The Nuts and Bolts of Proofs

The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition provides basic logic of mathematical proofs and how they work. The book offers techniques for both reading and writing proofs, discusses techniques in proving if/then statements by contrapositive and proofing by contradiction, includes the negation statement, and/or, examines various theorems, such as the if and only-if, equivalence theorems, existence theorems, and the uniqueness theorems. In addition, the use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are also covered. 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 accessible as well as invaluable. - Jumps right in with the needed vocabulary to get students thinking like mathematicians from the beginning - Offers a large variety of examples and problems with solutions for students to work through on their own - Includes a collection of exercises without solutions to help instructors prepare assignments - Contains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics

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.