Extended Graduate Orientation

Summer 2014



coordinator

phone #

office

e-mail

Rachel Roberts

5-8527

Cupples I, 106

roberts@math.wustl.edu 




Objective: The extended graduate orientation program is an optional, but strongly recommended, activity for beginning graduate students. The main purposes are to introduce incoming students to the style and pace of our graduate courses, bringing everybody up to speed for Fall classes; and to help create from the very beginning a supportive social environment in which  graduate students, faculty, and staff  can all work most effectively.

Course: The core of the orientation program is a minicourse on a subject chosen by the instructor. This is not meant to be a remedial course, and does not necessarily cover topics that will be seen again in the qualifying courses. For this year I have chosen the topic of Morse Theory. (More on the topic below.) In addition to attending lectures, students will work as a group on problems. 

Dates, times, and locations: Most activities will take place in Cupples I, room 199. Lunch in room 200, our department lounge. Bring your lunch! Our department lounge has a refrigerator, microwave oven and other amenities for general use. Mary Ann Stenner will provide cool beverages, chips and cookies.

The minicourse will run from August 11 through August 15, with classes on Monday (8/11), Wednesday (8/13), and Friday (8/15).

On each of these three days there will be a morning (10:00AM - 12:00PM) session. On Monday and Wednesday there will also be an afternoon (2:00PM - 4:00PM) session. Each session consists of one hour of lecture and one hour of group work. Tuesday and Thursday will be devoted to homework, with the students responsible for organizing their own time.

On Friday the 15th we will have lunch at Blueberry Hill, together with the staff and some of the faculty.

Topic: Roughly speaking, an n-manifold is a space which locally looks like euclidean n-space. So, locally, an n-manifold is completely understood. The challenge is "to see" the manifold in its entirety. One fun and extremely useful way to visualize n-manifolds is given by Morse Theory. Morse Theory describes how to analyze the topology of a manifold by using differentiable functions on that manifold. 

This minicourse will give an introduction to Morse Theory. Applications will include hands on constructions of 1-, 2-, 3-, and 4-manifolds.