An Introduction to Higher Mathematics
by Patrick Keef, David Guichard, Russ Gordon
Publisher: Whitman College 2010
Number of pages: 144
Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction, Indirect Proof); Number Theory (The Euclidean Algorithm, The Fundamental Theorem of Arithmetic); Functions (Injections and Surjections, Cardinality and Countability, Uncountability of the Reals).
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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 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 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.
by Elias Zakon - The Trillia Group
The book will help students complete the transition from purely manipulative to rigorous mathematics. It covers basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers, fields, etc.