Discovering Higher Mathematics

1st Edition

Four Habits of Highly Effective Mathematicians


  • Alan Levine
    • Not Applicable ISBN 9780124454606


    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.

    Key Features

    @bul:* 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


    Undergraduate mathematics majors.

    Table of Contents

    Preliminary Numbers Numbers and Numerals Polynomials and Complex Numbers Combinatorics and Graph Theory Difference Equations Additional Topics


    No. of pages:
    © 2000
    Academic Press
    Not Applicable ISBN:

    About the author

    Alan Levine

    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.

    Affiliations and Expertise

    Franklin and Marshall College, Lancaster, Pennsylvania, U.S.A.