Introduction to Mathematical Structures and Proofs [Hardcover]

Larry J. Gerstein (Author)

Book Description

Publication Date: April 4, 1996 | ISBN-10: 0387979972 | ISBN-13: 978-0387979977 | Edition: Corrected

"...Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. For instance, after his discussion of cardinals he has a section entitled Languages and Finite Automata. This allows him to illustrate some of the ideas he has been discussing with problems that almost anyone can understand, but most importantly he shows how these rather transparent problems can be subjected to a mathematical analysis. His discussion of how a machine might determine whether the sequence of words "Celui fromage de la parce que maintenant" is a legitimate French sentence is just delightful (and even more so if one knows a little French.)...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge. - Steven Krantz, American Mathematical Monthly "This very elementary book is intended to be a textbook for a one-term course which introduces students into the basic notions of any higher mathematics courses...The explanations of the basic notions are combined with some main theorems, illustrated by examples (with solutions if necessary) and complemented by exercises. The book is well written and should be easily understandable to any beginning student." - S. Gottwald, Zentralblatt This textbook is intended for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assortment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numerous exercises and a solutions manual for professors.

Editorial Reviews

From the Back Cover

"...Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. For instance, after his discussion of cardinals he has a section entitled Languages and Finite Automata. This allows him to illustrate some of the ideas he has been discussing with problems that almost anyone can understand, but most importantly he shows how these rather transparent problems can be subjected to a mathematical analysis. His discussion of how a machine might determine whether the sequence of words "Celui fromage de la parce que maintenant" is a legitimate French sentence is just delightful (and even more so if one knows a little French.)...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge. - Steven Krantz, American Mathematical Monthly "This very elementary book is intended to be a textbook for a one-term course which introduces students into the basic notions of any higher mathematics courses...The explanations of the basic notions are combined with some main theorems, illustrated by examples (with solutions if necessary) and complemented by exercises. The book is well written and should be easily understandable to any beginning student." - S. Gottwald, Zentralblatt This textbook is intended for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assortment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numerous exercises and a solutions manual for professors.

Product Details

• Hardcover: 360 pages
• Publisher: Springer; Corrected edition (April 4, 1996)
• Language: English
• ISBN-10: 0387979972
• ISBN-13: 978-0387979977
• Product Dimensions: 9.2 x 6.2 x 1.1 inches
• Shipping Weight: 1.2 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: #584,036 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

5.0 out of 5 stars Good intro for beginning, May 30, 2010

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SellerOnEarth (Virginia) - See all my reviews

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This review is from: Introduction to Mathematical Structures and Proofs (Paperback)

Before this book, I was still wondering through a maze of nonsensical calculus textbooks and couldn't get myself out of that trap. I think this book is a good start for going further in math. This book is clearly written and makes me think clearly, relative to other too concise books. Now I know what's going on when proofs are present in books. It's worth a buy. Also, selected exericise solutions are just enough to get the hint on how to approach a problem and also are motivating enough to solve a problem on my own. This book would probably better as a textbook in a course taught by a good instructor, but self-study is probably possible. You get to peak inside for table of contents and few pages, so why not have a look?

5.0 out of 5 stars No complaints, February 18, 2011

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Joe Butofsky (Virginia, USA) - See all my reviews

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This review is from: Introduction to Mathematical Structures and Proofs (Hardcover)

Using this for a college math class. It gets the point across pretty clearly. Can't argue with the price either

1 of 2 people found the following review helpful:

5.0 out of 5 stars Excellent, August 2, 2011

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collegekitty - See all my reviews

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This review is from: Introduction to Mathematical Structures and Proofs (Paperback)

I ordered this book two days ago, along with all of my other college textbooks. This one arrived today, and I couldn't be happier. Wonderfully fast service, and the book is in beautiful condition. Thank you!