Many students have trouble the first time they take a mathematics course in which proofs play a sigficant role. This book will prepare students for such courses by teaching them techniques for writing and reading proofs. No background beyond high school mathematics is assumed. The book begins with logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. This understanding of the language of mathematics serves as the basis for a detailed discussion of the most important techniques used in proofs, when and how to use them, and how they are combined to produce comples proofs. Material on the natural numbers, relations, functions, and infinite sets provides practice in writing and reading proofs, as well as supplying background that will be valuable in most theoretical mathematics courses.
|Publisher:||Cambridge University Press|
|Edition description:||Older Edition|
|Product dimensions:||5.98(w) x 8.98(h) x 0.75(d)|
About the Author
Daniel J. Velleman is Julian H. Gibbs '46 Professor of Mathematics, Emeritus at Amherst College, and was a professor at Amherst College from 1983 to 2017. He received his BA from Dartmouth College in 1976, and his PhD from the University of Wisconsin, Madison in 1980. His other books include Which Way Did the Bicycle Go? (with Stan Wagon and Joe Konhauser, 1996), Philosophies of Mathematics (with Alexander George, 2002), and Calculus: A Rigorous First Course (2016). Among his awards and distinctions are the Chauvenet Prize, the Paul R. Halmos-Lester R. Ford Award, the Carl B. Allendoerfer Award, and the Chandler Davis Prize for Expository Excellence. He was Editor of Dolciani Mathematical Expositions from 1999 to 2004 and the American Mathematical Monthly from 2007 to 2011.
Table of Contents1. Sentential Logic; 2. Quantificational Logic; 3. Proofs; 4. Relations; 5. Functions; 6. Mathematical Induction; 7. Number Theory; 8. Infinite Sets.