Computer Mathematics

Computer mathematics examines various aspects of mathematics including an extensiveoverview of computational mathematics. It includes definitions of predictable phenomena, theory of models and of groups, programming models, introduction to formalcomputer-aided proof, theory of the demonstration, working group on core courses, finite model theory, calculability and incompleteness, programming models, combinator, mathematical logic, foundations of computing, provides the reader with insightsinto the development of its history, so as to understand the general theory of algorithms, recursive functions, introduction to complexity, theory of finite models and applications, approximate verification and complexity, working on fundamental courses, preliminaryintensive logic. Cover......Page 1 Half Title Page......Page 3 Title Page......Page 5 Copyright Page......Page 6 About the Author......Page 7 Table of Contents......Page 9 List of Figures......Page 13 Preface......Page 27 Chapter 1 Preparatory Mathematical and Computer Science Studies......Page 29 Chapter 2 Predictable Phenomena......Page 39 2.1. Intensive Preliminary Courses of Logic......Page 42 Chapter 3 Theory of Models and of Groups......Page 45 Chapter 4 Programming Models......Page 47 Chapter 5 Introduction to Formal Computer-Aided Proof......Page 49 Chapter 6 Theory of the Demonstration......Page 51 6.1. Calculability And Incompleteness......Page 53 Chapter 7 Working Group on Core Courses......Page 61 7.2. Complexity......Page 63 Chapter 8 Finite Model Theory......Page 65 Chapter 9 Calculability and Incompleteness......Page 69 Chapter 10 Programming Models......Page 71 Chapter 11 Combinators......Page 81 Chapter 12 Mathematical Logic......Page 83 Chapter 13 Foundations of Computing......Page 85 Chapter 14 Formal Arithmetic......Page 87 Chapter 15 Database Object Component......Page 95 Chapter 16 Arithmetization of Logic......Page 97 Chapter 17 Computability and Complexity......Page 105 Chapter 18 Polarization and Classical Logic......Page 109 Chapter 19 Syntax and Semantics......Page 115 Chapter 20 Proofs and Types......Page 117 Chapter 21 Foundations for Programming Languages......Page 119 21.1. Basic Set Theory......Page 121 Chapter 22 Descriptive Set Theory......Page 125 22.1. Structures And Techniques......Page 127 Chapter 23 Semantics of Programming Languages......Page 129 Chapter 24 Stable Groups......Page 139 Chapter 25 General Theory of Algorithms......Page 141 Chapter 26 Recursive Functions......Page 143 26.1. Machine-Calculable Functions......Page 145 Chapter 27 Logical Characterization of Computable Functions......Page 153 Chapter 28 Notions of Reduction and Undecidable Problems......Page 155 Chapter 29 Introduction to Complexity......Page 157 Chapter 30 Theory of Finite Models and Applications......Page 159 Chapter 31 Approximate Verification and Complexity......Page 163 Chapter 32 Working on Fundamental Courses......Page 165 Chapter 33 Preliminary Intensive Logic......Page 167 Chapter 34 Classic Tools......Page 169 Chapter 35 An Introduction to Contemporary Mathematical Logic......Page 171 Chapter 36 A Course in Model Theory......Page 173 Chapter 37 Classes and Completeness......Page 175 Chapter 38 Axioms......Page 193 Chapter 39 The Incompleteness Theorems......Page 195 Chapter 40 Conceptual Perspectives......Page 213 Chapter 41 Programming Perspectives......Page 237 Chapter 42 Advances in Linear Logic......Page 241 Chapter 43 Symbolic Logic......Page 251 Bibliography......Page 259 Index......Page 265