Essentials of Elementary School Mathematics (eBook)

James L. Fejfar, Max D. Larsen (Autoren)

eBook Download: PDF

2014 | 1. Auflage
430 Seiten
Elsevier Science (Verlag)
978-1-4832-6488-2 (ISBN)

Infos

Essentials of Elementary School Mathematics is an introductory text on the essentials of mathematics taught in elementary schools. It presents a systematic development of the mathematics of arithmetic. A primary objective is to give students a background sufficient to understand and answer at an appropriate level the various quite penetrating questions asked by young students. Some examples and exercises are concerned primarily with pedagogical aspects of arithmetic. Comprised of 14 chapters, this book begins with an overview of the language of mathematics, focusing on concepts such as the conjunction (and); negation (not); disjunction (or); and conditional (if...then...). The discussion then turns to the theory of sets; the concept of binary operations; and recognition and identification of properties of various relations. The next section deals with the number systems of arithmetic: whole numbers, integers, rational numbers, and real numbers. Number theory and clock arithmetic are also examined, along with counting techniques and probability. The final section is devoted to motion geometry and analytic geometry. This monograph should be of interest to students and teachers of mathematicians at the elementary level.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 12.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Technik
• ISBN-10: 1-4832-6488-2 / 1483264882
• ISBN-13: 978-1-4832-6488-2 / 9781483264882