Murphy Modern Mathematics

Made Simple
1. Auflage 2014
ISBN: 978-1-4832-8003-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 286 Seiten, Web PDF

Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed. Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional statements; and biconditional sentences. Subsequent chapters focus on switching circuits; multibase arithmetic; finite systems; relations, vectors, and matrices; tessellations; and linear programming. The book concludes with an analysis of motion geometry and rubber sheet geometry, paying particular attention to radial enlargement and composite reflections as well as topological equivalence, networks for maps, and incidence matrices. This monograph is intended for students, parents, and teachers who are interested in modern mathematics.

Autoren/Hrsg.

Murphy, Patrick

Inhaltsverzeichnis

1;Front Cover;1
2;Modern Mathematics: Made Simple;4
3;Copyright Page;5
4;Table of Contents;8
5;Foreword;6
6;CHAPTER 1. SETS;12
6.1;Notation;12
6.2;Numbers;14
6.3;The Empty Set;15
6.4;Finite and Infinite Sets;15
6.5;Subsets;17
6.6;Universal Sets;19
6.7;Complement;20
6.8;Intersection;21
6.9;Union;25
6.10;Basic Operations on Sets;27
6.11;The Distributive Law;30
6.12;Equations;31
6.13;Solving Problems with Venn Diagrams;33
7;CHAPTER 2. ELEMENTARY MATHEMATICAL LOGIC;39
7.1;Inductive Reasoning;39
7.2;Deductive Reasoning;41
7.3;Mathematical Sentences;44
7.4;Replacement and Solution Sets;45
7.5;Compound Statements;46
7.6;Conjunctions;46
7.7;Disjunctions;47
7.8;Negation;50
7.9;Conditional Statements;52
7.10;Biconditional Sentences;55
8;CHAPTER 3. SWITCHING CIRCUITS;61
8.1;Connectiops in Series;61
8.2;Connection in Parallel;62
8.3;The Distributive Law;65
8.4;Obtaining Functions Direct From Truth Tables;67
8.5;Negation;70
8.6;Gates;74
9;CHAPTER 4. MULTIBASE ARITHMETIC;79
9.1;Notation;80
9.2;Conversion from Base 10;81
9.3;Approximation;84
9.4;Addition;87
9.5;Subtraction;87
9.6;Multiplication;89
9.7;Division;91
9.8;Fractions;92
9.9;Puzzles;94
10;CHAPTER 5. FINITE SYSTEMS;99
10.1;Clock Arithmetic;99
10.2;Subtraction;101
10.3;Additive Inverses;101
10.4;Multiplicative Inverses;103
10.5;Modular Arithmetic;104
10.6;Fractions;106
10.7;A More Formal Discussion;108
10.8;Other Finite Systems;111
10.9;Groups;114
10.10;Isomorhisms;115
10.11;Subgroups;116
11;CHAPTER 6. RELATIONS;118
11.1;Relation Diagrams;120
11.2;Types of Relations;122
11.3;Cartesian Product;125
11.4;Inverse Relations;127
11.5;Graphs;128
11.6;Correspondences;133
11.7;Functions;134
11.8;Inverse Functions;137
11.9;Composition of Functions;138
12;CHAPTER 7. LINEAR PROGRAMMING;142
12.1;Equations for Straight Lines;142
12.2;Optimisation;145
12.3;Extreme Points;147
12.4;A Further Constraint;149
12.5;Non-linear Programming;156
13;CHAPTER 8. VECTORS;160
13.1;The Triangle Law;163
13.2;Vector Subtraction;166
13.3;Multiplication of a Vector by a Scalar;167
13.4;The Associative Law;169
13.5;Vector Geometry;170
13.6;Unit Vectors;174
13.7;Perpendicular Unit Vectors;174
13.8;The Dot Product;176
13.9;The Distributive Law;177
13.10;More Dot Products;179
14;CHAPTER 9. MATRICES;182
14.1;Reflections in the Axes;182
14.2;Reflection in y = ± x;184
14.3;Matrices for Reflections;186
14.4;Dot Products;188
14.5;Rotations;189
14.6;Radial Expansion;191
14.7;Matrix Multiplication;193
14.8;The (2 x 2) Inverse Matrix;197
14.9;Simultaneous Equations;199
14.10;A Group of Matrices;201
14.11;Addition;202
15;CHAPTER 10. TESSELLATONS;205
15.1;Quadrilaterals;205
15.2;Quadrisides;207
15.3;Pentagons;209
15.4;Hexagons;212
15.5;Off Cuts;215
16;CHAPTER 11. MOTION GEOMETRY;217
16.1;Radial Enlargement;218
16.2;Reflection;221
16.3;Axes of Symmetry;222
16.4;Composite Reflections;223
16.5;Rotations;226
17;CHAPTER 12. RUBBER SHEET GEOMETRY;231
17.1;Topological Equivalence;232
17.2;Networks;235
17.3;Euler's Results;238
17.4;Networks for Maps;240
17.5;Incidence Matrices;243
17.6;V + F – E = 2;245
17.7;Surfaces;246
17.8;Experiments in Topology: The Moebius Strip;248
17.9;The Punctured Torus;249
17.10;The Four-colour Problem;251
18;SOLUTONS;252
19;APPENDIX: Some Abbreviations and Deflnitions;280
20;INDEX;284