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Proofs and Concepts: The Fundamentals of Abstract Mathematics

(3 reviews)

Dave Morris, University of Lethbridge

Joy Morris, University of Lethbridge

Pub Date: 2013

Publisher: Independent

Language: English

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Reviewed by Chris Hiatt, Associate Professor, University of Texas of the Permian Basin on 6/20/18

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


Reviewed by Jonathan Poritz, Associate Professor, Colorado State University - Pueblo on 2/2/18

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


Reviewed by Nic Gilbertson, Assistant Professor, Winona State University on 2/2/18

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
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.