Mathematical Proofs: A Transition to Advanced Mathematics

I bought Chartrand's book to teach myself how tounderstand and to do proofs. I worked every exercisein the text. Now taking some upper level proof basedcourses, after being out of school for 20 years, I amfinding that I am more comfortable with proofs thanmost of the people in my classes. The main thing thathelped me was the clear communication of the methodsand the ample opportunities to test out my knowledge.The only thing I that would have helped me more is thatmost problems at the end of the chapters do not provideexplanation. I had to trust my knowledge, which is notalways a good idea. Still, the authors do a goodjob of conveying the concepts and I do very much likechapter zero. I am a school teacher and I show thatchapter to my secondary students. Oh,that chapterexplains "good" mathematical writing style.

This text is a short but very deep tool to enable the understanding and learning of higher math. I would recommend it to anyone who wishes to take the next step in math.

This is a great tool that every math major should own. This helped me through my advance calculus class in college. I think this would also be a great buy for a high school student that wants to get ahead of the game.

This book is exactly as I expected .

COmpletely satisfied with the product. Arrived on time, and the book was in the described conditionaadada ad a a

Excellent book...and excellent service

This book is designed to prepare students for upper division math courses-like abstract algebra and advanced calculus-in which mathematical rigor and proofs are emphasized. The authors have made a serious effort to present the material with clarity and sufficient details to make it accessible to students who have completed two courses in calculus. Much of the material covered is fairly standard for such a textbook. Chapters 1-9 are devoted to basic topics from set theory and logic (including four proof techniques: direct proof, proof by contrapositive, proof by contradiction, and mathematical induction), equivalence relations, and functions, as well as a special chapter under the heading, "Prove or Disprove." Chapters 10-13 cover cardinalities of sets and proof techniques applied to results from number theory, calculus, and group theory. In addition, the authors have a web site which includes three additional chapters (Chapters 14-16) dealing with proofs from ring theory, linear algebra, and topology. Thus instructors using this book will have a wide choice of options in selecting the material they want to include after the basic concepts are covered.The emphasis throughout the book is on proofs and proof techniques--how to recognize proofs, understand them and, above all, how to create and write them. The presentation is leisurely and thorough. Many examples are given, and discussions are always presented with all the details that students at this level would need to follow the argument. There are ample exercises at the end of each chapter (including those in the web site) that range in difficulty from routine to moderately challenging. The book also contains answers and hints to odd-numbered exercises.There are two features of this textbook that I believe are helpful to students and that set this book apart from others at its level: the detailed way in which proofs are analyzed, and the inclusion of a chapter on how to write mathematics well. In most cases, before a proof is presented the authors offer a "proof strategy": a discussion pointing out what needs to be proved and how one might go about proving it. Also, many proofs are followed by "proof analyses" in which some of the interesting or unusual points of the proof are commented on. I believe that students would find these discussions very helpful. In particular, these discussions offer students concrete pointers from which they would learn how to cope with abstract mathematical proofs.The chapter on writing mathematics (Chapter 0) is unique. While some mathematics textbooks encourage good writing and might devote a few paragraphs to the subject, the present volume offers a brief manual on mathematical writing. The authors begin by explaining why writing is important in mathematics and follow that by offering detailed instructions that would help students in improving their writing. From specific advice like, "Never start a sentence with a symbol" to explanations of "common words and phrases that are peculiar to mathematics," there is a wealth of material on writing from which students can learn. I believe that, by its very existence, this chapter on writing would have a positive influence on students writing.This book can be used either as a textbook for a course such as the one described above or as a reference that students can consult on certain topics.Fawzi M. YaqubEmeritus Professor of MathematicsSUNY College at Fredonia

If you look at the "Customers Who Bought This Item Also Bought" section on this page you will see several highly rated books that cover similar topics. They all are priced approximately $100 less than this book because Addison-Wesley (the publisher) has decided to market _Mathematical Proofs_ as a text-book rather than a book-book.This is tragic. The only people who will encounter this fantastic text are students with no choice but to suffer the rapacious fancies of textbook publishers.I was once such a student. Everything Penelope W. Yaqub "Fawzi M. Yaqub" says in her review is spot on. I have kept only three books on my personal shelf from my days as an undergraduate in mathematics. This slim volume is one of those.I recommend this book to anyone -- whether a student or hobbyist -- wanting to better their understanding of what mathematics is really about. It is also great training for thinking logically about all topics, from mathematics to current eventsI would have rated this 5 stars if the cover price were not so outrageous.

Exactly as described. Thank you very much!