The Nuts and Bolts of Proofs : An Introduction to Mathematical 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. The "List of Symbols" has been extended. Set Theory section has been strengthened with more examples and exercises. It also includes the addition of "A Collection of Proofs".
- Paperback | 192 pages
- 150 x 224 x 12mm | 381.02g
- 08 Sep 2005
- Elsevier Science Publishing Co Inc
- Academic Press Inc
- San Diego, United States
- 3rd Revised edition
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.
Table of contents
Introduction and Basic Terminology General Suggestions Some basic Techniques Used in Proving a Theorem of the Form :If A then B Direct Proof Related Statements Proof by Contra positive How to Construct the Negation of a Statement Special Kinds of Theorems If and only if or Equivalence Theorems Use of Counterexamples Mathematical Induction Existence Theorems Uniqueness Theorems Equality of Sets Equality of Numbers Composite Statements Limits Review Exercises Exercises without Soultions Collection of Proofs Solutions of the Exercises at the End of the Sections and the Review Exercises Other Books on the Subject of Proofs and Mathematical Writing
About Antonella Cupillari
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.