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.

Click here for a PDF file of the August 2016 version (approx 200 pages and 0.9MB).



Table of Contents

Part I. Introduction to Logic and Proofs
    1. Propositional Logic
    2. Two-Column Proofs

Part II. Sets and First-Order Logic
    3. Sets
    4. First-Order Logic
    5. Sample Topics

Part III. Other Fundamental Concepts
    6. Functions
    7. Equivalence Relations
    8. Proof by Induction
    9. Cardinality

Index of Definitions
List of Notation