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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of series:
Pure and Applied Mathematics: A Wiley-Interscience Series of #82: Theorems, Corollaries, Lemmas, and Methods of Proofby Richard J. Rossi
Synopses & Reviews
A hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning
Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics.
This essential book:
A complete chapter is dedicated to the different methods of proof such as forward direct proofs, proof by contrapositive, proof by contradiction, mathematical induction, and existence proofs. In addition, the author has supplied many clear and detailed algorithms that outline these proofs.
Theorems, Corollaries, Lemmas, and Methods of Proof uniquely introduces scratch work as an indispensable part of the proof process, encouraging students to use scratch work and creative thinking as the first steps in their attempt to prove a theorem. Once their scratch work successfully demonstrates the truth of the theorem, the proof can be written in a clear and concise fashion. The basic structure of modern mathematics is discussed, and each of the key components of modern mathematics is defined. Numerous exercises are included in each chapter, covering a wide range of topics with varied levels of difficulty.
Intended as a main text for mathematics courses such as Methods of Proof, Transitions to Advanced Mathematics, and Foundations of Mathematics, the book may also be used as a supplementary textbook in junior- and senior-level courses on advanced calculus, real analysis, and modern algebra.
This book offers a basic discussion of the axiomatic nature of modern mathematics, covers algorithms for several different types of proofs, and introduces the concept of scratch work as part of the proof process. The primary purpose of this text is to introduce math majors, who have completed a calculus sequence, to the axiomatic makeup of modern mathematics. Emphasizing the writing of clear and understandable proofs, this book includes detailed algorithms for proving several different types of mathematical results including algorithms for forward direct proofs; proof by contrapositive; proof by contradiction and more.
About the Author
RICHARD J. ROSSI, PHD, is Professor in the Department of Mathematics at Montana Tech of The University of Montana in Butte, Montana. He served as President of the Montana Chapter of the American Statistical Association in 1996 and 2001 and as an Associate Editor for Biometrics from 1997–2000. He is a member of the American Mathematical Society, the Institute of Mathematical Statistics, and the American Statistical Association. Dr. Rossi received his PhD in statistics from Oregon State University in 1988.
Table of Contents
Chapter 1. Introduction to Modern Mathematics.
Chapter 2. An Introduction to Symbolic Logic.
Chapter 3. Methods of Proof.
Chapter 4. Introduction to Number Theory.
Chapter 5. The Foundations of Calculus.
Chapter 6. Foundations of Algebra.
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