Discrete mathematics Books
John Wiley & Sons Inc Finite Mathematics
Book SynopsisThis set includes Finite Mathematics: Models and Applications & Solutions Manual to accompany Finite Mathematics: Models and Applications Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences. The book features coverage including: Algebra Skills; Mathematics of Finance; Matrix Algebra; Geometric Solutions; Simplex Methods; Application Models; Set and Probability Relationships; Random Variables and Probability Distributions; Markov Chains; Mathematical Statistics; Enrichment in Finite MathematicsTable of ContentsPreface ix About the Authors xi 1 Linear Equations and Mathematical Concepts 1 1.1 Solving Linear Equations 2 1.2 Equations of Lines and Their Graphs 7 1.3 Solving Systems of Linear Equations 15 1.4 The Numbers 𝜋 and e 21 1.5 Exponential and Logarithmic Functions 24 1.6 Variation 32 1.7 Unit Conversions and Dimensional Analysis 38 2 Mathematics of Finance 47 2.1 Simple and Compound Interest 47 2.2 Ordinary Annuity 55 2.3 Amortization 59 2.4 Arithmetic and Geometric Sequences 63 3 Matrix Algebra 71 3.1 Matrices 72 3.2 Matrix Notation, Arithmetic, and Augmented Matrices 78 3.3 Gauss–Jordan Elimination 89 3.4 Matrix Inversion and Input–Output Analysis 100 4 Linear Programming – Geometric Solutions 116 Introduction 116 4.1 Graphing Linear Inequalities 117 4.2 Graphing Systems of Linear Inequalities 121 4.3 Geometric Solutions to Linear Programs 125 5 Linear Programming – Simplex Method 136 5.1 The Standard Maximization Problem (SMP) 137 5.2 Tableaus and Pivot Operations 142 5.3 Optimal Solutions and the Simplex Method 149 5.4 Dual Programs 161 5.5 Non-SMP Linear Programs 167 6 Linear Programming – Application Models 182 7 Set and Probability Relationships 203 7.1 Sets 204 7.2 Venn Diagrams 210 7.3 Tree Diagrams 216 7.4 Combinatorics 221 7.5 Mathematical Probability 231 7.6 Bayes’ Rule and Decision Trees 245 8 Random Variables and Probability Distributions 259 8.1 Random Variables 259 8.2 Bernoulli Trials and the Binomial Distribution 265 8.3 The Hypergeometric Distribution 273 8.4 The Poisson Distribution 279 9 Markov Chains 285 9.1 Transition Matrices and Diagrams 286 9.2 Transitions 291 9.3 Regular Markov Chains 295 9.4 Absorbing Markov Chains 304 10 Mathematical Statistics 314 10.1 Graphical Descriptions of Data 315 10.2 Measures of Central Tendency and Dispersion 323 10.3 The Uniform Distribution 331 10.4 The Normal Distribution 334 10.5 Normal Distribution Applications 348 10.6 Developing and Conducting a Survey 363 11 Enrichment in Finite Mathematics 371 11.1 Game Theory 372 11.2 Applications in Finance and Economics 385 11.3 Applications in Social and Life Sciences 394 11.4 Monte Carlo Method 403 11.5 Dynamic Programming 422 Answers to Odd Numbered Exercises 439 Using Technology 502 Glossary 506 Index 513
£116.06
John Wiley & Sons Inc Models for Life
Book SynopsisFeatures an authentic and engaging approach to mathematical modeling driven by real-world applications With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques. The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal finance, and body weight and provides an introduction to more advanced, multi-compartment models via applications in many areas, including military combat, infeTable of ContentsPreface xiii Acknowledgments xvii 1 Density-Independent Population Models 1 1.1 Exponential Growth 1 1.2 Exponential Growth with Stocking or Harvesting 22 1.3 Two Fundamental Excel Techniques 32 1.4 Explicit Formulas 40 1.5 Equilibrium Values and Stability 50 2 Personal Finance 59 2.1 Compound Interest and Savings 60 2.2 Borrowing for Major Purchases 77 2.3 Credit Cards 92 2.4 The Time Value of Money: Present Value 104 2.5 Car Leases 112 3 Combat Models 119 3.1 Lanchester Combat Model 120 3.2 Phase Plane Graphs 140 3.3 The Lanchester Model with Reinforcements 146 3.4 Hughes Aimed Fire Salvo Model 153 3.5 Armstrong Salvo Model with Area Fire 169 4 The Spread of Infectious Diseases 183 4.1 The S–I–R Model 184 4.2 S–I–R with Vital Dynamics 203 4.3 Determining Parameters from Real Data 216 4.4 S–I–R with Vital Dynamics and Routine Vaccinations 226 5 Density-Dependent Population Models 235 5.1 The Discrete Logistic Model 235 5.2 Logistic Growth with Allee Effects 248 5.3 Logistic Growth with Harvesting 254 5.4 The Discrete Logistic Model and Chaos 263 5.5 The Ricker Model 266 6 Blood Alcohol Concentration and Pharmacokinetics 273 6.1 Blood Alcohol Concentration 273 6.2 The Widmark Model 280 6.3 The Wagner Model 283 6.4 Alcohol Consumption Patterns 289 6.5 More General Drug Elimination 301 6.6 The Volume of Distribution 319 6.7 Common Drugs 321 7 Ranking Methods 329 7.1 Introduction to Markov Models 329 7.2 Ranking Sports Teams 342 7.3 Google PageRank 361 8 Body Weight and Body Composition 381 8.1 Constant Calorie Expenditure 382 8.2 Variable Calorie Expenditure 385 8.3 Health Metrics 394 8.4 Body Composition 397 8.5 The Body Composition Model for Body Weight 406 8.6 Points-based Systems: The Weight Watchers Model 419 Appendix A: The Geometric Series Formula 431 Appendix B: Lanchester’s Square Law and the Fractional Exchange Ratio 433 Appendix C: Derivation of the FER = 1 Line for the Hughes Salvo Model 439 Appendix D: The Waiting Time Principle 441 Appendix E: Creating Cobweb Diagrams in Excel 445 Appendix F: Proportion of Total Credit Distributed Does Not Exceed 1 449 Bibliography 451 Index 459
£92.70
John Wiley & Sons Inc Integer Programming
Book SynopsisA PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders' decompositiTable of ContentsPreface to the Second Edition xii Preface to the First Edition xiii Abbreviations and Notation xvii About the Companion Website xix 1 Formulations 1 1.1 Introduction 1 1.2 What Is an Integer Program? 3 1.3 Formulating IPs and BIPs 5 1.4 The Combinatorial Explosion 8 1.5 Mixed Integer Formulations 9 1.6 Alternative Formulations 12 1.7 Good and Ideal Formulations 15 1.8 Notes 18 1.9 Exercises 19 2 Optimality, Relaxation, and Bounds 25 2.1 Optimality and Relaxation 25 2.2 Linear Programming Relaxations 27 2.3 Combinatorial Relaxations 28 2.4 Lagrangian Relaxation 29 2.5 Duality 30 2.6 Linear Programming and Polyhedra 32 2.7 Primal Bounds: Greedy and Local Search 34 2.8 Notes 38 2.9 Exercises 38 3 Well-Solved Problems 43 3.1 Properties of Easy Problems 43 3.2 IPs with Totally Unimodular Matrices 44 3.3 Minimum Cost Network Flows 46 3.4 Special Minimum Cost Flows 48 3.4.1 Shortest Path 48 3.4.2 Maximum s − t Flow 49 3.5 Optimal Trees 50 3.6 Submodularity and Matroids 54 3.7 Two Harder Network Flow Problems 57 3.8 Notes 59 3.9 Exercises 60 4 Matchings and Assignments 63 4.1 Augmenting Paths and Optimality 63 4.2 Bipartite Maximum Cardinality Matching 65 4.3 The Assignment Problem 67 4.4 Matchings in Nonbipartite Graphs 73 4.5 Notes 74 4.6 Exercises 75 5 Dynamic Programming 79 5.1 Some Motivation: Shortest Paths 79 5.2 Uncapacitated Lot-Sizing 80 5.3 An Optimal Subtree of a Tree 83 5.4 Knapsack Problems 84 5.4.1 0–1 Knapsack Problems 85 5.4.2 Integer Knapsack Problems 86 5.5 The Cutting Stock Problem 89 5.6 Notes 91 5.7 Exercises 92 6 Complexity and Problem Reductions 95 6.1 Complexity 95 6.2 Decision Problems, and Classes NP and P 96 6.3 Polynomial Reduction and the Class NPC 98 6.4 Consequences of P =NP orP ≠NP 103 6.5 Optimization and Separation 104 6.6 The Complexity of Extended Formulations 105 6.7 Worst-Case Analysis of Heuristics 106 6.8 Notes 109 6.9 Exercises 110 7 Branch and Bound 113 7.1 Divide and Conquer 113 7.2 Implicit Enumeration 114 7.3 Branch and Bound: an Example 116 7.4 LP-Based Branch and Bound 120 7.5 Using a Branch-and-Bound/Cut System 123 7.6 Preprocessing or Presolve 129 7.7 Notes 134 7.8 Exercises 135 8 Cutting Plane Algorithms 139 8.1 Introduction 139 8.2 Some Simple Valid Inequalities 140 8.3 Valid Inequalities 143 8.4 A Priori Addition of Constraints 147 8.5 Automatic Reformulation or Cutting Plane Algorithms 149 8.6 Gomory’s Fractional Cutting Plane Algorithm 150 8.7 Mixed Integer Cuts 153 8.7.1 The Basic Mixed Integer Inequality 153 8.7.2 The Mixed Integer Rounding (MIR) Inequality 155 8.7.3 The Gomory Mixed Integer Cut 155 8.7.4 Split Cuts 156 8.8 Disjunctive Inequalities and Lift-and-Project 158 8.9 Notes 161 8.10 Exercises 162 9 Strong Valid Inequalities 167 9.1 Introduction 167 9.2 Strong Inequalities 168 9.3 0–1 Knapsack Inequalities 175 9.3.1 Cover Inequalities 175 9.3.2 Strengthening Cover Inequalities 176 9.3.3 Separation for Cover Inequalities 178 9.4 Mixed 0–1 Inequalities 179 9.4.1 Flow Cover Inequalities 179 9.4.2 Separation for Flow Cover Inequalities 181 9.5 The Optimal Subtour Problem 183 9.5.1 Separation for Generalized Subtour Constraints 183 9.6 Branch-and-Cut 186 9.7 Notes 189 9.8 Exercises 190 10 Lagrangian Duality 195 10.1 Lagrangian Relaxation 195 10.2 The Strength of the Lagrangian Dual 200 10.3 Solving the Lagrangian Dual 202 10.4 Lagrangian Heuristics 205 10.5 Choosing a Lagrangian Dual 207 10.6 Notes 209 10.7 Exercises 210 11 Column (and Row) Generation Algorithms 213 11.1 Introduction 213 11.2 The Dantzig–Wolfe Reformulation of an IP 215 11.3 Solving the LP Master Problem: Column Generation 216 11.4 Solving the Master Problem: Branch-and-Price 219 11.5 Problem Variants 222 11.5.1 Handling Multiple Subproblems 222 11.5.2 Partitioning/Packing Problems with Additional Variables 223 11.5.3 Partitioning/Packing Problems with Identical Subsets 224 11.6 Computational Issues 225 11.7 Branch-Cut-and-Price: An Example 226 11.7.1 A Capacitated Vehicle Routing Problem 226 11.7.2 Solving the Subproblems 229 11.7.3 The Load Formulation 230 11.8 Notes 231 11.9 Exercises 232 12 Benders’ Algorithm 235 12.1 Introduction 235 12.2 Benders’ Reformulation 236 12.3 Benders’ with Multiple Subproblems 240 12.4 Solving the Linear Programming Subproblems 242 12.5 Integer Subproblems: Basic Algorithms 244 12.5.1 Branching in the (x, 𝜂, y)-Space 244 12.5.2 Branching in (x, 𝜂)-Space and “No-Good” Cuts 246 12.6 Notes 247 12.7 Exercises 248 13 Primal Heuristics 251 13.1 Introduction 251 13.2 Greedy and Local Search Revisited 252 13.3 Improved Local Search Heuristics 255 13.3.1 Tabu Search 255 13.3.2 Simulated Annealing 256 13.3.3 Genetic Algorithms 257 13.4 Heuristics Inside MIP Solvers 259 13.4.1 Construction Heuristics 259 13.4.2 Improvement Heuristics 261 13.5 User-Defined MIP heuristics 262 13.6 Notes 265 13.7 Exercises 266 14 From Theory to Solutions 269 14.1 Introduction 269 14.2 Software for Solving Integer Programs 269 14.3 How Do We Find an Improved Formulation? 272 14.4 Multi-item Single Machine Lot-Sizing 277 14.5 A Multiplexer Assignment Problem 282 14.6 Integer Programming and Machine Learning 285 14.7 Notes 287 14.8 Exercises 287 References 291 Index 311
