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Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition) 2nd Edition
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About the Author
Albert D. Polimeni is an Emeritus Professor of Mathematics at the State University of New York at Fredonia. He received his Ph.D. degree in mathematics from Michigan State University. During his tenure at Fredonia he taught a full range of undergraduate courses in mathematics and graduate mathematics. In addition to the textbook on mathematical proofs, he co-authored a textbook in discrete mathematics. His research interests are in the area of finite group theory and graph theory, having published several papers in both areas. He has given addresses in mathematics to regional, national and international conferences. He served as chairperson of the Department of Mathematics for nine years.
Ping Zhang is Professor of Mathematics at Western Michigan University. She received her Ph.D. in mathematics from Michigan State University. Her research is in the area of graph theory and algebraic combinatorics. Professor Zhang has authored or co-authored more than 200 research papers and four textbooks in discrete mathematics and graph theory as well as the textbook on mathematical proofs. She serves as an editor for a series of books on special topics in mathematics. She has supervised 7 doctoral students and has taught a wide variety of undergraduate and graduate mathematics courses including courses on introduction to research. She has given over 60 lectures at regional, national and international conferences. She is a council member of the Institute of Combinatorics and Its Applications and a member of the American Mathematical Society and the Association of Women in Mathematics.
Top customer reviews
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understand and to do proofs. I worked every exercise
in the text. Now taking some upper level proof based
courses, after being out of school for 20 years, I am
finding that I am more comfortable with proofs than
most of the people in my classes. The main thing that
helped me was the clear communication of the methods
and the ample opportunities to test out my knowledge.
The only thing I that would have helped me more is that
most problems at the end of the chapters do not provide
explanation. I had to trust my knowledge, which is not
always a good idea. Still, the authors do a good
job of conveying the concepts and I do very much like
chapter zero. I am a school teacher and I show that
chapter to my secondary students. Oh,that chapter
explains "good" mathematical writing style.
The only downside, as some reviewers have mentioned, is the hefty price tag. C'est la vie. I actually like the presentation of this book so much that I'm now looking into other works that the authors have.
The other books I tried are
Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)
How to Prove It: A Structured Approach, 2nd Edition
This book is much better than the other two book.
The nice thing about the book is that the chapter is organized by method of proof (direct, contradiction, induction, ...).
This really helps to improve each proof method, instead of using only one method you are familiar over and over.