## Similar

Key features of Number Theory: Structures, Examples, and Problems:

* A rigorous exposition starts with the natural numbers and the basics.

* Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.

* Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.

* Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.

* Glossary, bibliography, and comprehensive index round out the text.

Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.

The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces.

The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Readership: Undergraduates, graduates and mathematicians.

keywords:Binomial Coefficients;Multinomial Coefficients;Euler Ï-Function;Enumerative Combinatorics;Addition Principle;Multiplication Principle;Combination;Permutation;Identities;Pigeon Hole Principle;Ramsey Numbers;Principle of Inclusion and Exclusion;Stirling Numbers;Derangements;Problem of MÃ©nages;Sieve of Eratosthenes;Generating Functions;Partitions of Integers;Exponential Generating Functions;Recurrence Relations;Characteristic Polynomial;Catalan Numbers

“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 Reviews“This book should be an essential part of the personal library of every practicing statistician.”—Technometrics

Thoroughly revised and updated, the new edition of Nonparametric Statistical Methods includes additional modern topics and procedures, more practical data sets, and new problems from real-life situations. The book continues to emphasize the importance of nonparametric methods as a significant branch of modern statistics and equips readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for any given situation.

Written by leading statisticians, Nonparametric Statistical Methods, Third Edition provides readers with crucial nonparametric techniques in a variety of settings, emphasizing the assumptions underlying the methods. The book provides an extensive array of examples that clearly illustrate how to use nonparametric approaches for handling one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. In addition, the Third Edition features:

The use of the freely available R software to aid in computation and simulation, including many new R programs written explicitly for this new edition New chapters that address density estimation, wavelets, smoothing, ranked set sampling, and Bayesian nonparametrics Problems that illustrate examples from agricultural science, astronomy, biology, criminology, education, engineering, environmental science, geology, home economics, medicine, oceanography, physics, psychology, sociology, and space science Nonparametric Statistical Methods, Third Edition is an excellent reference for applied statisticians and practitioners who seek a review of nonparametric methods and their relevant applications. The book is also an ideal textbook for upper-undergraduate and first-year graduate courses in applied nonparametric statistics.Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book’s computational approach helps you get a solid start.

Use your existing programming skills to learn and understand Bayesian statisticsWork with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testingGet started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockeyLearn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome.Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9 shows how to mix known algorithms and create new ones, while Chapter 10 presents the "Chop-Sticks" algorithm, used to obtain all minimum cuts in an undirected network without applying traditional maximum flow techniques. This algorithm has led to the new mathematical specialty of network algebra. The text assumes no background in linear programming or advanced data structure, and most of the material is suitable for undergraduates. 153 black-and-white illus. 23 tables. Exercises, with answers at the ends of chapters.

Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery.

Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.

Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems.

Elementary exercises at the end of each expository section prompt students to review the material Try This! sections encourage students to construct fundamental components of the concepts, theorems, and proofs discussed. Sets of discovery problems and illustrative examples reinforce learning. Bonus sections can be used for take-home exams, projects, or further study Instructor Notes sections offer suggestions on how to use the material in each chapter

Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics.

The authors introduce the core principles of modern cryptography, with an emphasis on formal definitions, clear assumptions, and rigorous proofs of security. The book begins by focusing on private-key cryptography, including an extensive treatment of private-key encryption, message authentication codes, and hash functions. The authors also present design principles for widely used stream ciphers and block ciphers including RC4, DES, and AES, plus provide provable constructions of stream ciphers and block ciphers from lower-level primitives. The second half of the book covers public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, and El Gamal cryptosystems (and others), followed by a thorough treatment of several standardized public-key encryption and digital signature schemes.

Integrating a more practical perspective without sacrificing rigor, this widely anticipated Second Edition offers improved treatment of:

Stream ciphers and block ciphers, including modes of operation and design principles Authenticated encryption and secure communication sessions Hash functions, including hash-function applications and design principles Attacks on poorly implemented cryptography, including attacks on chained-CBC encryption, padding-oracle attacks, and timing attacks The random-oracle model and its application to several standardized, widely used public-key encryption and signature schemes Elliptic-curve cryptography and associated standards such as DSA/ECDSA and DHIES/ECIESContaining updated exercises and worked examples, Introduction to Modern Cryptography, Second Edition can serve as a textbook for undergraduate- or graduate-level courses in cryptography, a valuable reference for researchers and practitioners, or a general introduction suitable for self-study.

