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The Nuts and Bolts of Proofs
An Introduction to Mathematical Proofs
3rd Edition - August 1, 2005
Author: Antonella Cupillari
Language: English
eBook ISBN:9780080537900
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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…Read more
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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"
Introduction and Basic TerminologyGeneral Suggestions Some basic Techniques Used in Proving a Theorem of the Form :If A then B”Direct ProofRelated StatementsProof by Contra positiveHow to Construct the Negation of a StatementSpecial Kinds of Theorems“If and only if” or Equivalence TheoremsUse of CounterexamplesMathematical InductionExistence TheoremsUniqueness TheoremsEquality of SetsEquality of NumbersComposite StatementsLimitsReview Exercises Exercises without Soultions Collection of ProofsSolutions of the Exercises at the End of the Sections and the Review ExercisesOther Books on the Subject of Proofs and Mathematical Writing
No. of pages: 192
Language: English
Edition: 3
Published: August 1, 2005
Imprint: Academic Press
eBook ISBN: 9780080537900
AC
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.
Affiliations and expertise
Associate Professor of Mathematics, Pennsylvania State Erie in Behrend College, Erie, PA, USA