£90.86
Taylor & Francis Ltd Automata and Computability
Book SynopsisAutomata and Computability is a class-tested textbook which provides a comprehensive and accessible introduction to the theory of automata and computation. The author uses illustrations, engaging examples, and historical remarks to make the material interesting and relevant for students. It incorporates modern/handy ideas, such as derivative-based parsing and a Lambda reducer showing the universality of Lambda calculus. The book also shows how to sculpt automata by making the regular language conversion pipeline available through a simple command interface. A Jupyter notebook will accompany the book to feature code, YouTube videos, and other supplements to assist instructors and studentsFeatures Uses illustrations, engaging examples, and historical remarks to make the material accessible Incorporates modern/handy ideas, such as derivative-based parsing and a Lambda reducer showing the universality of Lambda Trade Review"I have taught formal languages and automata theory for decades, and I have seen many, perhaps most, students struggle with the material because it is so abstract. I've often thought that computer science students would learn it better by programming it. Indeed, that's how I really learned these topics -- by implementing constructions directly in practical compiler generation and formal verification tools to do my research. Prof. Gopalakrishnan's approach is to have students learn by doing, while still going into greater depth than some purely pencil-and-paper courses." -Prof. David L. Dill, Donald E. Knuth Professor, Emeritus, in the School of Engineering, Stanford University "It is probably a safe assumption to make these days that many, if not most, computer science undergraduates have had programming experience, but few of them know the language of mathematics. Professor Gopalakrishnan’s book builds on the student’s experience in programming and animates the theory of automata, formal languages, and computability with actual programs which the student can easily modify and play with. Doing is the best way of learning. This book should enable the typical computer science student to acquire a more visceral, and therefore in the long run more useful, understanding of the theory." -Dr. Ching-Tsun Chou, Silicon Architecture Engineer, Intel Corporation "As a long-time researcher in programming languages and high-performance computing, I find the coverage of Automata and Computability in this book illuminating from a foundational perspective as well as timely from a practical perspective. In addition to classical topics such as automata theory and parsing, it allows a student to interactively study via Jupyter notebooks a wide range of topics including grammar disambiguation, Boolean satisfiability, Post Correspondence and Lambda Calculus --- all important topics for students who aspire to become proficient in computer science." -Vivek Sarkar, Professor, School of Computer Science & Stephen Fleming Chair for Telecommunications, College of Computing, Georgia Institute of Technology "I have taught formal languages and automata theory for decades, and I have seen many, perhaps most, students struggle with the material because it is so abstract. I've often thought that computer science students would learn it better by programming it. Indeed, that's how I really learned these topics -- by implementing constructions directly in practical compiler generation and formal verification tools to do my research. Prof. Gopalakrishnan's approach is to have students learn by doing, while still going into greater depth than some purely pencil-and-paper courses." -Prof. David L. Dill, Donald E. Knuth Professor, Emeritus, in the School of Engineering, Stanford University "It is probably a safe assumption to make these days that many, if not most, computer science undergraduates have had programming experience, but few of them know the language of mathematics. Professor Gopalakrishnan’s book builds on the student’s experience in programming and animates the theory of automata, formal languages, and computability with actual programs which the student can easily modify and play with. Doing is the best way of learning. This book should enable the typical computer science student to acquire a more visceral, and therefore in the long run more useful, understanding of the theory." -Dr. Ching-Tsun Chou, Silicon Architecture Engineer, Intel Corporation "As a long-time researcher in programming languages and high-performance computing, I find the coverage of Automata and Computability in this book illuminating from a foundational perspective as well as timely from a practical perspective. In addition to classical topics such as automata theory and parsing, it allows a student to interactively study via Jupyter notebooks a wide range of topics including grammar disambiguation, Boolean satisfiability, Post Correspondence and Lambda Calculus --- all important topics for students who aspire to become proficient in computer science." -Vivek Sarkar, Professor, School of Computer Science & Stephen Fleming Chair for Telecommunications, College of Computing, Georgia Institute of Technology Table of ContentsI Foundations 1 What Machines Think 2 Defining Languages: Patterns in Sets of Strings 3 Kleene Star: Basic Method of defining Repetitious Patterns II Machines 4 Basics of DFAs 5 Designing DFA 6 Operations on DFA 7 Nondeterministic Finite Automata 8 Regular Expressions and NFA 9 NFA to RE conversion 10 Derivative-based Regular Expression Matching 11 Context-Free Languages and Grammars 12 Pushdown Automata 13 Turing Machines III Concepts 14 Interplay Between Formal Languages 15 Post Correspondence, and Other Undecidability Proofs 16 NP-Completeness 17 Binary Decision Diagrams as Minimal DFA 18 Computability using Lambdas
£78.84
McGraw-Hill Education Connect Access Card for Discrete Mathematics and
Book Synopsis
£123.57
McGraw Hill Education India Loose Leaf for Discrete Mathematics and Its
Book Synopsis
£174.60
Cengage Learning, Inc Discrete Mathematics with Applications
Book Synopsis
£297.30
Random House USA Inc Proving Darwin
Book SynopsisGroundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin’s theory of evolution works on a mathematical level. For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth’s life-forms evolved by blind chance. But does Darwin’s theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It’s a question no one has yet answered—in fact, no one has attempted to answer it until now. In this illuminating and provocative book, Gregory Chaitin elucidates the mathematical scheme he’s developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Fascinating and thought-provoking, Proving Darwin makes clear how biology may have found its greatest ally in mathematics
£14.39
Taylor & Francis Ltd Combinatorial Pattern Matching Algorithms in
