T C M310 • Plan II Mathematics
9:00 AM-10:00 AM
Mathematics has three important sides: it is a supremely useful tool, it has an intrinsic beauty and elegance, and it illustrates effective methods of thinking. 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 abstract thought. Topics will include: Infinity: More accurately, infinities. We will see how mathematicians have made a previously ethereal notion accessible to reason. Number Theory: Interesting theorems in number theory have unexpected applications to codes. Topology: Imagine that the world is far more elastic than reality permits. Insights about that imaginary world have consequences in our own. Chaos and Fractals: When simple processes are repeated, chaos and infinitely detailed beauty emerge. Fairness: Can you divide a cake for three people so that each person will get his or her favorite piece? A mathematical argument shows that the answer is yes. Proofs: Some of the most striking thoughts are elegant proofs of mathematical theorems. Proofs show the sometimes deep connections between seemingly disparate ideas. Mathematical Reasoning: The course will strive to let the students experience the exhilaration of mathematical thought. Well see how methods of thinking about mathematical ideas can help us think more effectively and creatively in all areas of life.
About the Professor Michael Starbird is a professor of mathematics whose 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 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 championwitnessing 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.
Grades are based on students' learning to think more creatively by understanding mathematical ideas and how they are discovered.
Edward B. Burger and Michael Starbird, The Heart of Mathematics: An Invitation to Effective Thinking, 2nd edition