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An Introduction to Mathematical Reasoning [Paperback]

Peter J. Eccles
4.4 out of 5 stars  See all reviews (18 customer reviews)

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Book Description

January 28, 1998 0521597188 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.

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An Introduction to Mathematical Reasoning + How to Prove It: A Structured Approach + How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
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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: 361 pages
  • Publisher: Cambridge University Press (January 28, 1998)
  • Language: English
  • ISBN-10: 0521597188
  • ISBN-13: 978-0521597180
  • Product Dimensions: 9.1 x 5.9 x 0.8 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #346,372 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
46 of 47 people found the following review helpful
5.0 out of 5 stars Just buy this March 13, 2002
Format:Paperback|Verified Purchase
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!
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29 of 29 people found the following review helpful
5.0 out of 5 stars Fabulous So Far. November 30, 2001
Format: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.
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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
Format: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.
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29 of 31 people found the following review helpful
5.0 out of 5 stars Very well written book September 29, 2004
Format:Paperback
I have a mathematics degree. Like most math majors, I struggled with proofs all through college. This book really has help me understand the art of writing proofs. The book is very well written and easy to read. This is just an awesome book!!!
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11 of 11 people found the following review helpful
5.0 out of 5 stars Short and to the point April 11, 2006
Format:Paperback|Verified Purchase
This book is excellent! It chapters are broken down into short sections and the content in each section is to the point! I also bought the book Proofs and Fundamentals by Ethan D. Bloch but found it to be long and drawn out. If you liked The Nuts and Bolts of Proofs by Antonella Cupillari then this book is for you!
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14 of 15 people found the following review helpful
4.0 out of 5 stars Now I know how beautiful proofs can be December 12, 2002
Format:Paperback
This book provides a nice introduction to mathematical reasoning and proofs. My intention on purchasing this book was to learn how to perform mathematical proofs. I believe it has achieved that purpose. The text is easy to follow and the author presents the work clearly.
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10 of 11 people found the following review helpful
4.0 out of 5 stars love the binding and size! August 18, 2009
Format:Paperback
the binding and the size is just perfect! It's one of the few Mathematics book that i have read while traveling in train (to university and back home)...like a novel if you will.

As per the content of the book itself, let me begin by what i liked in this book.

First off, this book is pretty good for self-study. I realize there is a reviewer who claims "For a student who is just learning mathematical proofs, this book is just horrible" but i beg to differ. Prior to this book, i have had only Calc I (limit and derivatives), Calc II (integration), and Calc III (multivariate). Those courses did not have any proofs whatsoever. So, this really was my first attempt to learn proof and boy this book helped!

The same reviewer also claims that the examples on the book "are awful and the author shortcuts many proofs"...and here i was about to say the detailed proofs author provides is the another strength of the book. The author of this book understands that students must learn some basic proof techniques such as proof by contradiction and induction. He goes ahead and provides a very well written layout for proofs which a starter might just memorize. Furthermore, in proofs that follow he first shows us how he approached the proof and then only the writes an formal proof.

last but not least, all exercises have a complete solution at the end of the book. This is quite helpful especially if you are self-studying. Plus there is a "problem set" which do not have solutions and can be assigned for homework. Be warned though these are relatively harder than the rest. This isn't just me saying, my classmates thought the same...even the professor agreed and often assigned problems of his own.
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5 of 5 people found the following review helpful
5.0 out of 5 stars Great for the transition from Calculus to higher math January 9, 2009
Format:Paperback
This book was a great intro to formal mathematics, which I needed after my very informal Calculus AB class. It starts from very simple (basic proof techniques, set theory, and number theory) to more advanced topics in number theory. I didn't understand all of it, but it was a great book for learning the basics of formal math and proof writing.
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Most Recent Customer Reviews
5.0 out of 5 stars Great book!
Got this book for a class and really enjoyed working on it.

I strongly recommend for those who are learning how to write proofs and getting into higher level... Read more
Published 1 month ago by Fernando Cordeiro
2.0 out of 5 stars Like the price, but lots of typos
This online version was about half the price of the hard copy, but the formulas were inserted as graphics which did not enlarge, making them very tiny and hard to read... Read more
Published 1 month ago by Claire Gajary
4.0 out of 5 stars Some inaccuracies with the Kindle text
I agree with almost everyone else that the book is a great introduction to the topic. There's one problem with the Kindle version, though: The text appears to have been scanned... Read more
Published 3 months ago by R. Jacobson
5.0 out of 5 stars Best introduction to mathematical reasoning
This is hands down the best introduction to logic and mathematical reasoning in my current library. I highly recommend this to anyone who needs to learn the basics of mathematical... Read more
Published on March 28, 2011 by David Karapetyan
5.0 out of 5 stars Stand alone or as a textbook very good
Just as the other reviews describe, this is an excellent book that introduces proofs and mathematical reasoning. Read more
Published on January 2, 2010 by T. Hartwig
5.0 out of 5 stars One of the best books for learning and understanding mathematical...
In my view this book is one of the best books for learning and understanding mathematical proofs. The text is concise clearly written and easy to read. Read more
Published on December 16, 2008 by Gyesi Amaniampong
1.0 out of 5 stars Just horrible.
For a student who is just learning mathematical proofs, this book is just horrible. The examples are awful and the author shortcuts many proofs. Read more
Published on December 8, 2008 by D.S.
5.0 out of 5 stars no complaints
In less than a week I had the book and I'm happy with my purchase
Published on September 30, 2007 by Victor
5.0 out of 5 stars Intermediate Level
I'm biased. This is the sort of thing U.S. schools should require. Can't go wrong with this. This has 2X as much as "How to Read @ Do Proofs" (Daniel Solow). Wich is better? Read more
Published on August 20, 2007 by Richard Bell
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