Book SynopsisEmphasizing the search for patterns within and between biological sequences, trees, and graphs, Combinatorial Pattern Matching Algorithms in Computational Biology Using Perl and R shows how combinatorial pattern matching algorithms can solve computational biology problems that arise in the analysis of genomic, transcriptomic, proteomic, metabolomic, and interactomic data. It implements the algorithms in Perl and R, two widely used scripting languages in computational biology. The book provides a well-rounded explanation of traditional issues as well as an up-to-date account of more recent developments, such as graph similarity and search. It is organized around the specific algorithmic problems that arise when dealing with structures that are commonly found in computational biology, including biological sequences, trees, and graphs. For each of these structures, the author makes a clear distinction between problems that arise in the analysis of one strTrade ReviewI like the hands-on approach this book offers, and the very pedagogical structure it follows … . The book also has tons of examples, thoughtfully chosen and beautifully laid out … the book is very well-written and accessible, undoubtedly written by an author who takes great care in preparing his manuscripts and teaching about an area he enjoys working on.—Anthony Labarre, SIGACT News, July 2012This text provides a solid foundation to the field. It will work as a practical handbook for pattern matching applications in computational biology. —Michael Goldberg, Computing Reviews, February 2010… the book makes a clear distinction between problems that emerge in the analysis of the structure and in the comparative analysis of two or more structures. … Well-known computational biology tools that allow searching nucleotide and protein databases for local sequence alignment are based on CPM algorithms only. The techniques presented in this book go beyond that. … detailed algorithm solutions in pseudocode, full Perl and R implementation, and pointers to software and implementation are presented. This … is what makes Valiente’s effort unique. …—Ernesto D’Avanzo, Computing Reviews, February 2010… It is a well-sorted collection of pattern matching algorithms that are used to work with problems in computational biology. … You can find all of the sources on the author’s website, which come in handy when you actually want to use them, since you do not have to retype them. And there is an introduction to Perl as well as to R, showing how to decode DNA/RNA-triplets to amino acids and giving some basic overview over standard functions. … I certainly recommend this as an introduction and reference to some algorithms of pattern matching in computational biology. You actually learn how algorithms over the most important data types are designed in a straightforward, logical way. …—Jannik Pewny, IACR Book Reviews, 2009…after a few minutes of random browsing, I was left with a feeling of total appreciation of the book, admiration for Prof. Gabriel Valiente, and a realization that this book will be part of my fundamental library for me and my group from the moment it is published. There are so many good things to say that I do not know where to start. The organization is straightforward with major sections that extend from simple sequences to trees to graphs. … This parallel structure makes it easy to apply lessons used on the simplest object (sequences) to objects of medium (trees) and significant (graphs) difficulty. …a wonderful way to learn leveraging … The Perl is beautifully clear and the examples have already taught me how to improve my own code.—Michael Levitt, Professor and Chair, Department of Structural Biology, Stanford University, California, USA…Balancing a careful mixture of formal methods, programming, and examples, Gabriel Valiente has managed to harmoniously bridge languages and contents into a self-contained source of lasting influence. It is not difficult to predict that this book will be studied indifferently by the specialist of biology and computer science, helping each to walk a few steps toward the other. It will entice new generations of scholars to engage in its beautiful subject.—From the Foreword, Alberto Apostolico, Professor, College of Computing, Georgia Tech, Atlanta, USAUnlocks the power for R for Perl programmers, and vice versa. Reveals R to be a powerful and accessible tool for bioinformatics. The title is a mouthful, but the use of both R and Perl for bioinformatics is revealing.—Steven Skiena, Professor, Department of Computer Science, Stony Brook University, New York, USAI like the hands-on approach this book offers, and the very pedagogical structure it follows … . The book also has tons of examples, thoughtfully chosen and beautifully laid out … the book is very well-written and accessible, undoubtedly written by an author who takes great care in preparing his manuscripts and teaching about an area he enjoys working on.—Anthony Labarre, SIGACT News, July 2012This text provides a solid foundation to the field. It will work as a practical handbook for pattern matching applications in computational biology. —Michael Goldberg, Computing Reviews, February 2010… the book makes a clear distinction between problems that emerge in the analysis of the structure and in the comparative analysis of two or more structures. … Well-known computational biology tools that allow searching nucleotide and protein databases for local sequence alignment are based on CPM algorithms only. The techniques presented in this book go beyond that. … detailed algorithm solutions in pseudocode, full Perl and R implementation, and pointers to software and implementation are presented. This … is what makes Valiente’s effort unique. …—Ernesto D’Avanzo, Computing Reviews, February 2010… It is a well-sorted collection of pattern matching algorithms that are used to work with problems in computational biology. … You can find all of the sources on the author’s website, which come in handy when you actually want to use them, since you do not have to retype them. And there is an introduction to Perl as well as to R, showing how to decode DNA/RNA-triplets to amino acids and giving some basic overview over standard functions. … I certainly recommend this as an introduction and reference to some algorithms of pattern matching in computational biology. You actually learn how algorithms over the most important data types are designed in a straightforward, logical way. …—Jannik Pewny, IACR Book Reviews, 2009…after a few minutes of random browsing, I was left with a feeling of total appreciation of the book, admiration for Prof. Gabriel Valiente, and a realization that this book will be part of my fundamental library for me and my group from the moment it is published. There are so many good things to say that I do not know where to start. The organization is straightforward with major sections that extend from simple sequences to trees to graphs. … This parallel structure makes it easy to apply lessons used on the simplest object (sequences) to objects of medium (trees) and significant (graphs) difficulty. …a wonderful way to learn leveraging … The Perl is beautifully clear and the examples have already taught me how to improve my own code.—Michael Levitt, Professor and Chair, Department of Structural Biology, Stanford University, California, USA…Balancing a careful mixture of formal methods, programming, and examples, Gabriel Valiente has managed to harmoniously bridge languages and contents into a self-contained source of lasting influence. It is not difficult to predict that this book will be studied indifferently by the specialist of biology and computer science, helping each to walk a few steps toward the other. It will entice new generations of scholars to engage in its beautiful subject.—From the Foreword, Alberto Apostolico, Professor, College of Computing, Georgia Tech, Atlanta, USAUnlocks the power for R for Perl programmers, and vice versa. Reveals R to be a powerful and accessible tool for bioinformatics. The title is a mouthful, but the use of both R and Perl for bioinformatics is revealing.—Steven Skiena, Professor, Department of Computer Science, Stony Brook University, New York, USATable of ContentsIntroduction. SEQUENCE PATTERN MATCHING: Sequences. Simple Pattern Matching in Sequences. General Pattern Matching in Sequences. TREE PATTERN MATCHING: Trees. Simple Pattern Matching in Trees. General Pattern Matching in Trees. GRAPH PATTERN MATCHING: Graphs. Simple Pattern Matching in Graphs. General Pattern Matching in Graphs. Appendices. References. Index.
£180.50
Taylor & Francis Inc Handbook of Finite State Based Models and
Book SynopsisApplicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. Handbook of Finite State Based Models and Applications provides a complete collection of introductory materials on finite state theories, algorithms, and the latest domain applications. For beginners, the book is a handy reference for quickly looking up model details. For more experienced researchers, it is suitable as a source of in-depth study in this area. The book first introduces the fundamentals of automata theory, including regular expressions, as well as widely used automata, such as transducers, tree automata, quantum automata, and timed automata. It then presents algorithms for the minimization and incremental construction of finite automata and describes Esterel, an automata-based synchronous programming language for embedded system software development.Moving on to applications, the book explores regular path queries on graph-structured data, timed automata in model checking security protocols, pattern matching, compiler design, and XML processing. It also covers other finite state-based modeling approaches and applications, including Petri nets, statecharts, temporal logic, and UML state machine diagrams.Table of ContentsFinite Automata. Large-Scale Regular Expression Matching on FPGA. Finite State Transducers. Tree Automata. Timed Automata. Quantum Finite Automata. Finite Automata Minimization. Incremental Construction of Finite-State Automata. Esterel and the Semantics of Causality. Regular Path Queries on Graph-Structured Data. Applying Timed Automata to Model Checking of Security Protocols. Optimal Adaptive Pattern-Matching Using Finite State Automata. Finite State Automata in Compilers. Finite State Models for XML Processing. Petri Nets. Statecharts. Model Checking. System Modeling with UML State Machines. Index.
