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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"
Intended as a supplement for undergraduate courses in higher mathematics (including Linear Algebra and Geometry), discrete mathematics courses in computer science, and as a primer to assist engineering and physical science students on fundamental proof techniques
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
- No. of pages:
- © Academic Press 2005
- 1st August 2005
- Academic Press
- eBook ISBN:
- Paperback ISBN:
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.
Pennsylvania State Erie, Behrend College, U.S.A.
“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