Nuts and Bolts of Proofs

Name: Nuts and Bolts of Proofs
Price: 6.75 USD
Availability: InStock
ISBN: 9780121994518

ISBN-10: 0121994511

ISBN-13: 9780121994518

Edition: 2nd 2001 (Revised)

Authors: Antonella Cupillari

List price: $33.95

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Description:

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"

Book details

List price: $33.95
Edition: 2nd
Copyright year: 2001
Publisher: Elsevier Science & Technology Books
Publication date: 3/5/2001
Binding: Hardcover
Pages: 168
Size: 5.75" wide x 9.00" long x 0.50" tall
Weight: 0.594
Language: English

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.



List of Symbols


Preface


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 Contrapositive


How to Construct the Negation of a Statement


Special Types 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


Review Exercises


Exercises Without Solutions


Collection of "Proofs"


Solutions for the Exercises at the End of the Sections and the Review Exercises


Solutions for the Exercises at the End of the Sections


Solutions for the Review Exercises


Other Books on the Subject of Proofs and Mathematical Writing


Books on Mathematical Writing


Index