E-Book, Englisch, 334 Seiten, Web PDF
Goodstein / Sneddon Fundamental Concepts of Mathematics
2. Auflage 2014
ISBN: 978-1-4831-5405-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 334 Seiten, Web PDF
Reihe: International Series in Pure and Applied Mathematics
ISBN: 978-1-4831-5405-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people who want to gain a thorough understanding of the fundamental concepts of mathematics will find this book a good reference.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Fundamental Concepts of Mathematics;4
3;Copyright Page;5
4;Table of Contents;8
5;PREFACE TO THE SECOND EDITION;6
6;PREFACE;7
7;CHAPTER 1. NUMBERS FOR COUNTING;12
7.1;Addition;16
7.2;Mathematical Induction;25
7.3;Inequality;28
7.4;Subtraction;29
7.5;Multiplication;32
7.6;Prime Numbers;38
7.7;Division;40
7.8;Exponentiation;44
7.9;Representation in a scale;45
7.10;Tetration;52
7.11;The arithmetic of remainders;54
7.12;The fundamental theorem of arithmetic;58
7.13;The measuring problem;65
7.14;The explorer problem;66
7.15;Groups;67
7.16;Semigroups;76
7.17;The word problem for groups;81
7.18;Congruences;81
7.19;Format's Theorem;82
7.20;Tests for divisibility;87
7.21;Tests for powers;91
7.22;Pascal's Triangle;93
7.23;An Inequality;99
7.24;Ordinal numbers;100
7.25;Notes on Chapter 1;103
8;CHAPTER 2. NUMBERS FOR PROFIT AND LOSS
AND NUMBERS FOR SHARING;104
8.1;Positive and negative integers;104
8.2;The ring of integers;108
8.3;Inequalities;109
8.4;Numbers for sharing;111
8.5;Inequalities;121
8.6;Index laws for fractions;125
8.7;The field of rational numbers;126
8.8;Negative indices;131
8.9;Fractional indices;131
8.10;Polynomials;137
8.11;Remainder fields;142
8.12;Sequence of polynomials;145
8.13;Examples I;146
8.14;Solutions to Examples I;147
8.15;Notes on Chapter 2;150
9;CHAPTER 3.
NUMBERS UNENDING;151
9.1;Decimal fractions;151
9.2;Irrational decimals;156
9.3;Addition of infinite decimals;159
9.4;Multiplication of infinite decimals;160
9.5;Subtraction of infinite decimals;161
9.6;Division of infinite decimals;161
9.7;Positive and negative decimals;163
9.8;Examples II;164
9.9;Solutions to Examples II;164
9.10;Convergence;165
9.11;Examples III;167
9.12;Solutions to Examples III;168
9.13;Some important limits;171
9.14;Generalized binomial theorem;177
9.15;Decimal collision;183
9.16;Continuity;184
9.17;INTERVALS;186
9.18;CONTINUITY;190
9.19;Examples IV;198
9.20;Solutions to Examples IV;199
9.21;INTEGRATION;204
9.22;THE DERIVATIVE;215
9.23;Examples V;232
9.24;Solutions to Examples V;233
9.25;Pretender numbers;236
9.26;Notes on Chapter 3;240
10;CHAPTER 4. SETS AND TRUTH FUNCTIONS;241
10.1;Sentence logic;248
10.2;Switching circuits;259
10.3;Hilbert's tenth problem;282
10.4;Examples VI;283
10.5;Solutions to Examples VI;284
10.6;Notes on Chapter 4;286
11;CHAPTER 5.
NETWORKS AND MAPS;287
11.1;Connectivity;287
11.2;Networks;289
11.3;Euler's formula;292
11.4;Characteristic of a surface;295
11.5;The regular solids;296
11.6;MAP COLOURING;298
11.7;METRIC SPACES;314
11.8;Notes in Chapter 5;322
12;CHAPTER 6.
AXIOMATIC THEORY OF SETS;323
13;INDEX;328
14;OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS;332