Every chapter in SRRSLEH matches the corresponding chapter of DMwD. Chapters in SRRSLEH contain the following:

A list of the notation introduced in the corresponding chapter A list of definitions that students need to know from the corresponding chapter Theorems/facts of note appearing in the corresponding chapter A list of proof techniques introduced, with templates and/or examples given for each one A selection of examples from DMwD, written out formally and briefly rather than colloquially as in DMwDA quick refresher for any discrete math student, this handbook enables students to find information easily and reminds them of the terms and results they should know during their course.

Read reviews of DMwD.

Algebra, Logic and Combinatorics is the third volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Contents:Enumerative Combinatorics (Peter J Cameron)Introduction to the Finite Simple Groups (Robert A Wilson)Introduction to Representations of Algebras and Quivers (Anton Cox)The Invariant Theory of Finite Groups (Peter Fleischmann and James Shank)Model Theory (Ivan Tomašić)

Readership: Researchers, graduate or PhD mathematical-science students who require a reference book that covers algebra, logic or combinatorics.

This classroom-tested book covers the main subjects of a standard undergraduate probability course, including basic probability rules, standard models for describing collections of data, and the laws of large numbers. It also discusses several more advanced topics, such as the ballot theorem, the arcsine law, and random walks, as well as some specialized poker issues, such as the quantification of luck and skill in Texas Hold’em. Homework problems are provided at the end of each chapter.

The author includes examples of actual hands of Texas Hold’em from the World Series of Poker and other major tournaments and televised games. He also explains how to use R to simulate Texas Hold’em tournaments for student projects. R functions for running the tournaments are freely available from CRAN (in a package called holdem).

See Professor Schoenberg discuss the book.

Translated from a well-known Russian work entitled Non-Elementary Problems in an Elementary Exposition, the chief aim of the book is to acquaint the readers with a variety of new mathematical facts, ideas, and methods. And while the majority of the problems represent questions in higher ("non-elementary") mathematics, most can be solved with elementary mathematics. In fact, for the most part, no knowledge of mathematics beyond a good high school course is required.

Volume One contains 100 problems, with detailed solutions, all dealing with probability theory and combinatorial analysis. Topics include the representation of integers as sums and products, combinatorial problems on the chessboard, geometric problems on combinatorial analysis, problems on the binomial coefficients, problems on computing probabilities, experiments with infinitely many possible outcomes, and experiments with a continuum of possible outcomes.

Volume Two contains 74 problems from various branches of mathematics, dealing with such topics as points and lines, lattices of points in the plane, topology, convex polygons, distribution of objects, nondecimal counting, theory of primes, and more. In both volumes the statements of the problems are given first, followed by a section giving complete solutions. Answers and hints are given at the end of the book.

Ideal as a text, for self-study, or as a working resource for a mathematics club, this wide-ranging compilation offers 174 carefully chosen problems that will test the mathematical acuity and problem-solving skills of almost any student, teacher, or mathematician.

This book will be useful to everyone who has struggled with displaying data in an informative and attractive way. Some basic knowledge of R is necessary (e.g., importing data into R). ggplot2 is a mini-language specifically tailored for producing graphics, and you'll learn everything you need in the book. After reading this book you'll be able to produce graphics customized precisely for your problems, and you'll find it easy to get graphics out of your head and on to the screen or page.

The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces.

The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

The prediction of failures involves uncertainty, and problems associated with failures are inherently probabilistic. Their solution requires optimal tools to analyze strength of evidence and understand failure events and processes to gauge confidence in a design’s reliability.

Reliability Engineering and Risk Analysis: A Practical Guide, Second Edition has already introduced a generation of engineers to the practical methods and techniques used in reliability and risk studies applicable to numerous disciplines. Written for both practicing professionals and engineering students, this comprehensive overview of reliability and risk analysis techniques has been fully updated, expanded, and revised to meet current needs. It concentrates on reliability analysis of complex systems and their components and also presents basic risk analysis techniques. Since reliability analysis is a multi-disciplinary subject, the scope of this book applies to most engineering disciplines, and its content is primarily based on the materials used in undergraduate and graduate-level courses at the University of Maryland. This book has greatly benefited from its authors' industrial experience. It balances a mixture of basic theory and applications and presents a large number of examples to illustrate various technical subjects. A proven educational tool, this bestselling classic will serve anyone working on real-life failure analysis and prediction problems.

