Mathematics 499 (formerly known as Math 400)

University of Illinois Urbana-Champaign


Math 499 was created in the mid 1990's, and called Math 400 until the fall of 2004, when the University renumbered all its offerings. (The testimonials therefore refer to it as Math 400).

Each week one faculty member addresses all the first-year Mathematics graduate students (and other interested people) for about 45 minutes. Some professors give engaging lectures on specific topics; others provide. Graduate students are required to provide feedback on the talks.

Graduate Student Testimonial

I enjoyed attending Math 400 and listening to professors from different areas of mathematics. Although it did not change my original intention of studying logic, it did help me reaffirm my choice. As far as changing my behavior regarding the doctoral program, I believe my progress thus far would not have been too different without it.

I do believe that Math 400 is a positive aspect of the doctoral program for two reasons. One is that it provides a forum for students to meet each other and to know professors in the department, which is very important for a successful graduate career, especially during the first year. The other reason is it acclimates the new graduate student to attending seminars, which is a major part of graduate study that is not present in undergraduate programs.

Over all, although it has not dramatically changed my career path, Math 400 has attributed to the quality of my experience as a graduate student.

Zhou Dong

July 1, 2004

Graduate Student Testimonial

Math 400 was a valuable part of my introduction to graduate school and to the program at UIUC. The exposure it provided to the research interests of many professors in the department was particularly helpful because I did not initially know what I wanted to study. I appreciated the introduction to various options, the insight into the history and motivation of subjects and to connections between them. Additionally, Math 400 helped illustrate what math research is like, what sorts of questions are asked and how people proceed to study them. I also learned about techniques that make a talk effective, and some things to avoid. Lastly, being required to attend a seminar helped me get used to attending talks, something I might not have felt as comfortable doing as a first year student. In all these ways, Math 400 was instrumental in my transition from undergraduate to graduate study.

Sylvia Carlisle

July 3, 2004

Graduate Student Testimonial

Although Math 400 is conceptually very appealing, in my opinion it does not quite reach its goals. The class has two purposes: to expose incoming students to a variety of areas of mathematics (to orient themselves for their graduate career), and to force an introspective search about what makes a good instructor. In practice, the latter purpose has been deemphasized to make the course not be a burden, while the former has not been achieved (again in my opinion). The weekly seminars are often interesting, but little interaction between speaker and audience takes place. Each talk is too isolated an exposure to a prospective advisor. Students instead tend to use requisite classes to explore different areas of mathematics, and higher level classes to choose advisors. I think perhaps a less informal class at a slightly later point in a graduate's tenure would be more effective.

Lucas Sabalka

July 3, 2004.

Graduate Student Testimonial

Good points:

1) Students get to see a much larger section of the faculty than they would otherwise by going to class. Depending on the speaker they may get some idea about the research being carried out at UIUC in a particular area (and the opportunities for graduate student research).

Some speakers have used the opportunity to advertise a topics course the following semester, in the spirit of "If you want to find out more...". I think this is quite a good way to get students into topics courses, and away from the comp focused mentality that currently exists.

2) Even if a student has a reasonably clear idea of the area they want to work in and perhaps even the person they are going to work with, it is good to see what other people are doing. I found a number of the analysis/logic talks interesting when I was taking Math 400.

Bad points:

3) The style and approach that different speakers take to giving this kind of talk varies a lot (eg. general survey of an area vs focusing on some specific problem/example). This on its own is not bad but it often leads to a lot of variation in the level at which talks are pitched. Weaker students often tune out when the level is too high or the talk gets too techinical. It would be good if a signifcant portion of every talk was understandable by an average senior undergraduate student.

4) The current system is rather inflexible. First year students are required to take Math 400 during their first two semesters. In some cases (especially for students coming in with weak backgrounds) it might make sense to postpone this for a semester or two. They are more likely to follow the talks and get something out of them with some graduate level mathematics under the belt. Even students who are reasonable well prepared for graduate school might benefit from a semester delay since there is such a lot going on in that first semester (adjusting to teaching, graduate level courses etc.).

Michael Bush

July, 2004

Faculty Testimonial

In my three years as a faculty member at Illinois, I have given three talks in the Math 400 seminar series. My experience with this series has been very positive. This series is clearly an excellent way for students to learn about areas of research and about potential advisers. The talks offer a broad view of what research mathematics is like, and are therefore an excellent complement to the introductory graduate curriculum.

As a junior faculty member, I have also appreciated the exposure which this series provides. Many students who have attended these talks have gone on to take courses with me. Some of these continue to attend research seminars in my area, and several of these have gone on to do research with me. Of course, some of this may have happened without this series. But it is clear that the series creates and facilitates such connections. Therefore I feel that it is a valuable addition to the graduate program.

Scott Ahlgren

July 2, 2004

Faculty Testimonial

I have given a lecture in Math 400 each year since we began this idea. Preparing engaging talks that introduce graduate students to my area of research has been a delight. Each year I look forward to my week in Math 400. Nearly all of the student replies are positive and make me feel good; on the other hand there is little tangible follow-up. No one was ever come to work with me because of my math 400 talk. I get the feeling that, by the end of the year, few students even remember who said what in this series of talks.

In theory Math 400 seems to be an excellent idea. I have discussed it with both graduate students and faculty, and the consensus is positive. Graduate students see many faculty members they do not see in courses, simply because the department is so large; as a result their training is broadened.

One suggested change to Math 400 has been to make it required instead for second year students. This suggestion has both positive and negative elements.

John D'Angelo

July 3, 2004

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