Proofs
and
Concepts

the fundamentals of abstract mathematics

by Dave Witte Morris and Joy Morris
incorporating material by P D Magnus

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.

The book is being released online with a Creative Commons license (Attribution-NonCommercial-ShareAlike 2.0).  Although not in final form, it has already been used as a textbook for several semesters at the University of Lethbridge.  The preliminary version of November 2013 is approximately 200 pages.

Click here for a PDF file of the most recent version (approx 1.9MB).



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