Proofs and Concepts: The Fundamentals of Abstract Mathematics

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Dave Morris, University of Lethbridge
Joy Morris, University of Lethbridge

Pub Date: 2013

ISBN 13:

Publisher: Independent

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Table of Contents

Part I. Introduction to Logic and Proofs
1. What is Logic?
2. Propositional Logic
3. Two-Column Proofs

Part II. Sets and First-Order Logic
4. Sets, Subsets, and Predicates
5. Operations on Sets
6. First-Order Logic
7. Quantifier Proofs
8. Divisibility and Congruence

Part III. Other Fundamental Concepts
9. Functions
10. Cardinality
11. Proof by Induction
12. Equivalence Relations

About the Book

This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics.  It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.

About the Contributors


Dave Witte Morris is professor of mathematics at the University of Lethbridge. 

Joy Morris is associate professor of mathematics at the University of Lethbridge.