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Mathematical Proofs: A Transition to Advanced Mathematics
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Mathematical Proofs: A Transition to Advanced Mathematics

3.91 of 5 stars 3.91  ·  rating details  ·  67 ratings  ·  5 reviews
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. K ...more
Hardcover, Second Edition, 384 pages
Published October 13th 2007 by Pearson (first published May 28th 2002)
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Muhannad Alzahrani
Clear and accessible text for any one has a little background in mathematics ( basic algebra skills, some background in single variable calculus is preferred but not necessary).In my opinion it might be the best starting point to get into advanced pure mathematics.

The whole book can be divided into 4 main parts :

1- Introduction to simple logic and set theory.

2- Methods of proofs in Mathematics ( Trivial & Vacuous proofs, Direct proofs, Proofs by contrapositive, by contradiction, by a counter
Thomas Bell
Yay! Finally finished reading this book - and teaching it to my students. I really liked it actually, and yes, although I didn't teach sections 12.5 or 12.6 or chapter 13, I did actually read those as well. :-)

This book is not for everyone. At all. Just letting you know.
Chandra Kethi-reddy
Mar 06, 2014 Chandra Kethi-reddy rated it 3 of 5 stars
Recommended to Chandra by: Andrew Hunt
Shelves: maths
Clear, precise, and altogether excellent introduction of proofs and basic set theory. I'm glad historical context and facts about the development of logic were given (a move few maths textbooks have the balls to do). If you're looking to get into real maths, not the BS taught up to college, this is a great starting point.
Adam Centurione
Definitely one of the better Pearson text books ive read. Readin Pearson texts books is usually like standing in line at a government office. Mathematical Proofs really is a transition to advanced math, and I will definitely feel more complete studying advanced level calculus after reading this text. It offers a nice intro to set theory and logic that leads up to the basics of proving, and finishes off with the theoretically important proofs that found calculus, number theory and group theory.
Vince Manapat
I can't say enough good things about this textbooks -- it's definitely one of the best I have ever used. It's small and extremely concise and not burdened by tons of graphics and sidebars and sidenotes. Just exactly what you need to know, broken down into small pieces.
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Gary Theodore Chartrand is a professor emeritus of mathematics at Western Michigan University
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