Sets, Functions, and Logic: An Introduction to Abstract Mathematics, Third Edition (Chapman Hall CRC Mathematics Series)

✍ Scribed by Keith Devlin

• Publisher: Chapman and Hall/CRC
• Year: 2003
• Tongue: English
• Leaves: 154
• Edition: 3
• Category: Library

✦ Synopsis

Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students.Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead. Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read…and enjoy…and learn from.About the AuthorDr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,.Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.

✦ Table of Contents

Contents......Page 6
Preface......Page 8
Students Start Here......Page 10
1.1 It’sNotJust Numbers......Page 12
1.2 Mathematical Notation......Page 15
1.3 Making the Invisible Visible......Page 18
1.4 This Is Where You Come In......Page 20
1.5 The Stuff of Modern Mathematics......Page 22
2.1 The Language of Mathematics: Part 1......Page 24
2.2 Properties of the Language......Page 31
2.3 The Language of Mathematics: Part 2......Page 40
2.4 Properties of Quanti.cation......Page 44
2.5 Proofs in Mathematics......Page 51
2.6 The Integers......Page 61
2.7 Mathematical Truth......Page 65
3.1 Sets......Page 68
3.2 Operations on Sets......Page 72
3.3 Real Intervals......Page 79
3.4 Absolute Values......Page 80
3.5 Inequalities......Page 82
3.6 Arbitrary Unions and Intersections......Page 86
3.7 Cartesian Products......Page 89
3.8 The Historical Development of Set Theory......Page 92
4.1 The Function Concept......Page 98
4.2 Examples of Functions......Page 100
4.3 History of the Modern Function Concept......Page 104
4.4 One-One and Onto Functions......Page 106
4.5 Composition and Inverse Functions......Page 111
4.6 Denumerability......Page 115
4.7 Uncountability......Page 119
5.1 Binary Relations......Page 124
5.2 Properties of Relations......Page 126
5.3 Relations as Sets of Ordered Pairs......Page 129
5.4 Relations as Graphs......Page 132
5.5 Equivalence Relations......Page 133
5.6 Functions as Relations......Page 138
5.7 An Example: The Reals......Page 140
5.8 Upper Bounds. Completeness......Page 142
5.9 Sequences......Page 144
No Answers to the Exercises......Page 148
List of Symbols......Page 150
Index......Page 152