Author(s): Mark E. Watkins, Jeffrey L. Meyer
Series: Featured Titles for Transition to Advanced Mathematics
Edition: 1st
Publisher: Pearson
Year: 2011
Language: English
Pages: 253
Tags: Математика;Дискретная математика;
Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 8
Preface for the Instructor......Page 12
Preface for the Student......Page 18
1.1 Proofs, What and Why?......Page 22
1.2 Statements and Non-statements......Page 28
1.3 Logical Operations and Logical Equivalence......Page 31
1.4 Conditionals, Tautologies, and Contradictions......Page 37
1.5 Methods of Proof......Page 43
1.6 Quantifiers......Page 49
1.7 Further Exercises......Page 57
2.1 Basic Ideas of Sets......Page 64
2.2 Sets of Numbers......Page 65
2.3 Some Properties of N and Z......Page 68
2.4 Prime Numbers......Page 72
2.5 gcd’s and lcm’s......Page 73
2.6 Euclid’s Algorithm......Page 78
2.7 Rational Numbers and Algebraic Numbers......Page 81
2.8 Further Exercises......Page 85
3.1 Subsets......Page 89
3.2 Operations with Sets......Page 94
3.3 The Complement of a Set......Page 95
3.4 The Cartesian Product......Page 98
3.5 Families of Sets......Page 101
3.6 Further Exercises......Page 104
4.1 An Inductive Example......Page 109
4.2 The Principle of Mathematical Induction......Page 111
4.3 The Principle of Strong Induction......Page 119
4.4 The Binomial Theorem......Page 124
4.5 Further Exercises......Page 126
5.1 Functional Notation......Page 132
5.2 Operations with Functions......Page 135
5.3 Induced Set Functions......Page 141
5.4 Surjections, Injections, and Bijections......Page 147
5.5 Identity Functions, Cancellation, Inverse Functions, and Restrictions......Page 151
5.6 Further Exercises......Page 158
6.1 Partitions......Page 163
6.2 Equivalence Relations......Page 165
6.3 Order Relations......Page 170
6.4 Bounds and Extremal Elements......Page 174
6.5 Applications to Calculus......Page 179
6.6 Functions Revisited......Page 181
6.7 Further Exercises......Page 183
7.1 Counting......Page 188
7.2 Properties of Countable Sets......Page 191
7.3 Counting Countable Sets......Page 194
7.4 Binary Relations on Cardinal Numbers......Page 199
7.5 Uncountable Sets......Page 202
7.6 Further Exercises......Page 208
8.1 Binary Operations......Page 211
8.2 Modular Arithmetic......Page 221
8.3 Numbers Revisited......Page 229
8.4 Complex Numbers......Page 232
8.5 Further Exercises......Page 241
Index of Symbols and Notation......Page 246
D......Page 250
L......Page 251
S......Page 252
W......Page 253
