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Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)
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Binding: Hardcover
Dewey Decimal Number: 510
EAN: 9780130144126
Edition: 2
ISBN: 0130144126
Label: Prentice Hall
Manufacturer: Prentice Hall
Number Of Items: 1
Number Of Pages: 412
Publication Date: December 27, 1999
Publisher: Prentice Hall
Studio: Prentice Hall
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Editorial Review: 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.
Customer Reviews
Average Rating: 
Rating:  - Extremely Useful - Great Read
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, ... Read More
Rating: - Difficult but well worth it
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.
Rating: - Filled with Information
This is a great book filled with great proofs and just a great amount of information. Whenever I'm unsure of a proof or need confirmation of some obscure factoid of numbers, this is where I look first. Great for building the foundations needed for learning advanced mathematics.
Rating:  - no solutions
The material covered does not help you solve the exercises at the end of the chapter. I wish there was a solutions manual available, so I don't have to guess the answer and be left unsure of what to do to solve a problem.
Rating: - The best reference for Proofs
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.
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