PBIS 187 – Problem-based Inquiry Seminar (5 sections) :
Section 001 and 003
The math that you know and can do is profound. You possess a canon of our civilization. Through the ages, humankind has formed mathematics; math in return has formed the way we view our world and our lives. The great ideas that are present in math are comparable to works of Michaelangelo, Shakespeare, Plato and Dogen, and they can enrich our lives with the same type of texture and beauty if we look. The objective of this course is to revisit your knowledge with fresh eyes and see how it can render amazing, deep results. [Topics include items such as irrationality of numbers, surveying, probability, prime numbers, and infinity.]
Section 002
We will survey some interesting mathematical topics which you probably have not seen in previous courses, including networks (graph theory), secret codes, and counting and probability. Questions might include: given a map of the streets in a town, is it possible to plan a parade route that goes down every street exactly once? What do those bar codes on the backs of products mean? How is information kept safe on the Internet? How likely is it that someone else in this class will have the same birthday as you? Expect a hands-on course, with numerous and occasionally challenging problems to work on both in groups and individually, and some in-class presentations. Only minimal background is needed; the main prerequisites are willingness to participate and willingness to keep trying when you do not immediately solve a problem. The goal is for you to leave the class with stronger problem-solving and quantitative skills and a greater appreciation for mathematics.
Section 004 and 005
This course is designed to explore the historical development of problem solving in geometry, number theory, algebra, probability, and graph theory. The course will also include a look at both ancient and modern number systems. We will use a textbook, The Saga of Mathematics, priced under $45.00 by Prentice-Hall. The authors, Marty Lewinter and William Widulshi, write that their text is directed at non-majors and “math phobics.” The course will look at several famous problems, some already solved and other famous because they remain unsolved. The textbook offers several proofs, which are remarkable because they seem disguised as gentle explanations and are quite readable. For more information on the text see www.maa.org/reviews/saga.html and math.widulshi.net/
Page last modified: May 8, 2008