Proofs and Concepts: the fundamentals of abstract mathematics
by Dave Witte Morris, Joy Morris
Publisher: University of Lethbridge 2009
Number of pages: 220
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.
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by Peter J. Eccles - Cambridge University Press
This book introduces basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory.
by Larry W. Cusick - California State University, Fresno
Proofs are the heart of mathematics. What is the secret? The short answer is: there is no secret, no mystery, no magic. All that is needed is some common sense and a basic understanding of a few trusted and easy to understand techniques.
by Alexander Bogomolny - Interactive Mathematics Miscellany and Puzzles
I'll distinguish between two broad categories. The first is characterized by simplicity. In the second group the proofs will be selected mainly for their charm. Most of the proofs in this book should be accessible to a middle grade school student.
by James Franklin, Albert Daoud - Kew Books
This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs. The book takes a straightforward, no nonsense approach to explaining the core technique of mathematics.