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Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.
- Sales Rank: #73493 in Books
- Brand: Brand: Pearson
- Published on: 2012-09-27
- Original language: English
- Number of items: 1
- Dimensions: 9.37" h x .77" w x 7.91" l, 1.60 pounds
- Binding: Hardcover
- 416 pages
- Used Book in Good Condition
About the Author
Gary Chartrand is Professor Emeritus of Mathematics at Western Michigan University. He received his Ph.D. in mathematics from Michigan State University. His research is in the area of graph theory. Professor Chartrand has authored or co-authored more than 275 research papers and a number of textbooks in discrete mathematics and graph theory as well as the textbook on mathematical proofs. He has given over 100 lectures at regional, national and international conferences and has been a co-director of many conferences. He has supervised 22 doctoral students and numerous undergraduate research projects and has taught a wide range of subjects in undergraduate and graduate mathematics. He is the recipient of the University Distinguished Faculty Scholar Award and the Alumni Association Teaching Award from Western Michigan University and the Distinguished Faculty Award from the State of Michigan. He was the first managing editor of the Journal of Graph Theory. He is a member of the Institute of Combinatorics and Its Applications, the American Mathematical Society, the Mathematical Association of America and the editorial boards of the Journal of Graph Theory and Discrete Mathematics.
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.
Most helpful customer reviews
33 of 39 people found the following review helpful.
Best of Breed in Math Proof Books
By Let's Compare Options Preptorial
This new edition is a must have for anyone interested not only in mathematical proof, but math, logic and research writing in general. My job as CTO of a math formula software company is to present clear algorithmic ways to represent math symbols in many formats beyond LaTEX (eg e-readers). This volume takes that task a step further and shows potential authors, researchers, students and teachers how the best math articles are written today-- symbolically, logically and using natural language.
Math proofs come down to the degree of rigor. Formal proofs from Euclid to Euler, and the Islamic mathematicians who moved proofs from geometry to algebra, are considered "informal" by logicians of today, who consider proofs to be inductively defined data structures, in which competing axioms can even coexist (as in Non Euclidian geometry). Today's juried math journals allow plenty of natural language that would be considered informal, and now even accept brute force, computer assisted and even some probabilistic "arguments" as a kind of proof. This wonderful volume updates the author's outstanding 2007 edition by bringing both old topics up to date with algorithms, and introducing many new topics for our algorithm driven era.
There is no competing volume with this book's depth, breadth and currency, and certainly none that takes the trouble to give a tutorial on proof writing! Other older but worthy books include Discrete Math with Proof, Proof in Mathematics: An Introduction, How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, and The Nuts and Bolts of Proofs, Fourth Edition: An Introduction to Mathematical Proofs. In the more general field of research writing, The Craft of Research, Third Edition (Chicago Guides to Writing, Editing, and Publishing) and Critical Thinking, Reading, and Writing: A Brief Guide to Argument are must read classics for those publishing research and articles.
Since proofs take us into advanced math areas such as analysis, group theory, ring theory and number theory, at least Calc 1 is assumed, Calc 2 being better. ODE's and PDE's are not required, but would be a plus as the authors do not shy away from applications even in a proof oriented volume. What about Library Picks four standards for reviews (Scan/refer/read/study)? I'm giving this max stars for all four, whether you are into self study or are teaching/taking a course, or getting the volume for reference.
The authors' website has been updated for this edition, and thus researching encyclopedic keywords, as well as self study, are outstanding. The pedagogy also is sound for a one or two semester course dovetailing calc 1, 2 or 3 into more formal areas for math majors, engineering grad students, etc.
If their outstanding chapter on how to write proofs for publication isn't enough, Reading, Writing, and Proving: A Closer Look at Mathematics (Undergraduate Texts in Mathematics) is the current best of breed in weaving "how to do proofs" with "how to write them" for juried publication. Combining Cupellari and Daepp is an outstanding (albeit expensive) strategy to accomplish this combined learning - teaching agenda of both doing and writing outstanding proofs, whether you're a student or researcher. With less of an investment, you get a slice of both here in this volume.
On a personal note, our lives are executions of our own internal proofs, and most experiential logic is statistical--we execute those routines that seem to work best on average or in sum from our lives. Studying more formal proof structures (Direct, inductive, transposition, construction, contradiction, etc.) can really enhance our ability to make better choices. In addition, seeing the beauty of certain math proofs (check out Proofs from THE BOOK) can be inspiring and fun, just like an unexpectedly brilliant chess move. Euler was renowned for this, even in topics that seem "dry" to non mathematicians, like infinite series!
11 of 13 people found the following review helpful.
Good book.
By Rick Carmickle Jr
The biggest weakness with the text is explaining intermediate steps within each topic. I often need examples to increase in difficulty at a slower rate, or for a little more explanation over why each logical step is what it is This is particularly problematic because the whole idea of proofs is an orderly explanation of logic.
8 of 10 people found the following review helpful.
Great undergraduate text
By Tech_User
This is a wonderful text to prepare undergraduates for technical writing. That said, graduate students who did not get formal mathematical training as an undergraduate will also find this useful. I wish I had this when I was an undergraduate -- I had to learn on my own when I went to graduate school for my Ph.D. in mathematics! Chapter 0 is fantastic and discusses many of the nuances of proper mathematical writing. The authors do a fine job in explaining the concepts of various proof techniques, and the book itself is just full of great examples of proofs.
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