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 fundamentals of abstract mathematics
by Dave Witte Morris and Joy Morris
incorporating material by P D Magnus
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.
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
4. First-Order Logic
5. Sample Topics
Part III. Other Fundamental Concepts
7. Equivalence Relations
8. Proof by Induction
Index of Definitions
List of Notation