Lloyd / Plumpton Modern Syllabus Algebra

The Commonwealth and International Library: Mathematical Topics
1. Auflage 2014
ISBN: 978-1-4831-3980-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 246 Seiten, Web PDF

Modern Syllabus Algebra presents topics of traditional and modern algebra found in the Teachers Certificate and B.Ed, part I syllabuses of University Institutes of Education. It also contains additional exercises taken from examination papers of the University of London Institute of Education (the Teachers' Certificate). The book discusses several mathematical concepts such as sets, relations and functions, Boolean algebra, groups, and number systems. It also illustrates linear equations, matrices, and vector spaces and then demonstrates how to solve complex numbers and combine probabilities. Mathematics teachers will find this text a suitable and convenient way of bringing themselves up to date in what is now being taught in schools.

Autoren/Hrsg.

Lloyd, D. G. H. B.

Plumpton, C.

Inhaltsverzeichnis

1;Front Cover;1
2;Modern Syllabus Algebra;4
3;Copyright Page;5
4;Table of Contents;6
5;CHAPTER 0. PURPOSE AND METHOD;8
5.1;1. Purpose;8
5.2;2. Scope;9
5.3;3. Method;9
5.4;4. Definitions;10
5.5;5. Further Reading;11
6;CHAPTER 1. SETS;12
6.1;1. Definitions of Terms;12
6.2;2. The Algebra of Sets;14
6.3;3. Operations;15
6.4;4. Laws of Sets;18
6.5;5. Comparison of the Laws of Sets and Arithmetic;20
6.6;6. Demonstrations of the Laws;21
6.7;7. Use of Venn Diagrams in Problems;28
6.8;8. Other Set Operations;31
6.9;EXAMPLES 1C;33
7;CHAPTER 2. RELATIONS AND FUNCTIONS;36
7.1;1. Relations;36
7.2;2. Equivalence Relation;37
7.3;3. Finite Arithmetics;38
7.4;4. Functions;41
7.5;5. Mappings, Correspondences;42
7.6;6. Solution Sets;44
7.7;7. Graphical Solution of Linear Equations;48
7.8;EXAMPLES 2B;50
8;CHAPTER 3. BOOLEAN ALGEBRA;54
8.1;1. Boolean Algebra;54
8.2;2. Theorems of Boolean Algebra;57
8.3;3. Construction of Boolean Systems;59
8.4;4. Propositional Calculus;60
8.5;5. Other Connectives;63
8.6;6. Switching Circuits;67
8.7;EXAMPLES 3;71
9;CHAPTER 4. GROUPS;75
9.1;1. Group Structure;75
9.2;2. Group Axioms;78
9.3;3. Group Order and Isomorphism;79
9.4;4. Isometry Groups;80
9.5;5. Latin Square;83
9.6;6. Permutation Groups;85
9.7;7. Algebraic Substitution Groups;88
9.8;8. Finite Arithmetic Groups;88
9.9;EXAMPLES 4;90
10;CHAPTER 5. HIGHER STRUCTURE;94
10.1;1. Abelian Groups;94
10.2;2. Cyclic Groups;95
10.3;3. Rings;100
10.4;4. Fields;103
10.5;5. Summary of Structures so Far;104
10.6;6. Vector Space;104
10.7;EXAMPLES 5;107
11;CHAPTER 6. NUMBER SYSTEMS;109
11.1;1. Peano's Axioms;109
11.2;2. Operations on Natural Numbers;111
11.3;3. Structure in the Set of Natural Numbers;113
11.4;4. Integers;113
11.5;5. Rationals;116
11.6;6. Irrationals;118
11.7;7. Structure in the Irrationals;120
11.8;8. The Real Numbers;121
11.9;9. Connection with Traditional Arithmetic;122
11.10;10. Decimal Representation of Numbers;123
11.11;11. Enumerability;125
11.12;EXAMPLES 6;127
12;CHAPTER 7. LINEAR EQUATIONS;129
12.1;1. Linear Equations in Two Dimensions;129
12.2;2. Introduction to Determinants;131
12.3;3. Higher Order Determinants;133
12.4;4. Determinant Theorems;137
12.5;5. Determinant Expansion;139
12.6;6. Gaussian Condensation;140
12.7;7. Determinants Applied to Linear Equations;143
12.8;8. Geometrical Illustration;146
12.9;EXAMPLES 7;149
13;CHAPTER 8. MATRICES AND VECTOR SPACES;152
13.1;1. Introduction to Matrix Notation;152
13.2;2. Matrix Operations;153
13.3;3. Structure in Matrices;157
13.4;4. The General Inverse Matrix;161
13.5;5. Matrix Solution of Linear Equations;165
13.6;6. Rank of a Matrix;167
13.7;7. Linear Combination of Vectors;168
13.8;8. Linear Dependence and Independence;170
13.9;9. More about Vector Spaces;174
13.10;EXAMPLES 8B;176
14;CHAPTER 9. COMPLEX NUMBERS;179
14.1;1. Need to Extend the Number System;179
14.2;2. Operations on Complex Numbers;183
14.3;3. Alternative Notations;184
14.4;4. The Argand Diagram;188
14.5;5. DeMoivre's Theorem;190
14.6;EXAMPLES 9;196
15;CHAPTER 10. FURTHER MATRIX PROPERTIES;198
15.1;1. 2 X 2 Matrices as Operators;198
15.2;2. Invariant Lines and Points;201
15.3;3. Eigenvalues of the General 2 x 2 Matrix;204
15.4;4. Eigenvectors;205
15.5;5. Expansion of Matrix in Terms of Eigenvectors;206
15.6;6. Extension to Matrices of any Size;208
15.7;EXAMPLES 10;208
16;CHAPTER 11. PROBABILITY;212
16.1;1. Definitions of Probability;212
16.2;2. Combining Probabilities;213
16.3;3. Numerical Examples of Combining Probabilities;217
16.4;4. Permutations;219
16.5;5. Combinations;221
16.6;6. Binomial Distribution;223
16.7;EXAMPLES 11;225
17;APPENDIX 1 BIBLIOGRAPHY;230
18;APPENDIX 2 TABLE OF SYMBOLS;231
19;APPENDIX 3 FURTHER EXERCISES;234
20;INDEX;244