The Nuts and Bolts of Proofs

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.

“I really enjoyed the 'Collection of Proofs.' 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...The new material only makes a great book even greater.” -Robert Beezer, University of Puget Sound"It treats mathematical proofs, and mathematical thinking in general, as an art rather than a science, and does not descend into cookbook recipes for approaching their construction. Thus it empowers students to discover, write and analyze mathematical statements, and to think for themselves. It brings out important details to be considered in constructing proofs gradually and doesn’t overwhelm the reader..."-Andy Miller, University of Oklahoma