How To Write Proofs
by Larry W. Cusick
Publisher: California State University, Fresno 2009
Proofs are the heart of mathematics. If you are a math major, then you must come to terms with proofs--you must be able to read, understand and write them. What is the secret? What magic do you need to know? 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.
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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 Patrick Keef, David Guichard, Russ Gordon - Whitman College
Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction); Number Theory (The Euclidean Algorithm); Functions (Injections and Surjections, Cardinality and Countability).
by Martin Day - Virginia Tech
The book helps students make the transition from freshman-sophomore calculus to more proof-oriented upper-level mathematics courses. Another goal is to train students to read more involved proofs they may encounter in textbooks and journal articles.
by Richard Hammack - Virginia Commonwealth University
This textbook is an introduction to the standard methods of proving mathematical theorems. It is written for an audience of mathematics majors at Virginia Commonwealth University, and is intended to prepare the students for more advanced courses.