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.
Author(s): Gerard Prudhomme
Publisher: Arcler Press
Year: 2019
Language: English
Pages: 266
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
