Abstract

The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.
* The "List of Symbols" has been extended.
* Set Theory section has been strengthened with more examples and exercises.
* Addition of "A Collection of Proofs"
“I really enjoyed the “Collection of Proofs.” It is a great addition. These exercises will really stretch a student’s 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.