£147.25
Springer New York The Symmetric Group
Book Synopsis1 Group Representations.- 2 Representations of the Symmetric Group.- 3 Combinatorial Algorithms.- 4 Symmetric Functions.- 5 Applications and Generalizations.Trade ReviewFrom the reviews of the second edition: "This work is an introduction to the representation theory of the symmetric group. Unlike other books on the subject this text deals with the symmetric group from three different points of view: general representation theory, combinatorial algorithms and symmetric functions. ... This book is a digestible text for a graduate student and is also useful for a researcher in the field of algebraic combinatorics for reference." (Attila Maróti, Acta Scientiarum Mathematicarum, Vol. 68, 2002) "A classic gets even better. ... The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." (David M. Bressoud, Zentralblatt MATH, Vol. 964, 2001)Table of Contents* Group Representations * Representations of the Symmetric Group * Combinatorial Algorithms * Symmetric Functions * Applications and Generalizations
£47.49
Springer New York A Course in Topological Combinatorics 0 Universitext
Book SynopsisA Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, and other applied areas.Trade Review“This book is an excellent introduction into the subject. … The book contains a lot of figures and each chapter ends with a group of exercises which help the reader in understanding the hard constructions and proofs. The book may serve for a one- or two-semester undergraduate course depending on the preliminary knowledges of the students.” (János Kincses, Acta Scientiarum Mathematicarum, Vol. 81 (3-4), 2015)“The present book … presents a sequence of combinatorial themes which have shown an affinity for topological methods … . This book is filled with extremely attractive mathematics … and bringing topology into the play of combinatorics and graph theory is a wonderfully elegant manoeuvre. Here it is carried out coherently, and on a pretty grand scale, and we are thus afforded the opportunity to encounter (algebraic) topology in a very seductive uniform context. What a marvelous thing!” (Michael Berg, MAA Reviews, July, 2013)“In the book’s four main chapters, Longueville (Univ. of Applied Sciences, Germany) addresses fair-division problems; graph coloring; graph property evasiveness; and embeddings and mappings. … Basic results of algebraic topology already have powerful consequences for analysis, but the subject’s arcana can look like art for art’s sake. The author’s charting of a novel application domain for a core subject makes this book an essential acquisition. Summing Up: Essential. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 50 (8), April, 2013)“Topological combinatorics is concerned with the applications of the many powerful techniques of algebraic topology to problems in combinatorics. … The present book aims to give a clear and vivid presentation of some of the most beautiful and accessible results from the area. The text, based upon some courses by the author at Freie Universität Berlin, is designed for an advanced undergraduate student.” (Hirokazu Nishimura, zbMATH, Vol. 1273, 2013)Table of ContentsPreface.- List of Symbols and Typical Notation.- 1 Fair-Division Problems.- 2 Graph-Coloring Problems.- 3 Evasiveness of Graph Properties.- 4 Embedding and Mapping Problems.- A Basic Concepts from Graph Theory.- B Crash Course in Topology.- C Partially Ordered Sets, Order Complexes, and Their Topology.- D Groups and Group Actions.- E Some Results and Applications from Smith Theory.- References.- Index.
£76.49
Springer London Game of Life Cellular Automata
Book SynopsisIn the late 1960s British mathematician John Conway invented a virtual mathematical machine that operates on a two-dimensional array of square cell. A dead cell comes to life if it has exactly three live neighbours. A live cell remains alive if two or three of its neighbours are alive, otherwise the cell dies.Trade ReviewFrom the reviews:“This volume’s 27 papers offer some systematic methods and rigorous theorems that exhibit the study of Conway’s game and its variations, emerging out of the realm of merely recreational mathematics. … this unique book will have great value as both a state-of-the-art summary and a collection of proposals for new directions to explore. Summing Up: Highly recommended. Upper-division undergraduates through professionals.” (D. V. Feldman, Choice, Vol. 48 (4), December, 2010)“Andrew Adamatzky has assembled a superb collection of papers on Life that encompass work going back more than 20 years. … maintains a good balance between interconnectedness and recognition of the papers as independent contributions. … This book is a treasure trove of history, concepts, and models. It is a good starting place for a newcomer to the study of Conway’s Game of Life, an opening of vistas for the amateur hobbyist, and a serious handbook for the professional researcher.” (Anthony J. Duben, ACM Computing Reviews, February, 2011)Table of Contents1. Introduction to Cellular Automata and Conway’s Game of Life.- Part I Historical.- 2. Conway’s Game of Life: Early Personal Recollections.- 3. Conway’s Life.- 4. Life’s Still Lifes.- 5. A Zoo of Life Forms.- Part II Classical Topics.- 6. Growth and Decay in Life-Like Cellular Automata.- 7. The B36/S125 “2x2” Life-Like Cellular Automaton.- 8. Object Synthesis in Conway’s Game of Life and other Cellular Automata.- 9. Gliders and Glider Guns Discovery in Cellular Automata.- 10. Constraint Programming to Solve Maximal Density Still Life.- Part III Asynchronous, Continuous and Memory-Enriched Automata.- 11. Larger than Life’s Extremes: Rigorous Results for Simplified Rules and Speculation on the Phase Boundaries.- 12. RealLife.- 13. Variations on the Game of Life.- 14. Does Life Resist Asynchrony?.- 15. LIFE with Short-Term Memory.- 16. Localization Dynamics in a Binary Two-Dimensional Cellular Automaton: the Diffusion Rule.- Part IV Non-Orthogonal Lattices.- 17. The Game of Life in Non-Square Environments.- 18. The Game of Life Rules on Penrose Tilings: Still Life and Oscillators.- 19. A Spherical XOR Gate Implemented in the Game of Life.- Part V Complexity.- 20. Emergent Complexity in Conway’s Game of Life.- 21. Macroscopic Spatial Complexity of the Game of Life Cellular Automaton: A Simple Data Analysis.- Part VI Physics.- 22. The Enlightened Game of Life 23. Towards a Quantum Game of Life.- Part VII Music.- 24. Game of Life Music.- Part VIII Computation.- 25. Universal Computation and Construction in GoL Cellular Automata.- 26. A Simple Universal Turing Machine for the Game of Life Turing Machine.- 27. Computation with Competing Patterns in Life-like Automaton.- Index
£116.99
Springer New York An Introduction to Convex Polytopes Graduate Texts in Mathematics 90
Book SynopsisThe highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem.Table of Contents1 Convex Sets.- A7;1. The Affine Structure of ?d.- A7;2. Convex Sets.- A7;3. The Relative Interior of a Convex Set.- A7;4. Supporting Hyperplanes and Halfspaces.- A7;5. The Facial Structure of a Closed Convex Set.- A7;6. Polarity.- 2 Convex Polytopes.- A7;7. Polytopes.- A7;8. Polyhedral Sets.- A7;9. Polarity of Polytopes and Polyhedral Sets.- A7;10. Equivalence and Duality of Polytopes.- A7;11. Vertex-Figures.- A7;12. Simple and Simplicial Polytopes.- A7;13. Cyclic Polytopes.- A7;14. Neighbourly Polytopes.- A7;15. The Graph of a Polytope.- 3 Combinatorial Theory of Convex Polytopes.- A7;16. Eulerߣs Relation.- A7;17. The Dehn-Sommerville Relations.- A7;18. The Upper Bound Theorem.- A7;19. The Lower Bound Theorem.- A7;20. McMullenߣs Conditions.- Appendix 1 Lattices.- Appendix 2 Graphs.- Appendix 3 Combinatorial Identities.- Bibliographical Comments.- List of Symbols.
£42.74
Springer-Verlag New York Inc. Quadratic and Higher Degree Forms 31 Developments
Book SynopsisTable of ContentsPreface.- Toy Models for D. H. Lehmer's Conjecture II (E. Bannai, T. Miezaki).- On the Representation of an Integer by X2+Y2+Z2 and the Modular Equations of Degree 3 and 5 (A. Berkovich).- Almost Universal Ternary Sums of Squares and Triangular Numbers (W. Chan, A. Haensch).- Weighted Generating Functions for Type II Lattices and Codes (N. Elkies, S. Kominers).- Quadratic and Automorphic Forms (J. Hanke).- Integral Positive Ternary Quadratic Forms (W. Jagy).- Some Aspects of the Algebraic Theory of Quadratic Forms (R. Parimala).- On the Length of Binary Forms (B. Reznick).- Representation of Quadratic Forms by Integral Quadratic Forms (R. Schulze-Pillot).- Identifying the Matrix Ring (J. Voight).
£95.99
MP-AMM American Mathematical Asymptopia
Book SynopsisTrade ReviewThe style and the beauty make this book an excellent reading. Keep it on your coffee table or/and bed table and open it often, Asymptopia is a fascinating place." - Péter Hajnal, ACTA Sci. Math.Table of Contents An infinity of primes Stirling's formula Big Oh, little Oh and all that Integration in Asymptopia From integrals to sums Asymptotics of binomial coefficients (n k ) Unicyclic graphs Ramsey numbers Large deviations Primes Asymptotic geometry Algorithms Potpourri Really Big Numbers! Bibliography Index
£47.70
MP-AMM American Mathematical Linear Algebra and Matrices
Book SynopsisLinear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems.Trade ReviewLinear Algebra and Matrices: Topics for a Second Course by Helene Shapiro succeeds brilliantly at its slated purpose which is hinted at by its title. It provides some innovative new ideas of what to cover in the second linear algebra course that is offered at many universities...[this book] would be my personal choice for a textbook when I next teach the second course for linear algebra at my university. I highly recommend this book, not only for use as a textbook, but also as a source of new ideas for what should be in the syllabus of the second course." - Rajesh Pereira, IMAGETable of Contents Preliminaries Inner product spaces and orthogonality Eigenvalues, eigenvectors, diagonalization, and triangularization The Jordan and Weyr canonical forms Unitary similarity and normal matrices Hermitian matrices Vector and matrix norms Some matrix factorizations Field of values Simultaneous triangularization Circulant and block cycle matrices Matrices of zeros and ones Block designs Hadamard matrices Graphs Directed graphs Nonnegative matrices Error correcting codes Linear dynamical systems Bibliography Index
£68.40
MP-AMM American Mathematical Expansion in Finite Simple Groups of Lie Type
Book SynopsisTrade ReviewAsymptotic group theory is a recently emerging branch of group theory, that can be described as the study of groups whose order is finite—but large! Tao’s book is certainly a valuable introduction to that exciting new subject." - Alain Valette, Jahresbericht der Deutschen Mathematiker-VereinigungTable of Contents Expansion in Cayley graphs Expander graphs: Basic theory Expansion in Cayley graphs, and Kazhdan's property (T) Quasirandom groups The Balog-Szemeredi-Gowers lemma, and the Bourgain-Gamburd expansion machine Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality Non-concentration in subgroups Sieving and expanders Related articles Cayley graphs the algebra of groups The Lang-Weil bound The spectral theorem and its converses for unbounded self-adjoint operators Notes on Lie algebras Notes on groups of Lie type Bibliography Index
£108.00
MP-AMM American Mathematical Topological Recursion and its Influence in
Book SynopsisContains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, held in 2016. The papers present a snapshot of rapid and rich developments in the emerging research field known as topological recursion.Table of Contents J. E. Andersen, G. Borot, and N. Orantin, Modular functors, cohomological field theories, and topological recursion A. Brini, On the Gopakumar-Ooguri-Vafa correspondence for Clifford-Klein 3-manifolds L. Chen, Bouchard-Klemm-Marino-Pasquetti conjecture for $\mathbb{C}^3$ A. Chiodo and J. Nagel, The hybrid Landau-Ginzburg models of Calabi-Yau complete intersections P. Ciosmak, L. Hadasz, M. Manabe, and P. Sulkowski, Singular vector structure of quantum curves N. Do and M. Karev, Towards the topological recursion for double Hurwitz numbers O. Dumitrescu and M. Mulase, Quantization of spectral curves for meromorphic Higgs bundles through topological recursion P. Dunin-Barkowski, Topological recursion and Givental's formalism: Spectral curves for Gromov-Witten theories P. Dunin-Barkowski, P. Norbury, N. Orantin, A. Popolitov, and S. Shadrin, Primary invariants of Hurwitz Frobenius manifolds J. N. Esteves, Hopf algebras and topological recursion B. Fang and Z. Zong, Graph sums in the remodeling conjecture T. Kimura, Double quantization of Seiberg-Witten geometry and W-algebras M. Kontsevich and Y. Soibelman, Airy structures and symplectic geometry of topological recursion D. Korotkin, Periods of meromorphic quadratic differentials and Goldman bracket D. Lewanski, On ELSV-type formulae, Hurwitz numbers and topological recursion X. Liu, M. Mulase, and A. Sorkin, Quantum curves for simple Hurwitz numbers of an arbitrary base curve.
