This book introduces readers to the basics of proof writing. It effectively demonstrates how to construct different types of proofs (including direct proofs, proofs by contradiction, and inductive proofs), and provides numerous examples. It is clear, easy to understand, and is a great book to use as reference when writing mathematical proofs.
2. An Introduction to Number Theory, by Harold M. Stark.
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| borders.com |
I had the pleasure of taking a Number Theory course which was taught by Professor Stark about a year ago, and we used this book throughout the course. I consider this to be one of the best math textbooks that I have ever used. It introduces readers to the fundamentals of number theory by discussing important theorems and their proofs. Furthermore, the author provides some historical context for some of the ideas that are presented, which are compelling to read. In general, the theorems within the book avoid complex wording, and the proofs that are presented are easy to follow.
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| amazon.com |
3. Abstract Algebra, by John A. Beachy and William D. Blair.
This book is extremely helpful in that it goes beyond just stating theorems and proving them. This book provides numerous examples, which is something that many math books do not do. Furthermore, the book does a great job of not overcomplicating the material, so that it is fairly easy to comprehend.
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