The Nuts and Bolts of Proofs, Second Edition [Paperback]

Antonella Cupillari (Author)

Book Description

ISBN-10: 0121994511 | ISBN-13: 978-0121994518 | Publication Date: March 19, 2001 | Edition: 2

This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course.

This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments.


* Successfully class-tested over a number of years
* Index for easy reference
* Extensive list of definitions and concepts
* Updated biblography

Editorial Reviews

Review

"I really enjoyed the "Collection of Proofs." It is a great addition. These exercises will really stretch a student's imagination, and go a long way to impressing on them the standards for a believable proof and the necessity of understanding a proposition before embarking on its proof (or the search for a counter-example).
It should be clear that I find NBP an indispensable adjunct to my linear algebra course and to my efforts to increase my students' mathematical maturity. The new material only makes a great book even greater." Robert Beezer, University of Puget Sound. --This text refers to an alternate Paperback edition.

Book Description

This simple, updated guidebook shows how to read, understand and construct proofs --This text refers to an alternate Paperback edition.

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Product Details

• Paperback: 168 pages
• Publisher: Academic Press; 2 edition (March 19, 2001)
• Language: English
• ISBN-10: 0121994511
• ISBN-13: 978-0121994518
• Product Dimensions: 9 x 6 x 0.4 inches
• Shipping Weight: 9.8 ounces
• Average Customer Review: 5.0 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #1,850,366 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

52 of 54 people found the following review helpful:

5.0 out of 5 stars I own a previous edition, March 7, 2006

By 

Nicole Henry "nicole henry" (UCLA Los Angeles, CA) - See all my reviews
(REAL NAME)   

This review is from: The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs (Paperback)

I own the second edition of this book and find it incredibly well done. I am a math major, and this book was recommended to me by a caring professor to help aid my transition between computational mathematics and the more abstract area of Mathematical Proofs.

It is a complete and easy to follow introduction to proofs. It quickly goes over the basic properties of numbers and symbols, then goes into direct proofs. It then explains the logic of using the contrapositive instead of using direct proof by showing truth trees of the statements. After that she goes over special types of theorems.

Everything is well documented and there are tons of examples. In her examples Antonella first explains the peculiarities of the proof she is about to attempt, and then she does the proof. That discussion is enlightening and her proofs are easy to follow.

I found going through this book was invaluable to my mathematics career. The level of difficulty of this book is very EASY, so it is perfect for going though on ones own. You will likely have much more difficult proofs in class, but by going through this book will become familiar with the techniques and ideas of Proofs, which is where most students have difficulty!

The book is small and does not feel like a textbook. It has about 80 pages of text and the rest of the book is solutions to exercises. The new edition is larger, but still relatively small, and so hopefully it has this same feel, and if nothing else is light enough to carry around!

When I was going through this book, I would carry it around in my purse with me--that is how small and portable and useful this treasure is.

32 of 33 people found the following review helpful:

5.0 out of 5 stars WOW!!!!, April 11, 2006

By 

J. Scott (United Kingdom) - See all my reviews
(REAL NAME)   

This review is from: The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs (Paperback)

This book is like no other. Its short and to the point which means that the busy math major can actually sit down and read it! We all know how hard it is to try and read a wordy book on how to write proofs while at the same time trying to study abstract algebra! We dont need a full 100 pages on informal logic! Antonella Cupillari seems to understand this and sums up everything we need to know concerning logic in under 12 pages! Excellent book! Well worth the $32.95!

6 of 6 people found the following review helpful:

5.0 out of 5 stars Helped Me Very Much!!, August 19, 2010

By 

Robert "A life-long reader that learns most t... (Midwestern United States) - See all my reviews

This review is from: The Nuts and Bolts of Proofs, Third Edition: An Introduction to Mathematical Proofs (Paperback)

Learning to do proofs is a difficult task. I found this out in a course on abstract algebra: Solving a problem is one thing, doing a proof is another, and proofs require methods that are logically sound. Somehow I did get through the class, then ran across this book and snapped it up. It helped extremely much. Working through the book took a long time, partly because it is a lot to learn and partly because I had to supplement it with addtional resources. I also used Schaum's outline on Logic, to learn how to accurately build truth tables, and this worked out well. I also went through The Teaching Company course The Art and Craft of Mathematical Problem Solving by Paul Zeitz, and this was a huge help.