Essentials of Elementary School Mathematics (eBook)

Front Cover 1
Essentials of Elementary School Mathematics 4
Copyright Page 5
Table of Contents 8
Dedication 6
Preface 14
Note to the Instructor 18
Note to the Student 20
PART ONE: FUNDAMENTALS 22
Chapter 1. The Language of Mathematics 24
1 conjunction (and) negation (not)
2 disjunction (or) 28
3 conditional (if . . . , then . . .) 29
4 biconditional (if and only if) 33
5 quantifiers 39
QUIZ 41
Chapter 2. Sets 42
1 subset 44
2 intersection and union 48
3 complement 51
4 cartesian product 56
QUIZ 58
Chapter 3. Binary Operations 60
1 definition of binary operation 61
2 commutativity 67
3 associativity 69
4 distributivity 71
5 identity element 73
6 inverses 76
QUIZ 81
Chapter 4. Relations 83
1 reflexive relations 84
2 symmetric relations 85
3 transitive relations 86
4 equivalence relations 88
5 one-to-one correspondence 96
QUIZ 100
PART TWO: THE THEORY OF ARITHMETIC 102
Chapter 5. The System of Whole Numbers 104
1 definition of whole numbers 105
2 addition of whole numbers 106
3 multiplication of whole numbers 111
4 ordering of whole numbers 118
QUIZ 121
Chapter 6. The System of Integers 123
1 definition of integers 124
2 addition of integers 126
3 subtraction of integers 130
4 multiplication of integers 134
5 ordering of integers 138
QUIZ 140
Chapter 7. Place-Value Numeration Systems 142
1 the nature of our decimal numeration system 142
2 other bases 144
3 algorithms 147
4 addition 148
5 subtraction 152
6 multiplication 156
7 division 159
QUIZ 162
Chapter 8. Systems of Rational and Real Numbers 164
1 definition of rational numbers 165
2 addition of rational numbers 168
3 multiplication of rational numbers 173
4 ordering of rational numbers 174
5 division of rational numbers 179
6 real numbers 182
QUIZ 187
PART THREE: EXPANDING MATHEMATICAL EXPERIENCES 188
Chapter 9. Number Theory 190
1 divisors, factors, and primes 193
2 division algorithm 200
3 the greatest common divisor 203
QUIZ 209
Chapter 10. Clock Arithmetic 211
1 introduction 211
2 an equivalence relation 215
3 choosing clocks 225
QUIZ 227
Chapter 11. Counting Techniques and Probability 228
1 permutations 230
2 combinations 234
3 probability 241
QUIZ 244
PART FOUR: GEOMETRY 246
Chapter 12. Motion Geometry I 248
1 congruence 251
2 slides, turns, and flips 254
3 successive motions 265
4 invariance 272
5 angles 275
6 symmetry 283
QUIZ 292
Chapter 13. Motion Geometry II 293
1 parallel lines 293
2 perpendicular lines 300
3 triangles 303
4 quadrilaterals 308
5 area 312
6 similarity 319
7 constructions 328
QUIZ 335
Chapter 14. Functions and Coordinate Geometry 337
1 definition 337
2 onto and one-to-one functions 342
3 graphing functions 346
4 graphing in R X R 352
5 distance 358
6 lines 368
QUIZ 378
Appendix 380
Bibliography 390
Answers to Selected Exercises 398
Subject Index 430