Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition)
Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET: For all readers interested in advanced mathematics and logic.
Very Readable Textbook
By Penelope W. Yaqub "Fawzi M. Yaqub" - January 24, 2003
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... read more
A veil has been lifted...
By A Student - March 29, 2008
This book pretty much changed my life. My only regret is I didn't find it earlier. What different choices would I have made if I were comfortable with mathematical proofs in high school or early college? I recommend this book to anyone who has an interest in understanding mathematics but for whatever reason never learned or were never taught it by their teachers in school - I'm certain I was never taught these ideas. This book is great for self study and the material should be accessible to most high school students.
The book starts off with basic ideas about sets and some logic. The real "Aha!" moment for me was the explanation of implication and biconditional in chapter 2 and how they're used in direct proofs in chapter 3. The examples about even/odd numbers are perfect for someone feeling their way thru new ideas.
After reading this book I went back to college as an adult and obtained a BS in mathematics. It's foolish to dwell on what might have been,... read more
Learning Proofs, on your own
By Stephan Hartwell "Stephan Hartwell" - March 14, 2007
I bought Chartrand's book to teach myself how to
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
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