MATH 389: Explorations in Mathematics
Course Description: 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.
Course webpage: Here is a link to the course webpage.