Mathematical Thinking: Problem-Solving and Proofs (2nd Edition) (Hardcover)

~ (Author), Douglas B. West (Author)

Editorial Reviews

Product Description

This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers. For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.

From the Publisher

Offering a survey of both discrete and continuous mathematics, Mathematical Thinking begins with the fundamentals of mathematical language and proof techniques such as induction. These are applied to easily-understood questions in elementary number theory and counting. Further techniques of proofs are then developed via fundamental topics in discrete and continuous mathematics. The text can be used for courses emphasizing discrete mathematics, continuous mathematics, or a balance between the two. It contains many engaging examples and stimulating exercises. --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Hardcover: 412 pages
• Publisher: Prentice Hall; 2 edition (December 27, 1999)
• Language: English
• ISBN-10: 0130144126
• ISBN-13: 978-0130144126
• Product Dimensions: 9.1 x 6.1 x 1.1 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 3.6 out of 5 stars  See all reviews (8 customer reviews)
• Amazon.com Sales Rank: #448,796 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

5.0 out of 5 stars Extremely Useful - Great Read, February 2, 2008

By	mathmaven "gary j" (Springfield, Va) - See all my reviews

I ran into the first edition of this book ten years ago when taking courses at George Mason University, and really loved it. I still love it. It covers proofs from all basic "pieces" of mathematics and gives the reader a good feel for the "proofology," both in technique and fundamental nomenclature and results, that a student is expected to know when taking the first analysis and abstract algebra courses. It's not perfect though. I haven't bought the second edition, but in the first edition, Example 2.21, p.27 says: "An integer is even if and only if it is the sum of two odd integers." Obviously, it is easy to show the sum of two odd integers is even by forming the sum (2k+1) + (2l+1) = 2(k+l+1), which is twice an integer and thus even. But, if an integer is even, it can be the sum of two odd integers OR two even integers, so the statement is not complete. If small stuff like that doesn't bother you, this book is for you.

The author gives solutions or hints for one-third to one half the problems depending on the chapter, which is more than enough for self-study. I would disregard the whiny one star review that is posted for this book; it is typical of someone who wants to be spoonfed mathematics.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Difficult but well worth it, October 10, 2007

By	A. Townley - See all my reviews (REAL NAME)

I'm using this in an undergraduate introduction to proofs class with a focus on analysis. As a freshman, it seems a bit overwhelming at times - I wouldn't recommend it to most freshmen or even sophomores.
I do feel like this does a more than adequate job preparing me for more advanced math, and goes far above and beyond similar "proofs and problem solving" style books.

8 of 11 people found the following review helpful:

5.0 out of 5 stars The best reference for Proofs, July 27, 2000

By	Edward T. Pegg Jr. "Recreational mathematician" (Champaign, IL USA) - See all my reviews (REAL NAME)

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This is an advanced book, with a lot of information on every page. I use it as a reference book, since it has hundreds of wonderful proofs and problems, along with thorough and concise definitions for just about every major branch of mathematics.

It's highly recommended for anyone who is *serious* about mathematical proofs. Although the book is packed with material, it's a small book, so it's one of the first I choose to take with me when I travel.