Imhausen shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. Imhausen looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. She draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why.

Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, Mathematics in Ancient Egypt sheds new light on a civilization's unique mathematical evolution.

The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues.

The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.

The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine.

What else is new?

New chapters on measurement and analytic graph theory

Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing.

Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth

Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition

Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader

Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as well as how it contrasts with the conventional approach. The theory is built up step by step, and important notions such as sufficiency are brought out of a discussion of the salient features of specific examples.

This edition:

Includes expanded coverage of Gibbs sampling, including more numerical examples and treatments of OpenBUGS, R2WinBUGS and R2OpenBUGS. Presents significant new material on recent techniques such as Bayesian importance sampling, variational Bayes, Approximate Bayesian Computation (ABC) and Reversible Jump Markov Chain Monte Carlo (RJMCMC). Provides extensive examples throughout the book to complement the theory presented. Accompanied by a supporting website featuring new material and solutions.More and more students are realizing that they need to learn Bayesian statistics to meet their academic and professional goals. This book is best suited for use as a main text in courses on Bayesian statistics for third and fourth year undergraduates and postgraduate students.

Strengthening the analytic flavor of the book, this Second Edition:

Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions Demonstrates powerful techniques that do not require the residue theorem or complex integration Adds new exercises to all chapters, significantly extending coverage of the given topicsIntroduction to Enumerative and Analytic Combinatorics, Second Edition makes combinatorics more accessible, increasing interest in this rapidly expanding field.

The first part of the book presents the syntax and semantics of access control logic, basic access control concepts, and an introduction to confidentiality and integrity policies. The second section covers access control in networks, delegation, protocols, and the use of cryptography. In the third section, the authors focus on hardware and virtual machines. The final part discusses confidentiality, integrity, and role-based access control.

Taking a logical, rigorous approach to access control, this book shows how logic is a useful tool for analyzing security designs and spelling out the conditions upon which access control decisions depend. It is designed for computer engineers and computer scientists who are responsible for designing, implementing, and verifying secure computer and information systems.

Written by well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting introduces combinatorics alongside modern techniques, showcases the interdisciplinary aspects of the topic, and illustrates how to problem solve with a multitude of exercises throughout. The authors' approach is very reader-friendly and avoids the "scholarly tone" found in many books on this topic.

Concepts are presented in a readable and accessible manner, and applications are stressed throughout so the reader never loses sight of the powerful tools graph theory provides to solve real-world problems. Such diverse areas as job assignment, delivery truck routing, location of emergency or service facilities, network reliability, zoo design, exam scheduling, error-correcting codes, facility layout, and the critical path method are covered.

"An important contribution to the applied statistics literature.... I give the book high marks for unifying and making accessible much of the past and current work in this important area."

—William E. Strawderman, Rutgers University

"This book...provide[s] interesting real-life examples, stimulating end-of-chapter exercises, and up-to-date references. It should be on every applied statistician’s bookshelf."

—The Statistician

"The book should be studied in the statistical methods department in every statistical agency."

—Journal of Official Statistics

Statistical analysis of data sets with missing values is a pervasive problem for which standard methods are of limited value. The first edition of Statistical Analysis with Missing Data has been a standard reference on missing-data methods. Now, reflecting extensive developments in Bayesian methods for simulating posterior distributions, this Second Edition by two acknowledged experts on the subject offers a thoroughly up-to-date, reorganized survey of current methodology for handling missing-data problems.

Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe rigorous yet simple methods for multivariate analysis with missing values. They then provide a coherent theory for analysis of problems based on likelihoods derived from statistical models for the data and the missing-data mechanism and apply the theory to a wide range of important missing-data problems.

The new edition now enlarges its coverage to include:

Expanded coverage of Bayesian methodology, both theoretical and computational, and of multiple imputation Analysis of data with missing values where inferences are based on likelihoods derived from formal statistical models for the data-generating and missing-data mechanisms Applications of the approach in a variety of contexts including regression, factor analysis, contingency table analysis, time series, and sample survey inference Extensive references, examples, and exercisesAmstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Statistical Analysis With Missing Data was among those chosen.

