The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs

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Academic Press, Sep 8, 2005 - Mathematics - 192 pages
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"
 

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Contents

Chapter 1 Introduction and Basic Terminology
1
Chapter 2 General Suggestions
5
Chapter 3 Basic Techniques to Prove IfThen Statements
9
Chapter 4 Special Kinds of Theorems
35
Chapter 5 Review Exercises
103
Chapter 6 Exercises Without Solutions
107
Chapter 7 Collection of Proofs
115
Chapter 8 Solutions for the Exercises at the End of the Sections and the Review Exercises
123
Chapter 9 Other Books on the Subject of Proofs and Mathematical Writing
173
Index
177
A Guide to Selecting a Method of Proof
180
Copyright

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About the author (2005)

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.

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