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An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, by Peter J. Eccles
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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.
- Sales Rank: #438652 in Books
- Brand: Brand: Cambridge University Press
- Published on: 1998-01-28
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .83" w x 5.98" l, 1.15 pounds
- Binding: Paperback
- 361 pages
- Used Book in Good Condition
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
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Most helpful customer reviews
52 of 54 people found the following review helpful.
Just buy this
By Elliot Kleiman
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!
0 of 0 people found the following review helpful.
Five Stars
By Amazon Customer
nice book
25 of 27 people found the following review helpful.
User-Friendly! Almost makes learning analysis fun!
By A Customer
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.
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