Key features:

A coherent approach to evidence synthesis from multiple sources. Focus is given to Bayesian methods for evidence synthesis that can be integrated within cost-effectiveness analyses in a probabilistic framework using Markov Chain Monte Carlo simulation. Provides methods to statistically combine evidence from a range of evidence structures. Emphasizes the importance of model critique and checking for evidence consistency. Presents numerous worked examples, exercises and solutions drawn from a variety of medical disciplines throughout the book. WinBUGS code is provided for all examples.Evidence Synthesis for Decision Making in Healthcare is intended for health economists, decision modelers, statisticians and others involved in evidence synthesis, health technology assessment, and economic evaluation of health technologies.

New to the Third Edition

Reorganized material to reflect a more natural order of topics 278 new exercises and examples as well as better solutions to the problems New introductory chapter on stochastic processes More practical, nontrivial applications of probability and stochastic processes in finance, economics, and actuarial sciences, along with more genetics examples New section on survival analysis and hazard functions More explanations and clarifying comments in almost every sectionThis versatile text is designed for a one- or two-term probability course for majors in mathematics, physical sciences, engineering, statistics, actuarial science, business and finance, operations research, and computer science. It also accessible to students who have completed a basic calculus course.

The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.

Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.

This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.

Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian modelsChapter 3 contains an extended treatment of the principle of inclusion and exclusion which is indispensable to the enumeration of permutations with restricted position given in Chapters 7 and 8. Chapter 4 examines the enumeration of permutations in cyclic representation and Chapter 5 surveys the theory of distributions. Chapter 6 considers partitions, compositions, and the enumeration of trees and linear graphs.

Each chapter includes a lengthy problem section, intended to develop the text and to aid the reader. These problems assume a certain amount of mathematical maturity. Equations, theorems, sections, examples, and problems are numbered consecutively in each chapter and are referred to by these numbers in other chapters.

Balancing abstract ideas with specific topical coverage, the book utilizes real world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include:

• Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and/or short answers

• Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods

• A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations

• Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts

• A chapter-by-chapter review to clarify the most crucial concepts covered

Combinatorial Reasoning: An Introduction to the Art of Counting is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics.

In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous parameter Markov processes, and quasi-birth-and-death processes, to name a few. It describes a variety of applications including computer-communication networks, information systems, production operations, transportation, and service systems such as healthcare, call centers and restaurants.

This edition now offers a thorough development of the embedding of Latin squares and combinatorial designs. It also presents some pure mathematical ideas, including connections between universal algebra and graph designs.

The authors focus on several basic designs, including Steiner triple systems, Latin squares, and finite projective and affine planes. They produce these designs using flexible constructions and then add interesting properties that may be required, such as resolvability, embeddings, and orthogonality. The authors also construct more complicated structures, such as Steiner quadruple systems.

By providing both classical and state-of-the-art construction techniques, this book enables students to produce many other types of designs.

With a focus on statistical models as producers of data, the book enables students to more easily understand the machinery of advanced statistics. It also downplays the "population" interpretation of statistical models and presents Bayesian methods before frequentist ones. Requiring no prior calculus experience, the text employs a "just-in-time" approach that introduces mathematical topics, including calculus, where needed. Formulas throughout the text are used to explain why calculus and probability are essential in statistical modeling. The authors also intuitively explain the theory and logic behind real data analysis, incorporating a range of application examples from the social, economic, biological, medical, physical, and engineering sciences.

Enabling your students to answer the why behind statistical methods, this text teaches them how to successfully draw conclusions when the premises are flawed. It empowers them to use advanced statistical methods with confidence and develop their own statistical recipes. Ancillary materials are available on the book’s website.

Divided into 11 cohesive sections, the handbook’s 44 chapters focus on graph theory, combinatorial optimization, and algorithmic issues. The book provides readers with the algorithmic and theoretical foundations to:

Understand phenomena as shaped by their graph structures Develop needed algorithmic and optimization tools for the study of graph structures Design and plan graph structures that lead to certain desirable behavior

With contributions from more than 40 worldwide experts, this handbook equips readers with the necessary techniques and tools to solve problems in a variety of applications. Readers gain exposure to the theoretical and algorithmic foundations of a wide range of topics in graph theory and combinatorial optimization, enabling them to identify (and hence solve) problems encountered in diverse disciplines, such as electrical, communication, computer, social, transportation, biological, and other networks.

