Discovering Higher Mathematics: Four Habits of Highly Effective Mathematicians

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9780124454606: Discovering Higher Mathematics: Four Habits of Highly Effective Mathematicians

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

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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.

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Book Description Elsevier Science Publishing Co Inc, United States, 1999. Hardback. Book Condition: New. 232 x 154 mm. Language: English . Brand New Book. 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. Bookseller Inventory # AA59780124454606

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Book Description Elsevier Science Publishing Co Inc, United States, 1999. Hardback. Book Condition: New. 232 x 154 mm. Language: English . Brand New Book. 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. It includes guidelines for effective mathematical thinking, covering a variety of interrelated topics. It contains numerous problems and exercises designed to reinforce the key themes. Bookseller Inventory # AA59780124454606

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