The Nuts and Bolts of Proofs
An Introduction to Mathematical Proofs

This valuable resource demonstrates the construction of proofs to help students develop the skills they need to transition to higher-level, more abstract math courses

Antonella Cupillari (Author)

9780123822178, Elsevier Science

Paperback / softback, published 14 February 2012

296 pages
23.4 x 19 x 1.9 cm, 0.62 kg

"It is written with great accuracy and a level of enthusiasm necessary for the Herculean task of launching mathematical handle-turners into the world of mathematical thinking…for those required to teach ‘transition courses’, I recommend perusal of this book as a possible course text." --MAA online, December 3, 2013

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book invaluable.

1. Getting Started2. Basic Techniques to Prove If/Then Statements3. Special kinds of Theorems4. Some mathematical topics on which to practice proof techniques5. Review Exercises

Subject Areas: Mathematical logic [PBCD]