£109.80
MP-AMM American Mathematical The TriangleFree Process and the Ramsey Number
Book SynopsisIn 2009, Bohman succeeded in following this process for a positive fraction of its duration, and thus obtained a second proof of Kim's celebrated result that $R(3,k) = \Theta \big ( k^2 / \log k \big )$. In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end.Table of Contents Introduction An overview of the proof Martingale bounds: the line of peril and the line of death Tracking everything else Tracking $Y_e$, and mixing in the $Y$-graph Whirlpools and Lyapunov functions Independent sets and maximum degrees in $G_n,\triangle $ Bibliography.
£72.20
MP-AMM American Mathematical An Introductory Course on Mathematical Game
Book SynopsisAn introductory and up-to-date course on game theory for mathematicians, economists and other scientists with a basic mathematical background. This self-contained book provides a formal description of classic game-theoretic concepts alongside rigorous proofs and illustrates the theory through abundant examples, applications, and exercises.Table of Contents Introduction to decision theory Strategic games Extensive games Games with incomplete information Fundamentals of cooperative games Applications of cooperative games Bibliography Notations Index Index of solution concepts Subject Index
£106.20
American Mathematical Society The Tiling Book
£49.40
MP-AMM American Mathematical Finite Fields with Applications to Combinatorics
Book SynopsisUses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. The book constructs all finite fields from scratch and shows that they are unique up to isomorphism.Table of Contents Primes and factorization Primes in the integers Congruences in rings Primes in polynomial rings: Constructing finite fields The additive and multiplicative structures of finite fields Understanding the structures of $\mathbb{Z}/n\mathbb{Z}$ Combinatorial applications of finite fields The AKS primality test Synopsis of finite fields Bibliography Index
£47.70
American Mathematical Society Topological and Ergodic Theory of Symbolic
Book SynopsisIntroduces symbolic dynamics from a perspective of topological dynamical systems. After introducing symbolic and topological dynamics, the core of the book consists of discussions of subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and the ergodic properties of these systems.Table of Contents First examples and general properties of subshifts Topological dynamics Subshifts of positive entropy Subshifts of zero entropy Further minimal Cantor systems Methods from ergodic theory Automata and linguistic complexity Miscellaneous background topics Solutions to exercises Bibliography Index
£98.80
American Mathematical Society Topological and Ergodic Theory of Symbolic
Book SynopsisIntroduces symbolic dynamics from a perspective of topological dynamical systems. After introducing symbolic and topological dynamics, the core of the book consists of discussions of subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and the ergodic properties of these systems.Table of Contents First examples and general properties of subshifts Topological dynamics Subshifts of positive entropy Subshifts of zero entropy Further minimal Cantor systems Methods from ergodic theory Automata and linguistic complexity Miscellaneous background topics Solutions to exercises Bibliography Index
£67.45
MP-AMM American Mathematical An Introductory Course on Mathematical Game
Book SynopsisPresents an introductory and up-to-date course on game theory addressed to mathematicians and economists, and to other scientists having a basic mathematical background. The book is self-contained, providing a formal description of the classic game-theoretic concepts together with rigorous proofs of the main results in the field.Table of Contents Introduction to decision theory Strategic games Extensive games Games with incomplete information Fundamentals of cooperative games Applications of cooperative games Bibliography Notations Index Index of solution concepts Subject index.
£71.10
American Mathematical Society Combinatorial Game Theory
Book SynopsisIt is wonderful to see advanced combinatorial game theory made accessible. Siegel's expertise and enjoyable writing style make this book a perfect resource for anyone wanting to learn the latest developments and open problems in the field. --Erik Demaine, MIT Aaron Siegel has been the major contributor to Combinatorial Game Theory over the last decade or so. Now, in this authoritative work, he has made the latest results in the theory accessible, so that the subject will achieve the place in mathematics that it deserves. --Richard Guy, University of Calgary Combinatorial game theory is the study of two-player games with no hidden information and no chance elements. The theory assigns algebraic values to positions in such games and seeks to quantify the algebraic and combinatorial structure of their interactions. Its modern form was introduced thirty years ago, with the publication of the classic Winning Ways for Your Mathematical Plays by Berlekamp, Conway, and Guy, and interest has raTable of Contents Combinatorial games Short games The structure of $\mathbb{G}$ Impartial games Misere play Loopy games Temperature theory Transfinite games Open problems Mathematical prerequisites A finite loopfree history Bibliography Glossary of notation Author index Index of games Index.
£66.60
John Murray Press Basic Mathematics: An Introduction: Teach Yourself
Basic Mathematics teaches you all the maths you need for everyday situations. If you are terrified by maths, this is the book for you.Do you shy away from using numbers? Basic Mathematics can help. An easy-to-follow guide, it will ensure you gain the confidence you need to tackle maths and overcome your fears. It offers simple explanations of all the key areas, including decimals, percentages, measurements and graphs, and applies them to everyday situations, games and puzzles to help you understand mathematics quickly and enjoyably.Everything you need is here in this one book. Each chapter includes clear explanations, worked examples and test questions. At the end of the book there are challenges and games to give you new and interesting ways to practise your new skills.
£13.49
Birkhauser Boston Infinite Dimensional Lie Algebras An Introduction Progress in Mathematics 44
Table of Contents1. Basic definitions.- 2. The invariant bilinear form and the generalized Casimir operator.- 3. Integrable representations and the Weyl group of a Kac-Moody algebra.- 4. Some properties of generalized Cartan matrices.- 5. Real and imaginary roots.- 6. Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group.- 7. Affine Lie algebras: the realization (case k = 1).- 8. Affine Lie algebras: the realization (case k = 2 or 3). Application to the classification of finite order automorphisms.- 9. Highest weight modules over the Lie algebra g(A).- 10. Integrable highest weight modules: the character formula.- 11. Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem.- 12. Integrable highest weight modules over affine Lie algebras. Application to ?-function identities.- 13. Affine Lie algebras, theta functions and modular forms.- 14. The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations.- Index of notations and definitions.- References.
£85.49
Taylor & Francis Inc Set Theoretical Aspects of Real Analysis
Book SynopsisSet Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary between fundamental concepts of measurability and nonmeasurability for point sets and functions. The remainder of the book deals with more specialized material on set theoretical real analysis. The book focuses on certain logical and set theoretical aspects of real analysis. It is expected that the first eleven chapters can be used in a course on Lebesque measure theory that highlights the fundamental concepts of measurability and non-measurability for point sets and functions. Provided in the book are problems of varying difficulty that range from simple observations to advanced results. Relatively difficult Table of ContentsZF theory and some point sets on the real line. Countable versions of AC and real analysis. Uncountable versions of AC and Lebesgue nonmeasurable sets. The Continuum Hypothesis and Lebesgue nonmeasurable sets. Measurability properties of sets and functions. Radon measures and nonmeasurable sets. Real-valued step functions with strange measurability properties. Relationships between certain classical constructions of Lebesgue nonmeasurable sets. Measurability properties of Vitali sets. A relationship between the measurability and continuity of real-valued functions. A relationship between absolutely nonmeasurable functions and Sierpinski-Zygmund functions. Sums of absolutely nonmeasurable injective functions. A large group of absolutely nonmeasurable additive functions. Additive properties of certain classes of pathological functions. Absolutely nonmeasurable homomorphisms of commutative groups. Measurable and nonmeasurable sets with homogeneous sections. A combinatorial problem on translation invariant extensions of the Lebesgue measure. Countable almost invariant partitions of G-spaces. Nonmeasurable unions of measure zero sections of plane sets. Measurability properties of well-orderings. Appendices. Bibliography. Subject Index.
