, University of NottinghamTable of ContentsPreface; Notation; 1. Introduction to combinatorics; 2. Probabilistic Moments and Cumulants; 3. Quantum probability; 4. Quantum fields; 5. Combinatorial species; 6. Combinatorial aspects of quantum fields: Feynman diagrams; 7. Entropy, large deviations and legendre transforms; 8. Introduction to Fock spaces; 9. Operators and fields on the Boson Fock space; 10. L2-representations of the Boson Fock space; 11. Local fields on the Boson Fock space: free fields; 12. Local fields on the Boson Fock space: interacting fields; 13. Quantum stochastic calculus; 14. Quantum stochastic limits; Bibliography; Index.

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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.

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Book SynopsisThis 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, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for mTrade Review'David Eppstein has managed to unify a huge swath of research on planar point sets through monotone properties and forbidden configurations. For example, finding grid points that avoid the obstacle of a 3-point line is a century-old problem still not entirely resolved. The author's unification naturally uncovers research lacuna, several of which he fills, while others are formulated as sharp new open problems. This rare synthesis of previous work will reinvigorate and redirect the field.' Joseph O'Rourke, Smith College, Massachusetts'David Eppstein takes us on an adventure tour to the study of point configurations in Discrete Geometry. It visits many different topics, connected by the original viewpoint of 'forbidden configurations'. This is interesting, instructive - and fun!' Günter M. Ziegler, Freie Universität Berlin'This unique volume collects and unifies almost a century of work on point configurations on the plane, and their properties that depend on whether each subset of three points is oriented clockwise, oriented counterclockwise, or collinear. Beginning with the Happy Ending Theorem, the author takes us through entertaining problems and into computational geometry. A delight to read as well as a persuasive case for the method of forbidden configurations, the book will be a valuable addition to the library of any discrete or computational geometer.' Peter Winkler, Dartmouth College, New Hampshire'This is a fun read on certain topics in discrete and computational geometry. It begins with 'A Happy Ending' and ends with 'Only the Beginning'. Eppstein's journey through various problems of pointset configurations offers a new view of the subject even to experts of the field. Recommended to everyone who likes geometry and computer science.' Jozsef Solymosi, University of British Columbia'David Eppstein has brought the weight of his formidable expertise and expositional talents on the simplest of shapes: points and lines. He gently guides the reader through a vast array of fascinating topics, their greatest hits to the state-of-the-art. This lovely book will be found on the shelves of mathematicians and computer scientists for many years to come.' Satyan Devadoss, University of San Diego'Erdős's many beautiful, notoriously difficult geometric problems on finite point configurations led to the birth of a new discipline: combinatorial geometry. The field gained additional significance in the 1980s, when it was discovered to be relevant to basic questions in computational geometry. Eppstein's elegantly written and illustrated book takes a fresh algorithmic look at the theory of forbidden geometric patterns. It can be read by specialists as a survey, but it can also serve as an excellent textbook for an introductory course on point configurations.' János Pach, École Polytechnique Fédérale de Lausanne and Rényi Institute, Budapest'There is a lot to like about this book, as Eppstein does a good job of introducing the material to his readers … A reader who sticks with Eppstein will learn a lot about this exciting area that lies on the border of mathematics and computer science.' Darren Glass, MAA Reviews'The result is a first-class treatment: Eppstein deftly sells the subject to the uninitiated, yet carries it to depths experts will appreciate. A generous supply of diagrams gracefully projects many ideas, and the professional-quality design makes the reading experience a pleasure. Summing Up: Highly recommended.' D. V. Feldman, Choice'The book is a great read. It is a valuable addition to the library of any discrete or computational geometer. Moreover, it can also serve as an excellent textbook for an introductory course on point configurations.' László Szabó, MathSciNet'This book is distinguished by a number of attractive features. Perhaps most prominent is its strong unity of approach. The first 7 chapters establish a coherent foundation and language for expressing and investigating the subjects studied in the remaining 10 … Another is its clarity of presentation and reader-friendliness. In most chapters the author adopts the strategy of introducing the topic in terms of an easily-understood problem that is accessible to virtually any reader … If you have any interest in learning about this field, I highly recommend this book.' Frederic Green, SIGACT NewsTable of Contents1. A happy ending; 2. Overview; 3. Configurations; 4. Subconfigurations; 5. Properties, parameters, and obstacles; 6. Computing with configurations; 7. Complexity theory; 8. Collinearity; 9. General position; 10. General-position partitions; 11. Convexity; 12. More on convexity; 13. Integer realizations; 14. Stretched permutations; 15. Configurations from graphs; 16. Universality; 17. Stabbing; 18. The big picture.

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Book SynopsisFamous mathematical constants include the ratio of circular circumference to diameter, p = 3.14 , and the natural logarithm base, e = 2.718 . Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, PoissonVoronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, PrandtlBlasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, GaltonWatson trees, electrical capacitance (from potential theory), Zermelo''s navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly atTrade Review'Like the best sequels, this one covers similar ground to the original but finds ways to stay fresh and interesting … any mathematician or math student who picks it up and spends a few minutes with it is likely to find something that is new and of interest to them. … Finch has once again written a collection of essays about a wide range of topics that I expect I will enjoy flipping through for another decade and a half until I look forward to having Volume III land on my desk.' Darren Glass, MAA reviews'This is a remarkable book … [which] can be thought of as a collection of essays that recount stories that are both successful and tangible.' Paul F. Bracken, MathSciNet'Some of the most intriguing formulas of mathematics (like those of Ramanujan) adorn this treasure trove of mathematical gems … Steven R. Finch's incredible labor of love, an encyclopedia of mathematical constants … contain a total of 269 meticulously documented essays from all fields of mathematics.' Osmo Peokonen, The Mathematical Intelligencer'Taken together, Mathematical Constants and Mathematical Constants II form a comprehensive and unique work that is a welcome addition to the mathematician's reference library.' Steven R. Finch, Notices of the AMS'Great care is taken about numerical results and the precise determination of constants. The choice of the material complements the first volume; overall, the topics seem also to be more advanced, but every now and then there is a little pearl which is indeed accessible at high school level. The text is certainly not intended for linear reading - although this might well be possible - but for eclectic readers who want to enjoy themselves and broaden their horizons, or for researchers who need information on a particular constant and further stepping stones.' Rene L. Schilling, The Mathematical Gazette'Great care is taken about numerical results and the precise determination of constants. The choice of the material complements the first volume; overall, the topics seem also to be more advanced, but every now and then there is a little pearl which is indeed accessible at high school level. The text is certainly not intended for linear reading - although this might well be possible - but for eclectic readers who want to enjoy themselves and broaden their horizons, or for researchers who need information on a particular constant and further stepping stones.' Rene L. Schilling, The Mathematical GazetteTable of Contents1. Number theory and combinatorics; 2. Inequalities and approximation; 3. Real and complex analysis; 4. Probability and stochastic processes; 5. Geometry and topology; Index.

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