This Fall I will be teaching a course in the Honors College, Math 197: Introduction to mathematical thought.
The goal of the course is to present an introduction to the mathematical method, the way mathematics is reasoned, discovered, and advanced. This will be accomplished through a presentation of selected (real world) examples, and an emphasis on the key notion of mathematical proof. Particular attention is paid to aesthetic, historical, and philosophical aspects of mathematics.
Pre-requisites: Instructor’s approval.
Text: We will use several texts and articles. Particularly recommended are:
- T.W. Körner. The pleasures of counting, Cambridge University Press (1996). ISBN: 0-521-56087-X (hardback), 0-521-56823-4 (paperback).
(This will be our official textbook, but we will draw material from all three.)
- Sh. Stein. How the other half thinks. Adventures in mathematical reasoning, McGraw-Hill (2001). ISBN-10: 0071407987, ISBN-13: 978-0071407984.
- W. Dunham. Journey through genius. The great theorems of mathematics, John Wiley & Sons, Inc (1991). ISBN-10: 014014739X, ISBN-13: 978-0140147391.
I will provide additional handouts and references as needed. Supplementary recommendations include:
- I. Lakatos. Proofs and refutations. The logic of mathematical discovery, Cambridge University Press (1976). ISBN-10: 052121078X, ISBN-13: 978-0521210782.
- Ph.J. Davies and R. Hersh. The mathematical experience, Mariner Books (1999). ISBN-10: 0395929687, ISBN-13: 978-0395929681.
- S.G. Krantz. The proof is in the pudding. The changing nature of mathematical proof, Springer (2011). ISBN-10: 0387489088, ISBN-13: 978-0387489087.
Contents: We will present a series of examples illustrating how mathematics is used in the real world, and how it is conceived. We will discuss the nature of mathematical proof, and some of the philosophical issues surrounding it, as well as how it has evolved through the ages. The goal is to see how mathematicians actually reason, and how mathematical ideas are a natural part of the cultural legacy of humankind.
Speciﬁc examples may be chosen depending on the audience background and motivation. Particular examples I would like to include are the mathematics of
codes, how populations evolve through time, the mathematics of inﬁnity, and computer generated proofs.
Grading: Grades will be determined based on homework (60%), a written project (20%), and class participation (20%). There will be no exams.
Attendance to lecture is not required but highly recommended.
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