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

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