Math 389 Winter 2013
Explorations in Mathematics
This course is not like any other in the mathematics department. The course is designed to show you how new mathematics is actually created: how to take a problem, make models and guesses, experiment with them, and search for underlying structure. It is suitable for students at many levels. This course serves also to develop useful skills, including how to write and typeset a math paper, making an oral presentation, and computing with a mathematics software system such as Mathematica or Maple.
The class will be split into groups, typically of 3 students, who will choose a project, work on it, and submit a written report describing their findings. We will also have oral reports of some of the projects. Often, though not necessarily always, your research will involve computer experiments. Findings should be stated precisely, either as facts or as conjectures; proofs will be viewed favorably, but are not required.
Topics range from ones that are treated in mathematics books to ones that lead to open problems. Few are well defined. In contrast to homework assignments for your other classes, you will not be told precisely what to compute or to prove. The topics have been chosen because they display interesting phenomena, but we do not necessarily have a particular result in mind. And if we did, you might discover something else.
There will be no examinations. Your grade will be based on the quality of your team's project work and on the quality of its written reports, weighted approximately equally. The class will meet as a group once a week, Wednesday 5:00 --6:30 pm in the computer lab in East Hall, B743. In addition, staff will be available for consultation in East Hall B743 from 5:00pm --- 7:00pm Monday through Friday. Teams will typically meet once a week during these other hours. Organizational details including a timetable for the projects (assuming three lab projects) are given on the calendar. The number of projects to be completed by each group during the term will be discussed at the opening meeting; it will be either three projects or two (longer) projects.
This course is modelled after one designed by Prof. Mike Artin at M. I. T. It has projects suitable for various levels of experience.
There are no formal prerequisites, though the course needs an ability to think mathematically. Students should have taken the equivalent of three college level mathematics courses, although talented freshman have successfully taken the course. Familiarity with a computer program suitable for mathematical modeling is recommended, but not required. There is no course text. You will need an override from the math department to register. This course counts as one of the four electives required for an honors degree.
Jeff Lagarias [uniqname: lagarias]
Scott Schneider [uniqname: sschnei]
Wei Qian (Undergraduate) [uniqname: ]
Alexander Cope (Undergraduate) [uniqname: alexcope]