{"product_id":"combinatorial-and-algorithmic-mathematics-isbn-9781394235940","title":"Combinatorial and Algorithmic Mathematics","description":"\u003cp\u003e\u003cb\u003eDetailed review of optimization from first principles, supported by rigorous math and computer science explanations and various learning aids\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eSupported by rigorous math and computer science foundations, \u003ci\u003eCombinatorial and Algorithmic Mathematics: From Foundation to Optimization\u003c\/i\u003e provides a from-scratch understanding to the field of optimization, discussing 70 algorithms with roughly 220 illustrative examples, 160 nontrivial end-of-chapter exercises with complete solutions to ensure readers can apply appropriate theories, principles, and concepts when required, and Matlab codes that solve some specific problems. This book helps readers to develop mathematical maturity, including skills such as handling increasingly abstract ideas, recognizing mathematical patterns, and generalizing from specific examples to broad concepts. \u003c\/p\u003e\u003cp\u003eStarting from first principles of mathematical logic, set-theoretic structures, and analytic and algebraic structures, this book covers both combinatorics and algorithms in separate sections, then brings the material together in a final section on optimization. This book focuses on topics essential for anyone wanting to develop and apply their understanding of optimization to areas such as data structures, algorithms, artificial intelligence, machine learning, data science, computer systems, networks, and computer security. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eCombinatorial and Algorithmic Mathematics\u003c\/i\u003e includes discussion on: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ePropositional logic and predicate logic, set-theoretic structures such as sets, relations, and functions, and basic analytic and algebraic structures such as sequences, series, subspaces, convex structures, and polyhedra\u003c\/li\u003e\n\u003cli\u003eRecurrence-solving techniques, counting methods, permutations, combinations, arrangements of objects and sets, and graph basics and properties\u003c\/li\u003e\n\u003cli\u003eAsymptotic notations, techniques for analyzing algorithms, and computational complexity of various algorithms\u003c\/li\u003e\n\u003cli\u003eLinear optimization and its geometry and duality, simplex and non-simplex algorithms for linear optimization, second-order cone programming, and semidefinite programming\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eCombinatorial and Algorithmic Mathematics \u003c\/i\u003eis an ideal textbook resource on the subject for students studying discrete structures, combinatorics, algorithms, and optimization. It also caters to scientists across diverse disciplines that incorporate algorithms and academics and researchers who wish to better understand some modern optimization methodologies. \u003c\/p\u003e\u003cp\u003eAbout the Author xiii\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Foundations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Mathematical Logic 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Propositions 3\u003c\/p\u003e \u003cp\u003e1.2 Logical Operators 6\u003c\/p\u003e \u003cp\u003e1.3 Propositional Formulas 15\u003c\/p\u003e \u003cp\u003e1.4 Logical Normal Forms 24\u003c\/p\u003e \u003cp\u003e1.5 The Boolean Satisfiability Problem 29\u003c\/p\u003e \u003cp\u003e1.6 Predicates and Quantifiers 30\u003c\/p\u003e \u003cp\u003e1.7 Symbolizing Statements of the Form \"All P Are Q\" 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Set-Theoretic Structures 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Induction 51\u003c\/p\u003e \u003cp\u003e2.2 Sets 54\u003c\/p\u003e \u003cp\u003e2.3 Relations 59\u003c\/p\u003e \u003cp\u003e2.4 Partitions 64\u003c\/p\u003e \u003cp\u003e2.5 Functions 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Analytic and Algebraic Structures 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Sequences 77\u003c\/p\u003e \u003cp\u003e3.2 Summations and Series 81\u003c\/p\u003e \u003cp\u003e3.3 Matrices, Subspaces, and Bases 87\u003c\/p\u003e \u003cp\u003e3.4 Convexity, Polyhedra, and