An Introduction to Mathematical Reasoning [Paperback]

Peter J. Eccles (Author)

Book Description

Publication Date: January 28, 1998 | ISBN-10: 0521597188 | ISBN-13: 978-0521597180

This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

Editorial Reviews

Review

"A student planning to study advanced mathematics would be well served by first mastering the material in this book...a rigorous study of sevearl fundamental topics pervasive in mathematics, including sets, functions, cardinality, combinatorics, and modular arithmetic." D.S. Larson, Choice

Book Description

The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

Product Details

• Paperback: 362 pages
• Publisher: Cambridge University Press (January 28, 1998)
• Language: English
• ISBN-10: 0521597188
• ISBN-13: 978-0521597180
• Product Dimensions: 9 x 6 x 0.8 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #427,493 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

43 of 44 people found the following review helpful:

5.0 out of 5 stars Just buy this, March 13, 2002

By 

Elliot Kleiman "technophilic" (San Diego, CA United States) - See all my reviews
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This review is from: An Introduction to Mathematical Reasoning (Paperback)

I needed a book that covered fundamental background information behind mathematical proof techniques for an undergraduate univeristy level linear algebra class.

With this book, I was able to truly learn and understand the major concepts behind mathematical logic and proof. This text brings a whole new meaning to teaching the reader about being precise; and I mean the author does an extremely terrific job of doing just that. Wow!

Seriously, the focus here is on content so you won't find any sexy graphs or anything. The content is so good that I often felt that just by reading it I was propelled into a quasi- pseudo-lecture meeting.

After following this text, I can say that I now appreciate the act of being precise to the point that is required for mathematical proof. If you want to extend the knowledge of your 'white board' then just buy this thing. I am so glad I did.

BTW, I only needed the content from the first five chapters, I can't say much about the rest of the text. However, taking an inductive approach, I must assume that the other chapters are also very excellent. Yess, see it worked!

25 of 25 people found the following review helpful:

5.0 out of 5 stars Fabulous So Far., November 30, 2001

By 

Alex Chaney (Potsdam, NY United States) - See all my reviews

This review is from: An Introduction to Mathematical Reasoning (Paperback)

I'm at the end of my first discrete mathematics course and have struggled to find clear explainations of how to write a proof, meaning how to choose what method and how to choose what the next statement should be to lead to the desired conclusion. I'm only on chapter five and it is a breath of fresh air to read this. Rather than just showing the completed proof Eccles shows the "scratch" work that goes into making the proof, discusses the reasoning and alternative paths, and then has the final proof that is easily understood.

An excellent supplement for a typical college text.

25 of 26 people found the following review helpful:

5.0 out of 5 stars User-Friendly! Almost makes learning analysis fun!, October 11, 1999

By A Customer

This review is from: An Introduction to Mathematical Reasoning (Hardcover)

If you are struggling with a first analysis course or any course that uses proofs, this is the book for you! It introduces basic analysis topics like logic, sets, and the real numbers. And it is written in almost plain english! Moreover, the author focuses on teaching proof writing.