£175.75
CRC Press Graph Theory and Its Applications
Book SynopsisGraph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authorsâ unparalleled treatment is an ideal text 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.Features of the Third Edition Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions) Provides better coverage of algorithms and algebraic and topological graph theory than any otherTable of ContentsIntroduction to Graph Models Graphs and Digraphs. Common Families of Graphs. Graph Modeling Applications. Walks and Distance. Paths, Cycles, and Trees. Vertex and Edge Attributes. Structure and Representation Graph Isomorphism. Automorphism and Symmetry. Subgraphs. Some Graph Operations. Tests for Non-Isomorphism. Matrix Representation. More Graph Operations. Trees Characterizations and Properties of Trees. Rooted Trees, Ordered Trees, and Binary Trees. Binary-Tree Traversals. Binary-Search Trees. Huffman Trees and Optimal Prefix Codes. Priority Trees. Counting Labeled Trees. Counting Binary Trees. Spanning Trees Tree Growing. Depth-First and Breadth-First Search. Minimum Spanning Trees and Shortest Paths. Applications of Depth-First Search. Cycles, Edge-Cuts, and Spanning Trees. Graphs and Vector Spaces. Matroids and the Greedy Algorithm. Connectivity Vertex and Edge-Connectivity. Constructing Reliable Networks. Max-Min Duality and Menger’s Theorems. Block Decompositions. Optimal Graph Traversals Eulerian Trails and Tours. DeBruijn Sequences and Postman Problems. Hamiltonian Paths and Cycles. Gray Codes and Traveling Salesman Problems. Planarity and Kuratowski’s Theorem Planar Drawings and Some Basic Surfaces. Subdivision and Homeomorphism. Extending Planar Drawings. Kuratowski’s Theorem. Algebraic Tests for Planairty. Planarity Algorithm. Crossing Numbers and Thickness. Graph Colorings Vertex-Colorings. Map-Colorings. Edge-Colorings. Factorization. Special Digraph Models Directed Paths and Mutual Reachability. Digraphs as Models for Relations. Tournaments. Project Scheduling. Finding the Strong Components of a Digraph. Network Flows and Applications Flows and Cuts in Networks. Solving the Maximum-Flow Problem. Flows and Connectivity. Matchings, Transversals, and Vertex Covers. Graph Colorings and Symmetry Automorphisms of Simple Graphs. Equivalence Classes of Colorings. Appendix
£80.74
Springer Computing the Continuous Discretely
Trade Review“This book is an outstanding book on counting integer points of polytopes … . The book contains lots of exercises with very helpful hints. Another essential feature of the book is a vast collection of open problems on different aspects of integer point counting and related areas. … The book is reader-friendly written, self-contained and contains numerous beautiful illustrations. The reader is always accompanied with deep research jokes by famous researchers and valuable historical notes.” (Oleg Karpenkov, zbMATH 1339.52002, 2016)Reviews of the first edition:“You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.”— MAA Reviews“The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the material, exercises, open problems and an extensive bibliography.”— Zentralblatt MATH“This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.”— Mathematical Reviews“Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.”— CHOICETable of ContentsPreface.- The Coin-Exchange Problem of Frobenius.- A Gallery of Discrete Volumes.- Counting Lattice Points in Polytopes: The Ehrhart Theory.- Reciprocity.- Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms.- Magic Squares.- Finite Fourier Analysis.- Dedekind Sums.- The Decomposition of a Polytope into Its Cones.- Euler-MacLaurin Summation in Rd.- Solid Angles.- A Discrete Version of Green's Theorem Using Elliptic Functions.- Appendix A: Triangulations of Polytopes.- Appendix B: Hints for Selected Exercises.- References.- Index.- List of Symbols.-
£41.24
Springer New York The Grassmannian Variety Geometric and RepresentationTheoretic Aspects 42 Developments in Mathematics
Trade Review“The present book gives a detailed treatment of the standard monomial theory (SMT) for the Grassmannians and their Schubert subvarieties along with several applications of SMT. It can be used as a reference book by experts and graduate students who study varieties with a reductive group action such as flag and toric varieties.” (Valentina Kiritchenko, zbMATH 1343.14001, 2016)“The book under review is more elementary; it is exclusively devoted to Grassmannians and their Schubert subvarieties. The book is divided into three parts. … This is a nicely written book, one that may appeal to students and researchers in related areas.” (Felipe Zaldivar, MAA Reviews, maa.org, December, 2015)Table of ContentsPreface.- 1. Introduction.- Part I. Algebraic Geometry—A Brief Recollection - 2. Preliminary Material.- 3. Cohomology Theory.- 4. Gröbner Bases.- Part II. Grassmannian and Schubert Varieties.- 5. The Grassmannian and Its Schubert Varieties.- 6. Further Geometric Properties of Schubert Varieties.- 7. Flat Degenerations.- Part III. Flag Varieties and Related Varieties.- 8. The Flag Variety: Geometric and Representation-Theoretic Aspects.- 9. Relationship to Classical Invariant Theory.- 10. Determinantal Varieties.- 11. Related Topics.- References.- List of Symbols.- Index.
£59.99
CRC Press Introduction to Number Theory
Book SynopsisIntroduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbertâs tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Eulerâs theorem in RSA encryption, and quadratic residues in the construction of tournaments. Ideal for a one- or two-semester undergraduate-level course, this Second Edition: Features a more flexible structure that offers a greater range of options for course design Adds new sections on the representations of integTrade ReviewPraise for the Previous Edition "The authors succeed in presenting the topics of number theory in a very easy and natural way, and the presence of interesting anecdotes, applications, and recent problems alongside the obvious mathematical rigor makes the book even more appealing. … a valid and flexible textbook for any undergraduate number theory course."—International Association for Cryptologic Research Book Reviews, May 2011 "… a welcome addition to the stable of elementary number theory works for all good undergraduate libraries."—J. McCleary, Vassar College, Poughkeepsie, New York, USA, from CHOICE, Vol. 46, No. 1, August 2009 "… a reader-friendly text. … provides all of the tools to achieve a solid foundation in number theory."—L’Enseignement Mathématique, Vol. 54, No. 2, 2008 The theory of numbers is a core subject of mathematics. The authors have written a solid update to the first edition (CH, Aug'09, 46-6857) of this classic topic. There is no shortage of introductions to number theory, and this book does not offer significantly different information. Nonetheless, the authors manage to give the subject a fresh, new feel. The writing style is simple, clear, and easy to follow for standard readers. The book contains all the essential topics of a first-semester course and enough advanced topics to fill a second. In particular, it includes several modern aspects of number theory, which are often ignored in other texts, such as the use of factoring in computer security, searching for large prime numbers, and connections to other branches of mathematics. Each section contains supplementary homework exercises of various difficulties, a crucial ingredient of any good textbook. Finally, much emphasis is placed on calculating with computers, a staple of modern number theory. Overall, this title should be considered by any student or professor seeking an excellent text on the subject. --A. Misseldine, Southern Utah University, Choice magazine 2016 Praise for the Previous Edition "The authors succeed in presenting the topics of number theory in a very easy and natural way, and the presence of interesting anecdotes, applications, and recent problems alongside the obvious mathematical rigor makes the book even more appealing. … a valid and flexible textbook for any undergraduate number theory course."—International Association for Cryptologic Research Book Reviews, May 2011 "… a welcome addition to the stable of elementary number theory works for all good undergraduate libraries."—J. McCleary, Vassar College, Poughkeepsie, New York, USA, from CHOICE, Vol. 46, No. 1, August 2009 "… a reader-friendly text. … provides all of the tools to achieve a solid foundation in number theory."—L’Enseignement Mathématique, Vol. 54, No. 2, 2008 The theory of numbers is a core subject of mathematics. The authors have written a solid update to the first edition (CH, Aug'09, 46-6857) of this classic topic. There is no shortage of introductions to number theory, and this book does not offer significantly different information. Nonetheless, the authors manage to give the subject a fresh, new feel. The writing style is simple, clear, and easy to follow for standard readers. The book contains all the essential topics of a first-semester course and enough advanced topics to fill a second. In particular, it includes several modern aspects of number theory, which are often ignored in other texts, such as the use of factoring in computer security, searching for large prime numbers, and connections to other branches of mathematics. Each section contains supplementary homework exercises of various difficulties, a crucial ingredient of any good textbook. Finally, much emphasis is placed on calculating with computers, a staple of modern number theory. Overall, this title should be considered by any student or professor seeking an excellent text on the subject. --A. Misseldine, Southern Utah University, Choice magazine 2016 Table of ContentsIntroduction. Divisibility. Greatest Common Divisor. Primes. Congruences. Special Congruences. Primitive Roots. Cryptography. Quadratic Residues. Applications of Quadratic Residues. Sums of Squares. Further Topics in Diophantine Equations. Continued Fractions. Continued Fraction Expansions of Quadratic Irrationals. Arithmetic Functions. Large Primes. Analytic Number Theory. Elliptic Curves.
