Sets, Functions, and Logic: An Introduction to Abstract Mathematics, Third Edition

by Devlin; Keith

• ISBN13: 9781584884491
• ISBN10: 1584884495
• Edition: 3rd
• Format: Paperback
• Copyright: 2003-11-24
• Publisher: Chapman & Hall/

Summary

Since its first edition published in 1981, Set, Function and Logic has smoothed the road to higher mathematics for legions of undergraduate students. Now in its third edition, the author--a leading popularizer of mathematics -- has fully revised his text to reflect a new generation. The narrative is more lively, less textbook-like. Remarks and asides link the various topics to the real world. The chapter on complex numbers and discussion of formal symbolic logic is gone in favor of a new introductory chapter on the nature of mathematics and more exercises. The result is an affordable, thoroughly engaging book that every student making the transition from calculus to higher mathematics will welcome.

Author Biography

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.

Table of Contents

Preface	vii
Students Start Here	ix
1 What Is Mathematics and What Does It Do for Us?	1	(12)
1.1 It's Not Just Numbers	1	(3)
1.2 Mathematical Notation	4	(3)
1.3 Making the Invisible Visible	7	(2)
1.4 This Is Where You Come In	9	(2)
1.5 The Stuff of Modern Mathematics	11	(2)
2 Math Speak	13	(44)
2.1 The Language of Mathematics: Part 1	13	(7)
2.2 Properties of the Language	20	(9)
2.3 The Language of Mathematics: Part 2	29	(4)
2.4 Properties of Quantification	33	(7)
2.5 Proofs in Mathematics	40	(10)
2.6 The Integers	50	(4)
2.7 Mathematical Truth	54	(3)
3 Set Theory	57	(30)
3.1 Sets	57	(4)
3.2 Operations on Sets	61	(7)
3.3 Real Intervals	68	(1)
3.4 Absolute Values	69	(2)
3.5 Inequalities	71	(4)
3.6 Arbitrary Unions and Intersections	75	(3)
3.7 Cartesian Products	78	(3)
3.8 The Historical Development of Set Theory	81	(6)
4 Functions	87	(26)
4.1 The Function Concept	87	(2)
4.2 Examples of Functions	89	(4)
4.3 History of the Modern Function Concept	93	(2)
4.4 One-One and Onto Functions	95	(5)
4.5 Composition and Inverse Functions	100	(4)
4.6 Denumerability	104	(4)
4.7 Uncountability	108	(5)
5 Relations	113	(24)
5.1 Binary Relations	113	(2)
5.2 Properties of Relations	115	(3)
5.3 Relations as Sets of Ordered Pairs	118	(3)
5.4 Relations as Graphs	121	(1)
5.5 Equivalence Relations	122	(5)
5.6 Functions as Relations	127	(2)
5.7 An Example: The Reals	129	(2)
5.8 Upper Bounds. Completeness	131	(2)
5.9 Sequences	133	(4)
No Answers to the Exercises	137	(2)
List of Symbols	139	(2)
Index	141