Sets, Functions and Logic : An Introduction to Abstract Mathematics - 3rd edition

Devlin, Keith : Stanford University, Stanford, California, USA

Dr. 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.

PREFACE
STUDENTS START HERE
WHAT IS MATHEMATICS AND WHAT DOES IT DO FOR US?

It's Not Just Numbers
Mathematical Notation
Making the Invisible Visible
This is Where You Come In
The Study of Modern Mathematics

MATH SPEAK

The Language of Mathematics: Part 1
Properties of the Language
The Language of Mathematics: Part 2
Properties of Quantification
Proofs in Mathematics
The Integers
Mathematical Truth

SET THEORY

Sets
Operations on Sets
Real Intervals
Absolute Values
Inequalities
Arbitrary Unions and Intersections
Cartesian Products
The Historical Development of Set Theory

FUNCTIONS

The Function Concept
Examples of Functions
History of the Modern Function Concept
One-One and onto Functions
Composition and Inverse Functions
Denumerability
Uncountability

RELATIONS

Binary Relations
Properties of Relations
Relations as Sets of Ordered Pairs
Relations as Graphs
Equivalence Relations
Functions as Relations
An Example: the Reals
Upper Bounds. Completeness
Sequences
No Answers to the Exercises

List of Symbols
Index

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