Title:
An introduction to abstract mathematics
Personal Author:
Publication Information:
Pacific Grove, Calif. : Brooks/Cole, 1999
ISBN:
9780534950507
Subject Term:
Added Author:
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000004465955 | QA37.2 B67 1999 | Open Access Book | Book | Searching... |
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Summary
Summary
The goal of this book is to show students how mathematicians think and to glimpse some of the fascinating things they think about. Bond and Keane develop students' ability to do abstract mathematics by teaching the form of mathematics in the context of real and elementary mathematics. Students learn the fundamentals of mathematical logic; how to read and understand definitions, theorems, and proofs; and how to assimilate abstract ideas and communicate them in written form. Students will learn to write mathematical proofs coherently and correctly.
Table of Contents
| Preface for the instructor |
| Introduction to the student |
| 1 Mathematical reasoning Introduction: Early Greek Mathematicians |
| Statements |
| Compound Statements |
| Implications |
| Contrapositive and Converse |
| 2 Sets Sets and Subsets |
| Combining Sets |
| Collections of Sets |
| 3 Functions Definition and Basic Properties |
| Surjective and Injective Functions |
| Composition and Invertible Functions |
| 4 Binary operations and relations Binary Operations |
| Equivalence Reactions |
| 5 The integers Axioms and Basic Properties |
| Induction |
| The Division Algorithm and the Greatest Common Divisors |
| Primes and Unique Factorization |
| Congruences |
| Generalizing a The orem |
| 6 Infinite sets Introduction |
| Countable Sets |
| Uncountable Sets, Cantor's The orem, and the Schroeder-Bernstein The orem |
| Collections of Sets |
| 7 The real and complex numbers Fields |
| The Real Numbers |
| The Complex Numbers |
| 8 Polynomials Polynomials |
| Unique Factorization |
| Polynomials over C, R, and Q |
| Answers and hints to selected exercises |
| Index |
