Learning to Reason: An Introduction to Logic, Sets, and Relations [Paperback]

Nancy Rodgers (Author)

Book Description

Publication Date: July 20, 2000 | ISBN-10: 047137122X | ISBN-13: 978-0471371229 | Edition: 1

Learn how to develop your reasoning skills and how to write well-reasoned proofs

Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. You'll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques and syntax for constructing well-written arguments. Through in-depth coverage of logic, sets, and relations, Learning to Reason offers a meaningful, integrated view of modern mathematics, cuts through confusing terms and ideas, and provides a much-needed bridge to advanced work in mathematics as well as computer science. Original, inspiring, and designed for maximum comprehension, this remarkable book:
* Clearly explains how to write compound sentences in equivalent forms and use them in valid arguments
* Presents simple techniques on how to structure your thinking and writing to form well-reasoned proofs
* Reinforces these techniques through a survey of sets--the building blocks of mathematics
* Examines the fundamental types of relations, which is "where the action is" in mathematics
* Provides relevant examples and class-tested exercises designed to maximize the learning experience
* Includes a mind-building game/exercise space at www.wiley.com/products/subject/mathematics/

Editorial Reviews

Review

"A primary strength is its broad attention to ideas from logic, set theory and relations while focusing the key notions of symbolism and writing proofs." (Choice, Vol. 38, No. 7, March 2001)

"In this textbook for mathematics and computer science majors, Rodgers explains how to write compound sentences in equivalent forms and use them in valid arguments..." (SciTech Book News, March 2001)

From the Back Cover

Learn how to develop your reasoning skills and how to write well-reasoned proofs

Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. You’ll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques and syntax for constructing well-written arguments. Through in-depth coverage of logic, sets, and relations, Learning to Reason offers a meaningful, integrated view of modern mathematics, cuts through confusing terms and ideas, and provides a much-needed bridge to advanced work in mathematics as well as computer science. Original, inspiring, and designed for maximum comprehension, this remarkable book:

• Clearly explains how to write compound sentences in equivalent forms and use them in valid arguments
• Presents simple techniques on how to structure your thinking and writing to form well-reasoned proofs
• Reinforces these techniques through a survey of sets—the building blocks of mathematics
• Examines the fundamental types of relations, which is "where the action is" in mathematics
• Provides relevant examples and class-tested exercises designed to maximize the learning experience
• Includes a mind-building game/exercise space at www.wiley.com/products/subject/mathematics/

See all Editorial Reviews

Product Details

• Paperback: 454 pages
• Publisher: Wiley-Interscience; 1 edition (July 20, 2000)
• Language: English
• ISBN-10: 047137122X
• ISBN-13: 978-0471371229
• Product Dimensions: 9.4 x 7.4 x 1 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,510,304 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

8 of 8 people found the following review helpful:

5.0 out of 5 stars Well written introductory text, February 21, 2001

By 

Abraman "TM" (Roseville, Ca) - See all my reviews

This review is from: Learning to Reason: An Introduction to Logic, Sets, and Relations (Paperback)

A well written book. Unlike many other authors that present a theorem and left readers to be perplexed at some point, Nancy Rodgers provide a thorough guidance toward the subject. Explaining the meaning of each theorem with enough examples, guiding readers how to express their logical thought by manipulating mathematical symbol and operator. Suitable not only for math or science students, but also for anyone (with some math background) interested to learn the subject (thus improving the way they express their thought).

6 of 6 people found the following review helpful:

5.0 out of 5 stars An Excellent Book, June 12, 2005

By 

K. R. Ampel - See all my reviews
(REAL NAME)   

This review is from: Learning to Reason: An Introduction to Logic, Sets, and Relations (Paperback)

For those first trying to learn mathematical sets, relations, proof, and logic, this is an excellent book. The writing is lucid and the proofs are clear. The book clears away much of the fog in the arcane world of symbolic thought.

The book includes a glossary of terms and numerous exercise sets with solutions for odd-numbered problems.

I found the book more clear and helpful than books by Eccles and Velleman.

I would highly recommend this book for college or high school students wanting to learn mathematical logic and proof for the first time, either as a primary course text, a supplemental text, or for learning on your own.

5.0 out of 5 stars Excellent for introduction to proof-making, June 13, 2011

By 

reader (ALEXANDRIA, VIRGINIA United States) - See all my reviews

Amazon Verified Purchase

This review is from: Learning to Reason: An Introduction to Logic, Sets, and Relations (Paperback)

This book is excellent for a beginner in proof-making. It teaches the basics and step by step process of building proofs. The book takes small steps at a time. And has good structure. Most proof-making textbook often don't contain anything useful for beginner student. As a result most people are never able to construct a proof. I have bachelor of science in mathematics and this was the first book ever to teach me how to start building proof.