# The Nuts and Bolts of Proofs

## A. Cupillari

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This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments.

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Review:

I really enjoyed the Collection of Proofs. It is a great addition. These exercises will really stretch a students imagination, and go a long way to impressing on them the standards for a believable proof and the necessity of understanding a proposition before embarking on its proof (or the search for a counter-example). It should be clear that I find NBP an indispensable adjunct to my linear algebra course and to my efforts to increase my students mathematical maturity. The new material only makes a great book even greater. Robert Beezer, University of Puget Sound.

Antonella Cupillari is an associate professor of mathematics at Pennsylvania State Erie in Behrend College. She received her Laurea in Mathematics in Italy, and her M.A. and Ph.D. at the State University of New York at Albany. She has been a participant in the Mathematical Association of America/National Science Foundation Institute on the "History of Mathematics and Its Use in Teaching." Cupillari is the author of several papers in analysis, mathematics education, and the history of mathematics. She is also the author of the first edition of The Nuts and Bolts of Proofs.

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