Proofs and Concepts: The Fundamentals of Abstract Mathematics
Dave Morris, University of Lethbridge
Joy Morris, University of Lethbridge
Pub Date: 2013
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Conditions of Use
This book is a very comprehensive look at proof methods. It appropriately covers the subject starting at logic and moving to various topics. One difference from other books of its type is that the text on proof y induction is not with the other... read more
The book gives a beautiful, complete, and careful exposition of its central material -- logic and proofs -- and of several beautiful and powerful applications in different areas of mathematics. The methods of logic taught here are so central to... read more
This is a well-written text, that can be readily used for introduction to proofs and logic course at the undergraduate level. The text covers topics one would expect to see in first course on logic and proofs, including proofs by contradiction and... read more
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
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.