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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.
• 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
Audience: Undergraduate mathematics majors.
Numbers and Numerals
Polynomials and Complex Numbers
Combinatorics and Graph Theory