Theorems, Corollaries, Lemmas, and Methods of Proof

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.

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.