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Michael Stoff, Director 305 East 23rd St, CLA 2.102, (G3600) Austin, TX 78712-1250 • 512-471-1442

Spring 2004

T C M310 • M 310: Plan II Mathematics

Unique Days Time Location Instructor
55030 MWF
9:00 AM-9:30 AM
bur 130
Starbird

Course Description

This course is for students who do not intend to take the standard calculus sequence, M 408C and M 408D. Mathematics has two important sides. On the one hand, it is a supremely useful tool. On the other hand, it has an intrinsic beauty and elegance. To appreciate any mathematics, people must do it themselves. Students in this class will do some mathematical thinking, and will enjoy seeing some unexpected consequences of apparently abstract thought. Topics: 1. Infinity More accurately—Infinities. We will see how mathematicians have made a previously ethereal notion accessible to reason. 2. Number Theory Interesting theorems in number theory have unexpected applications to codes. 3. Topology Can you divide a cake for three people so that each will get their favorite piece? A topological argument shows that the answer is yes. 4. Geometry The Pythagorean Theorem connects us with ancient thinkers while the fourth dimension takes us into a world beyond our senses. 5. Chaos and fractals Fractal images have literally infinite detail. 6. Coincidences and randomness Surprising coincidences are to be expected. That sounds paradoxical, but it is true. 7. Proofs Some of the most striking thoughts are elegant proofs of mathematical theorems. Proofs show the sometimes deep connections between seemingly disparate ideas. 8. Mathematical reasoning The course will strive to let the students experience the exhilaration of mathematical thought and find methods of effective thinking applicable well beyond mathematics.

About the Professor: Michael Starbird is a professor of mathematics. His excellence in teaching has been recognized with numerous awards, including the Minnie Stevens Piper Professorship (awarded to ten professors each year in the state of Texas), the Jean Holloway Teaching Excellence Award, the Friar Society Teaching Award, and the 1996-97 Chad Oliver Plan II Teaching Award. Professor Starbird holds a doctorate from the University of Wisconsin. He is the 1989 Recreational Sports Super Racquets champion—witnessing a misspent youth devoted to acquiring considerable skill in all racquet sports. He sings, plays the piano, and performs a moving rendition of The Jabberwocky in German.

Grading Policy

Grades are based on students' learning to think more creatively by understanding mathematical ideas and how they are discovered.

Texts

Burger, Edward B. and Starbird, Michael. The Heart of Mathematics: An invitation to effective thinking. 2000.

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