£92.14
Taylor & Francis Inc Representation Theory of Symmetric Groups
Book SynopsisRepresentation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today's students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovatiTrade Review"The book will be most useful as a reference for researchers...I believe it is a valuable contribution to the literature onthe symmetric group and related algebras." ~Mark J. Wildon, Mathematical Reviews, March 2018Table of ContentsI Symmetric groups and symmetric functions Representations of finite groups and semisimple algebras Finite groups and their representations Characters and constructions on representations The non-commutative Fourier transform Semisimple algebras and modules The double commutant theory Symmetric functions and the Frobenius-Schur isomorphism Conjugacy classes of the symmetric groups The five bases of the algebra of symmetric functions The structure of graded self-adjoint Hopf algebra The Frobenius-Schur isomorphism The Schur-Weyl dualityCombinatorics of partitions and tableaux Pieri rules and Murnaghan-Nakayama formula The Robinson-Schensted-Knuth algorithmConstruction of the irreducible representations The hook-length formula II Hecke algebras and their representationsHecke algebras and the Brauer-Cartan theory Coxeter presentation of symmetric groups Representation theory of algebras Brauer-Cartan deformation theory Structure of generic and specialised Hecke algebras Polynomial construction of the q-Specht modulesCharacters and dualities for Hecke algebras Quantum groups and their Hopf algebra structure Representation theory of the quantum groupsJimbo-Schur-Weyl duality Iwahori-Hecke duality Hall-Littlewood polynomials and characters of Hecke algebras Representations of the Hecke algebras specialised at q = 0 Non-commutative symmetric functionsQuasi-symmetric functions The Hecke-Frobenius-Schur isomorphisms III Observables of partitions The Ivanov-Kerov algebra of observablesThe algebra of partial permutations Coordinates of Young diagrams and their momentsChange of basis in the algebra of observables Observables and topology of Young diagrams The Jucys-Murphy elements The Gelfand-Tsetlin subalgebra of the symmetric group algebraJucys-Murphy elements acting on the Gelfand-Tsetlin basis Observables as symmetric functions of the contents Symmetric groups and free probabilityIntroduction to free probability Free cumulants of Young diagrams Transition measures and Jucys-Murphy elementsThe algebra of admissible set partitions The Stanley-Féray formula and Kerov polynomials New observables of Young diagrams The Stanley-Féray formula for characters of symmetric groups Combinatorics of the Kerov polynomials IV Models of random Young diagrams Representations of the infinite symmetric group Harmonic analysis on the Young graph and extremal charactersThe bi-infinite symmetric group and the Olshanski semigroup Classification of the admissible representations Spherical representations and the GNS construction Asymptotics of central measuresFree quasi-symmetric functions Combinatorics of central measures Gaussian behavior of the observablesAsymptotics of Plancherel and Schur-Weyl measures The Plancherel and Schur-Weyl models Limit shapes of large random Young diagrams Kerov’s central limit theorem for characters Appendix A Representation theory of semisimple Lie algebras Nilpotent, solvable and semisimple algebras Root system of a semisimple complex algebra The highest weight theory
£175.75
Taylor & Francis Inc Handbook of Geometric Constraint Systems
Book SynopsisThe Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures CTrade ReviewBroadly speaking, a geometric constraint system (GCS) consists of basic geometric objects such as points, lines, or rigid bodies that satisfy some specified geometric relationships such as distances, angles, or incidences. Such systems arise in many prac-tical applications, including computer-aided design, molecular and materials modelling, robotics, sensor networks, and machine learning. This handbook is a wide-ranging reference work on the core principles, methods, and results in GCS research. It makes this topic fully accessible to nonspecialists as well as to experts who work in this area professionally, either as academics or as practitioners in fields such as engineering or robotics. The book is divided into four major parts. The first part (Chapters 2–7) deals with geometric reasoning techniques, with many of the approaches based on algebraic meth-ods. It starts with a discussion of techniques for automated geometry theorem proving. In particular, it introduces the bracket algebra and Grassmann-Cayley algebra in the context of proving theorems in projective and Euclidean geometry. These algebras are also discussed in relation to algebraic conditions (and their geometric interpretations) that make realisations of a GCS special. After a discussion of molecular distance geome-try and algebraic invariants in geometric reasoning, the first part of the book concludes with a description of various triangle-decomposable GCSs and algorithms for solving such systems via recursive decompositions and recombinations, as well as generalisations of this method to non-triangle-decomposable GCSs. The second part (Chapters 8–12) discusses techniques for understanding dependent constraints and certain types of rigidity (such as dimensional or universal rigidity) arising from the structure of the Euclidean distance cone. This is followed by a discussion of the structure of general metric cones. Additional topics include Cayley configuration spaces and constraint varieties of mechanisms. The second part of the book concludes with an introduction to real algebraic geometry for geometric constraints. The third part (Chapters 13–17) is dedicated to geometric results and techniques for analysing the rigidity and flexibility of GCSs, with a particular focus on bar-joint frameworks. It discusses the rigidity of polyhedra in 3-space, the rigidity of tensegrity frameworks (i.e., distance-constrained point configurations with equality and inequality constraints), geometric conditions of rigidity in nongeneric settings, methods and results for analysing global rigidity of generic bar-joint frameworks in general dimension, and transformations between metric spaces that preserve various types of rigidity. Finally, the fourth part of the book (Chapters 18–24) is concerned with methods and results in combinatorial rigidity theory, which looks for polynomial-time deterministic algorithms for testing the rigidity of GCSs that are in generic position. It gives detailed discussions of the generic rigidity and global rigidity of bar-joint frameworks (and related structures) in the Euclidean plane, and of frameworks in general dimension consisting of rigid bodies that are connected by bars or hinges. Moreover, it discusses the rigidity of generic point-line and body-and-cad frameworks, the rigidity of bar-joint frameworks where the underlying metric is governed by a polyhedral norm, and the rigidity of frameworks that are as generic as possible subject to certain symmetry or periodicity constraints. Many proofs in combinatorial rigidity are obtained via recursive graph constructions that preserve generic rigidity or global rigidity, and hence a whole chapter is dedicated to this topic. - Bernd Schulze - Mathematical Reviews Clippings - June 2019 Table of ContentsOverview and preliminaries. Computer-assisted Theorem Proving in Synthetic Geometry. Coordinate-Free Theorem Proving in Incidence Geometry. Special positions of frameworks and the Grassmann-Cayley Algebra. From Molecular Distance Geometry to Conformal Geometric Algebra. Tree-decomposable and Underconstrained Geometric Constraint Problems. Geometric Constraint Decomposition: The General Case. Dimensional and Universal Rigidities of Bar Frameworks. Computations of metric/cut polyhedra and their relatives. Cayley Configuration Spaces. Constraint Varieties in Mechanism Science. Real Algebraic Geometry for Geometric Constraints. Polyhedra in 3-Space. Tensegrity. Geometric Conditions of Rigidity in Nongeneric settings. Generic Global Rigidity in General Dimension. Change of Metrics in Rigidity Theory. Planar Rigidity. Inductive constructions for combinatorial local and global rigidity. Rigidity of Body-bar-hinge Frameworks. Global rigidity of two-dimensional frameworks. Point-line frameworks. Generic rigidity of body-and-cad frameworks. Rigidity with polyhedral norms. Combinatorial rigidity of symmetric and periodic frameworks.
£218.50
Taylor & Francis Inc An Invitation to the RogersRamanujan Identities
Book SynopsisThe Rogers--Ramanujan identities are a pair of infinite seriesinfinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the RogersRamanujan identities and will include related historical material that is unavailable elsewhere.Trade ReviewThis one-of-a-kind text, best suited for graduate level students and above, focuses exclusively on the Rogers-Ramanujan identities and their history. These two identities from number theory involve both infinite series and infinite products. The identities were independently discovered by Leonard James Rogers (1894 with proof), Srinivasa Ramanujan (before 1913 without proof), and Issai Schur (1917 with proof). The identities are relevant to the study of integer partitions, Lie algebras, statistical mechanics, computer science, and several other areas. Sills (Georgia Southern Univ.) begins with a review of partition theory and hypergeometric series. In the next two chapters, he moves on to prove the Rogers-Ramanujan identities and to explain their combinatorial aspects, as well as related identities and extensions. The final two chapters treat applications including continued fractions and knot theory. One appendix lists 236 related identities. A second appendix enhances the book's historical utility by providing transcriptions of letters between key researchers from 1943 to 1961. The book also includes more than 60 enlightening exercises.—D. P. Turner, Faulkner University, CHOICE Reviews"In recent years ¿-series have arisen in knot theory, and Sills discusses a few ¿-series that arise in the study of certain simple fundamental knots. While there have been systematic discussions of many of the topics mentioned above in various books, monographs, and survey articles, Sills’s book is the first comprehensive discussion of R-R type identities in all their forms, describing the state of the art. Since the subject is so vast, he does not provide proofs for most of the identities discussed, but he provides an interesting and illuminating historical context for each topic, gives good motivation, and describes the key ideas underlying the proofs. He also provides a substantial number of references that will lead both the studenTable of ContentsBackground and the Pre-History. The Golden Age and its Modern Legacy. Infinite Families...Everywhere! From Infinite to Finite. Motivated Proofs, Connections to Lie Algebras, and More Identities. But wait...there's more!
£99.75
Taylor & Francis Inc Algorithmics of Nonuniformity
Book SynopsisAlgorithmics of Nonuniformity is a solid presentation about the analysis of algorithms, and the data structures that support them. Traditionally, algorithmics have been approached either via a probabilistic view or an analytic approach. The authors adopt both approaches and bring them together to get the best of both worlds and benefit from the advantage of each approach. The text examines algorithms that are designed to handle general datasort any array, find the median of any numerical set, and identify patterns in any setting. At the same time, it evaluates average performance, typical behavior, or in mathematical terms, the expectations of the random variables that describe their operations.Many exercises are presented, which are essential since they convey additionalmaterial complementing the content of the chapters. For this reason, the solutions are more than mere answers, but explain and expandTable of Contents1 Algorithmics 2 Counting: Tools and Strategies 3 Symbolic Calculus 4 Languages and Their Generating Functions 5 Probability in Algorithmics 6 Data Models 7 Sorting Nonuniform Data 8 Nonuniform Pólya Urn Schemes 9 Nonuniform trees
£199.50
Taylor & Francis Inc Beyond First Order Model Theory Volume I
Book SynopsisModel theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.Table of ContentsAbstract elementary classes. Generalized logics in set theory. Topological methods in abstract model theory. Randomizations of structures. First Order logics with dependent sorts. Applications of infinitary logics.
£175.75
Taylor & Francis Inc Buildings and Schubert Schemes
Book SynopsisThe first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck''s SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.Table of ContentsGrassmannians and Flag Varieties. Schubert Cell Decomposition of Grassmannians and Flag Varieties. Resolution of Singularities of a Schubert Variety. The Singular Locus of a Schubert Variety. The Flag Complex. Configurations and Galleries Varieties. Configurations Varieties as Galleries Varieties. The Coxeter Complex. Minimal Generalized Galleries in a Coxeter Complex. Minimal Generalized Galleries in a Reductive Group Building. Parabolic Subgroups in a Reductive Group Scheme. Associated Schemes to the Relative Building. Incidence Type Schemes of the Relative Building. Smooth Resolutions of Schubert Schemes. Contracted Products and Galleries Configurations Schemes. Functoriality of Schubert Schemes Smooth Resolutions and Base Changes. About the Coxeter Complex. Generators and Relations and the Building of a Reductive Group.
£175.75
Taylor & Francis Inc A Bridge to Higher Mathematics
Book SynopsisA Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next Trade ReviewThis is one of the shorter books for a course that introduces students to the concept of mathematical proofs. The brevity is due to the "bare-bones" nature of the treatment. The number of topics covered, the number of examples, and the number of exercises are not smaller than what appears in competing textbooks; what is shorter is the text that one finds between theorems, lemmas, examples, and exercises. Besides the topics found in similar textbooks (i.e., proof techniques, logic, set theory, relations, and functions), there are chapters on (very) elementary number theory, combinatorial counting techniques, and Peano axioms on the set of positive integers. Several chapters are devoted to the construction of various kinds of numbers, such as integers, rationals, real numbers, and complex numbers. Answers to around half the exercises are included at the end of the book, and a few have complete solutions. This reviewer finds the book more enjoyable than the average competing textbook. --M. Bona, University of FloridaTable of ContentsElements of logicTrue and false statementsLogical connectives and truth tablesLogical equivalenceQuantifiersProofs: Structures and strategiesAxioms, theorems and proofsDirect proofContrapositive proofProof by equivalent statementsProof by casesExistence proofsProof by counterexampleProof by mathematical inductionElementary Theory of Sets. FunctionsAxioms for set theoryInclusion of setsUnion and intersection of setsComplement, difference and symmetric difference of setsOrdered pairs and the Cartersian productFunctionsDefinition and examples of functionsDirect image, inverse imageRestriction and extension of a functionOne-to-one and onto functionsComposition and inverse functions*Family of sets and the axiom of choiceRelationsGeneral relations and operations with relationsEquivalence relations and equivalence classesOrder relations*More on ordered sets and Zorn's lemmaAxiomatic theory of positive integersPeano axioms and additionThe natural order relation and subtractionMultiplication and divisibilityNatural numbersOther forms of inductionElementary number theoryAboslute value and divisibility of integersGreatest common divisor and least common multipleIntegers in base 10 and divisibility testsCardinality. Finite sets, infinite setsEquipotent setsFinite and infinite setsCountable and uncountable setsCounting techniques and combinatoricsCounting principlesPigeonhole principle and parityPermutations and combinationsRecursive sequences and recurrence relationsThe construction of integers and rationals Definition of integers and operationsOrder relation on integersDefinition of rationals, operations and orderDecimal representation of rational numbersThe construction of real and complex numbersThe Dedekind cuts approachThe Cauchy sequences approachDecimal representation of real numbersAlgebraic and transcendental numbersComples numbersThe trigonometric form of a complex number
£73.14
Taylor & Francis Inc Matrix Inequalities for Iterative Systems
Book SynopsisThe book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.Table of ContentsIntroduction. Notation and Basic Facts. Motivation. Diagonalization and Spectral Decomposition. Undirected Graphs / Hermitian Matrices. General Results. Restricted Graph Classes. Directed Graphs / Nonsymmetric. Walks and Alternating Walks in Directed Graphs. Powers of Row and Column Sums. Applications. Bounds for the Largest Eigenvalue. Iterated Kernels. Conclusion. Bibliography. Index.
£142.50
Taylor & Francis Inc Combinatorics
Book SynopsisCombinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorTable of ContentsPART 1: ENUMERATION. Chapter 1: Basic Counting; Chapter 2: Combinatorial Identities and Recursions; Chapter 3: Counting Problems in Graph Theory; Chapter 4: Inclusion-Exclusion and Related Techniques; New Chapter 5: Generating Functions; Chapter 6: Ranking, Unranking, and Successor Algorithms; PART 2: ALGEBRAIC COMBINATORICS; Chapter 7: Permutation Statistics and q-Analogues; Chapter 8: Permutations and Group Actions; Chapter 9: Tableaux and Symmetric Polynomials. Chapter 10: Abaci and Antisymmetric Polynomials; Chapter 11: Additional Topics. New Appendix: Background in Abstract Algebra.
£104.50
Hodder Education AQA A Level Further Mathematics Discrete
Book SynopsisExam board: AQALevel: A levelSubject: MathsFirst teaching: September 2017First exams: Summer 2019Provide full support for the AQA Discrete content of the new specification with worked examples, stimulating activities and assessment support to help develop understanding, reasoning and problem solving. - Help prepare students for assessment with skills-building activities and fully worked examples and solutions tailored to the changed criteria.- Build understanding through carefully worded expositions that set out the basics and the detail of each topic, with call-outs to add clarity.- Test knowledge and develop understanding, reasoning and problem solving with banded Exercise questions that increase in difficulty (answers provided in the back of the book and online). - Gain a full understanding of the logical steps that are used in creating each individual algorithm - Encourages students to track their progress using learning outcomes and Key Points listed at the end of each chapter.
£29.34
Taylor & Francis Inc Logic Colloquium '99: Lecture Notes in Logic 17
Book SynopsisA compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active areas of logic, geometric model theory and descriptive set theory of group actions. The other articles cover current reseach topics in all areas of mathematical logic, including logic in computer science, proof theory, set theory, model theory, computability theory, and philosophy.Trade Review… The collection gives a good picture of the situation in logic at the millenium.-C.W. Kilmister, The Mathematical Gazette, July 2005
£74.09
Taylor & Francis Inc Logic Colloquium '99: Lecture Notes in Logic 17
Book SynopsisA compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active areas of logic, geometric model theory and descriptive set theory of group actions. The other articles cover current reseach topics in all areas of mathematical logic, including logic in computer science, proof theory, set theory, model theory, computability theory, and philosophy.Trade Review… The collection gives a good picture of the situation in logic at the millenium.-C.W. Kilmister, The Mathematical Gazette, July 2005
£40.84
Taylor & Francis Inc Logic Colloquium 2000 (hardcover): Lecture Notes
Book SynopsisThis compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities. The presentations include tutorials and research articles from some of the world's preeminent logicians. Three long articles are based on tutorials given at the meeting, and present accessible expositions of devloping research in three active areas of logic: model theory, computability, and set theory. The eleven subsequent articles cover seperate research topics in all areas of mathematical logic, including: aspects in Computer Science, Proof Theory, Set Theory, Model Theory, Computability Theory, and aspects of Philosophy.Table of ContentsTutorials; Model Theory and Geometry; Notions of Computability at Higher Types I; The Continuum Hypothesis; Participant Photographs; Articles; Bounded Forcing Axioms and the Size of the Continuum; Hilbert's Wide Program; Rigidity Conjectures; Metapredicative and Explicit Mahlo: a Proof-Theoretic Perspective; A Two-Dimensional Tree Ideal; Psychology Looks Hopefully to Logic; Russell's Logics; Partitioning Pairs of Uncountable Sets; Aspects of the Turing Jump; Liouville Functions; Analytic and Pseudo-Analytic Structures
£40.84
Taylor & Francis Inc Logical Dilemmas: The Life and Work of Kurt Gödel
Book SynopsisThis authoritative biography of Kurt Goedel relates the life of this most important logician of our time to the development of the field. Goedel's seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from the turn of the century Austria to the Institute for Advanced Study in Princeton.Trade ReviewDawson's book remains a starting point for our view into the life and work of the man who gave the world incompleteness. -- The Review of Modern Logic, March 2007Table of Contents1. Der Herr Warum (1920-1924) 2. Intellectual Maturation (1924-29) 3. Excursus: A Capsule History of the Development of Logic to 1928 4. Moment of Impact (1929-31) 5. Dozent in absentia (1932-37) 6. “Jetzt, Mengenlehre” (1937-39) 7. Homecoming and Hegira (1939-40) 8. Years of Transition (1940-46) 9. Philosophy and Cosmology (1946-51) 10. Recognition and Reclusion (1951-61) 11. New Light on the Continuum Problem (1961-68) 12. Withdrawal (1969-78) 13. Aftermath 14. Reflections on Gödel’s Life and Legacy
£40.84