Cones 91\u003c\/p\u003e \u003cp\u003e3.5 Farkas' Lemma and Its Variants 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Combinatorics 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Graphs105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Basic Graph Definitions 106\u003c\/p\u003e \u003cp\u003e4.2 Isomorphism and Properties of Graphs 113\u003c\/p\u003e \u003cp\u003e4.3 Eulerian and Hamiltonian Graphs 118\u003c\/p\u003e \u003cp\u003e4.4 Graph Coloring 122\u003c\/p\u003e \u003cp\u003e4.5 Directed Graphs 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Recurrences 133\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Guess-and-Confirm 133\u003c\/p\u003e \u003cp\u003e5.2 Recursion-Iteration 136\u003c\/p\u003e \u003cp\u003e5.3 Generating Functions 138\u003c\/p\u003e \u003cp\u003e5.4 Recursion-Tree 140\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Counting149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Binomial Coefficients and Identities 149\u003c\/p\u003e \u003cp\u003e6.2 Fundamental Principles of Counting 154\u003c\/p\u003e \u003cp\u003e6.3 The Pigeonhole Principle 161\u003c\/p\u003e \u003cp\u003e6.4 Permutations 163\u003c\/p\u003e \u003cp\u003e6.5 Combinations 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Algorithms 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Analysis of Algorithms 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Constructing and Comparing Algorithms 182\u003c\/p\u003e \u003cp\u003e7.2 Running Time of Algorithms 189\u003c\/p\u003e \u003cp\u003e7.3 Asymptotic Notation 199\u003c\/p\u003e \u003cp\u003e7.4 Analyzing Decision-Making Statements 211\u003c\/p\u003e \u003cp\u003e7.5 Analyzing ProgramsWithout Function Calls 213\u003c\/p\u003e \u003cp\u003e7.6 Analyzing Programs with Function Calls 219\u003c\/p\u003e \u003cp\u003e7.7 The Complexity Class NP-Complete 224\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Array and Numeric Algorithms 241\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Array Multiplication Algorithms 241\u003c\/p\u003e \u003cp\u003e8.2 Array Searching Algorithms 244\u003c\/p\u003e \u003cp\u003e8.3 Array Sorting Algorithms 248\u003c\/p\u003e \u003cp\u003e8.4 Euclid's Algorithm 253\u003c\/p\u003e \u003cp\u003e8.5 Newton's Method Algorithm 255\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Elementary Combinatorial Algorithms 267\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Graph Representations 267\u003c\/p\u003e \u003cp\u003e9.2 Breadth-First Search Algorithm 270\u003c\/p\u003e \u003cp\u003e9.3 Applications of Breadth-First Search 273\u003c\/p\u003e \u003cp\u003e9.4 Depth-First Search Algorithm 277\u003c\/p\u003e \u003cp\u003e9.5 Applications of Depth-First Search 279\u003c\/p\u003e \u003cp\u003e9.6 Topological Sort 283\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Optimization 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Linear Programming 295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Linear Programming Formulation and Examples 296\u003c\/p\u003e \u003cp\u003e10.2 The Graphical Method 302\u003c\/p\u003e \u003cp\u003e10.3 Standard Form Linear Programs 309\u003c\/p\u003e \u003cp\u003e10.4 Geometry of Linear Programming 311\u003c\/p\u003e \u003cp\u003e10.5 The Simplex Method 320\u003c\/p\u003e \u003cp\u003e10.6 Duality in Linear Programming 339\u003c\/p\u003e \u003cp\u003e10.7 A Homogeneous Interior-Point Method 347\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Second-Order Cone Programming 363\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Second-Order Cone and Its Algebraic Structure 363\u003c\/p\u003e \u003cp\u003e11.2 Second-Order Cone Programming Formulation 368\u003c\/p\u003e \u003cp\u003e11.3 Applications in Engineering and Finance 370\u003c\/p\u003e \u003cp\u003e11.4 Duality in Second-Order Cone Programming 375\u003c\/p\u003e \u003cp\u003e11.5 A Primal-Dual Path-Following Algorithm 379\u003c\/p\u003e \u003cp\u003e11.6 A Homogeneous Self-Dual Algorithm 386\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Semidefinite Programming and Combinatorial Optimization 395\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 The Cone of Positive Semidefinite Matrices 395\u003c\/p\u003e \u003cp\u003e12.2 Semidefinite Programming Formulation 399\u003c\/p\u003e \u003cp\u003e12.3 Applications in Combinatorial Optimization 401\u003c\/p\u003e \u003cp\u003e12.4 Duality in Semidefinite Programming 405\u003c\/p\u003e \u003cp\u003e12.5 A Primal–Dual Path-Following Algorithm 408\u003c\/p\u003e \u003cp\u003eExercises 417\u003c\/p\u003e \u003cp\u003eNotes and Sources 418\u003c\/p\u003e \u003cp\u003eReferences 418\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Solutions to Chapter Exercises 421\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 487\u003c\/p\u003e \u003cp\u003eBibliography 489\u003c\/p\u003e \u003cp\u003eIndex 501\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eBaha Alzalg\u003c\/b\u003e is a Professor in the Department of Mathematics at the University of Jordan in Amman, Jordan. He has also held the post of visiting associate professor in the Department of Computer Science and Engineering at the Ohio State University in Columbus, Ohio. His research interests include topics in optimization theory, applications, and algorithms, with an emphasis on interior-point methods for cone programming.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eDetailed review of optimization from first principles, supported by rigorous math and computer science explanations and various learning aids\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eSupported by rigorous math and computer science foundations, \u003ci\u003eCombinatorial and Algorithmic Mathematics: From Foundation to Optimization\u003c\/i\u003e provides a from-scratch understanding to the field of optimization, discussing 70 algorithms with roughly 220 illustrative examples, 160 nontrivial end-of-chapter exercises with complete solutions to ensure readers can apply appropriate theories, principles, and concepts when required, and Matlab codes that solve some specific problems. This book helps readers to develop mathematical maturity, including skills such as handling increasingly abstract ideas, recognizing mathematical patterns, and generalizing from specific examples to broad concepts. \u003c\/p\u003e\u003cp\u003eStarting from first principles of mathematical logic, set-theoretic structures, and analytic and algebraic structures, this book covers both combinatorics and algorithms in separate sections, then brings the material together in a final section on optimization. This book focuses on topics essential for anyone wanting to develop and apply their understanding of optimization to areas such as data structures, algorithms, artificial intelligence, machine learning, data science, computer systems, networks, and computer security. \u003c\/p\u003e\u003cp\u003e\u003ci\u003eCombinatorial and Algorithmic Mathematics\u003c\/i\u003e includes discussion on: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ePropositional logic and predicate logic, set-theoretic structures such as sets, relations, and functions, and basic analytic and algebraic structures such as sequences, series, subspaces, convex structures, and polyhedra\u003c\/li\u003e\n\u003cli\u003eRecurrence-solving techniques, counting methods, permutations, combinations, arrangements of objects and sets, and graph basics and properties\u003c\/li\u003e\n\u003cli\u003eAsymptotic notations, techniques for analyzing algorithms, and computational complexity of various algorithms\u003c\/li\u003e\n\u003cli\u003eLinear optimization and its geometry and duality, simplex and non-simplex algorithms for linear optimization, second-order cone programming, and semidefinite programming\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eCombinatorial and Algorithmic Mathematics \u003c\/i\u003eis an ideal textbook resource on the subject for students studying discrete structures, combinatorics, algorithms, and optimization. It also caters to scientists across diverse disciplines that incorporate algorithms and academics and researchers who wish to better understand some modern optimization methodologies.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988948140261,"sku":"NP9781394235940","price":115.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781394235940.jpg?v=1761782168","url":"https:\/\/k12savings.com\/es\/products\/combinatorial-and-algorithmic-mathematics-isbn-9781394235940","provider":"K12savings","version":"1.0","type":"link"}