Discovering Higher Mathematics: Four Habits of Highly Effective Mathematicians [Hardcover]

Alan Levine (Author)

Book Description

Publication Date: November 12, 1999 | ISBN-10: 0124454607 | ISBN-13: 978-0124454606 | Edition: 1

Funded by a National Science Foundation grant, Discovering Higher Mathematics emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses.
* Constructed around four key themes: Experimentation, Conjecture, Proof, and Generalization
* Guidelines for effective mathematical thinking, covering a variety of interrelated topics
* Numerous problems and exercises designed to reinforce the key themes

Editorial Reviews

From the Back Cover

Discovering Higher Mathematics: Four Habits of Highly Effective Mathematicians provides an interactive transition to the abstraction of higher mathematics. Levine stresses the importance of four main themes (or habits), experimentation, conjecture, proof, and generalization, emphasizing them as processes critical to mathematical thinking.
The book presents elementary topics such as number theory, polynomials, combinatorics, and discrete mathematics as useful tools for learning the four main themes. The author encourages experimentation and derivation of results through a series of guided lessons.
Key Features
* Constructed around four key themes: Experimentation, Conjecture, Proof, and Generalization
* Guidelines for effective mathematical thinking, covering a variety of interrelated topics
* Numerous problems and exercises designed to reinforce the key themes

About the Author

Alan Levine is a graduate of the State University of New York at Stony Brook with a degree in Operations Research and Applied Math. Since 1983 he has taught at Franklin and Marshall College. He is the co-author, with George Rosenstein, of Discovering Calculus.

Product Details

• Hardcover: 174 pages
• Publisher: Academic Press; 1 edition (November 12, 1999)
• Language: English
• ISBN-10: 0124454607
• ISBN-13: 978-0124454606
• Product Dimensions: 9.3 x 6.2 x 0.7 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,570,222 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

5 of 7 people found the following review helpful:

5.0 out of 5 stars Do it yourself proofs!, December 30, 1999

By 

Owen Densmore (Santa Fe, NM USA) - See all my reviews
(REAL NAME)   

This review is from: Discovering Higher Mathematics: Four Habits of Highly Effective Mathematicians (Hardcover)

I needed a refresher course (after being away from grad school for 30 years!) and was intrigued by the approach: discover the flavor of the topic by experimenting, then often resolving this into a formal proof by your self.

The book is sufficiently short to be quite approcable yet reasonably complete. It has stimulated me to reading other more formal books such as A First Course in Abstract Algebra by John Fraleigh and Elements of Modern Algebra by Jimmie & Linda Gilbert.