This classroom-tested book covers the main subjects of a standard undergraduate probability course, including basic probability rules, standard models for describing collections of data, and the laws of large numbers. It also discusses several more advanced topics, such as the ballot theorem, the arcsine law, and random walks, as well as some specialized poker issues, such as the quantification of luck and skill in Texas Hold’em. Homework problems are provided at the end of each chapter.

The author includes examples of actual hands of Texas Hold’em from the World Series of Poker and other major tournaments and televised games. He also explains how to use R to simulate Texas Hold’em tournaments for student projects. R functions for running the tournaments are freely available from CRAN (in a package called holdem).

See Professor Schoenberg discuss the book.

Suitable for middle school age readers, the book traces Leibniz’s life from his early years as a young boy and student to his later work as a court historian. It discusses the intellectual and social climate in which he fought for his ideas, including his rather contentious relationship with Newton (both claimed to have invented calculus). The text describes how Leibniz developed the first mechanical calculator that could handle addition, subtraction, multiplication, and division. It also examines his passionate advocacy of rational arguments in all controversial matters, including the law, expressed in his famous exclamation calculemus: let us calculate to see who is right.

Leibniz made groundbreaking contributions to mathematics and philosophy that have shaped our modern views of these fields.

Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.

Contents:Preliminaries:SetsManifoldsCurvesTransversalityRegular deformationsComplexesFilling Dehn Surfaces:Dehn Surfaces in 3-manifoldsFilling Dehn SurfacesNotationSurgery on Dehn Surfaces. Montesinos TheoremJohansson Diagrams:Diagrams Associated to Dehn SurfacesAbstract Diagrams on SurfacesThe Johansson TheoremFilling DiagramsFundamental Group of a Dehn Sphere:Coverings of Dehn SpheresThe Diagram GroupCoverings and RepresentationsApplicationsThe Fundamental Group of a Dehn g-torusFilling Homotopies:Filling HomotopiesBad Haken Moves"Not so Bad" Haken MovesDiagram MovesDuplicationAmendola's MovesProof of Theorem 5.8:Pushing DisksShellings. Smooth TriangulationsComplex f-movesInflating TriangulationsFilling PairsSimultaneous GrowingsProof of Theorem 5.8The Triple Point Spectrum:The Shima's SpheresSome Examples of Filling Dehn SurfacesThe Number of Triple Points as a Measure of Complexity: Montestinos ComplexityThe Triple Point SpectrumSurface-complexityKnots, Knots and Some Open Questions:2-Knots: Lifting Filling Dehn Surfaces1-KnotsOpen Problems

Readership: Graduate students and researchers interested in low-dimensional topology.

Key Features:It provides deep results in a new subject of mathematical research. Moreover, it introduces new mathematical tools and techniques useful in different areas of low-dimensional topologyThe book uses topological and combinatorial tools developed all along the twentieth century making the volume a trip along the history of low-dimensional topologyA spectacular set of pictures, in the better tradition of low-dimensional topology books, which give deep insight of the techniques and constructions done in the book

The book provides a conceptual understanding of probability and its structure. It is intended to augment existing calculus-based textbooks on probability and statistics and is specifically targeted to researchers and advanced undergraduate and graduate students in the applied research fields of the social sciences, psychology, and health and healthcare sciences.

Materials are presented in three sections. The first section provides an overall introduction and presents some mathematical concepts used throughout the rest of the text. The second section presents the basic structure of measure theory and its special case of probability theory. The third section provides the connection between a conceptual understanding of measure-theoretic probability and applied research. This section starts with a chapter on its use in understanding basic models and finishes with a chapter that focuses on more complicated problems, particularly those related to various types and definitions of analyses related to hierarchical modeling.

In a clear and refreshing departure from this trend, Introducing Game Theory and its Applications presents an easy-to-read introduction to the basic ideas and techniques of game theory. After a brief introduction, the author begins with a chapter devoted to combinatorial games--a topic neglected or treated minimally in most other texts. The focus then shifts to two-person zero-sum games and their solution. Here the author presents the simplex method, based on linear programming, for solving these games and develops within his presentation the required background in linear programming. The final chapter presents some of the fundamental ideas and tools of non-zero-sum games and games with more than two players, including an introduction to cooperative game theory.

This book will not only satisfy the curiosity of those whose interest in the subject was piqued by the 1994 Nobel Prize awarded to Harsanyi, Nash, and Selten. It also prepares its readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences.