The information below should be helpful to graduate students and their advisors in planning programs of study. If you find inaccuracies or can suggest improvements please send me your comments or come by my office to talk. - M. Day
You can read the Mathematics Department's Policies and Degree Requirements brochure and the Graduate School's Graduate Catalogue and Procedures on-line. Consult these publications for general information. However be aware that recent changes may not yet appear in them. Check with your advisor or the Graduate Program Director if you have heard rumors of a change that might affect you.
GTAs must register for 12 hours! Regardless of how many courses you take, if you are on a GTA you must register for (at least) 12 hours. Masters students and beginning Ph.D. students generally take 3 courses (9 hours) per term plus an additional 3 hours of 5994 to fill out their schedule to 12 hours. Doctoral students who have completed their coursework may take no courses at all, in which case they should register for12 hours of 7994. There are occasions in which a masters degree student has good reason to take less than 9 hours of courses, in which case additional hours of 5994 should be added to bring your total to 12 hours. (Talk to your advisor if you think you might be in that situation.) There have been cases in which a student dropped a course in mid-term and failed to add an additional 3 hours of 5994 to their schedule. As a consequence they did not qualify for the automatic stipend increase (small though it is) for second year students. In other words it cost them money down the road! To enroll for over 18 hours requires the Dean of the Graduate School's signature.
Comments About Your Program of Study. In your first year you should form an advisory committee of 3 faculty (5 for Ph.D.) of whom one will be your advisor, and develop your program of study, which must then be submitted to the graduate school. Your program of study should list only the courses necessary to satisfy your degree requirements. It is not a complete list of everything have or hope to have taken. There is a program of study form available from the Department office for you to fill out in consultation with your advisor. The members of your advisory committee then review it and sign their approval before your return it to the Department office. After that the Graduate Program Director reviews it and gives it final departmental approval. At that point it goes on record with the graduate school and can be altered one time only prior to graduation, so any changes that become necessary (due to changes of interest or course cancellations) should made in your final semester, not before. Masters students cannot use hours of 5994 on their program of study unless they are writing a master's thesis. Your program can include a limited number of 4000-level courses that approved for graduate credit.
Master's Presentations. To complete a masters degree you need to 1) write a masters thesis, or 2) pass two Ph.D. preliminary exams, or 3) give a masters presentation. A set of guidelines for masters presentations is available to explain this in more detail. You should start planning a masters presentation before the end of your next to last semester in the graduate program. Copies of written summaries from past masters presentations are available, if you want to get an idea of the topics others have selected in the past.
The following course combinations may compliment each other nicely on your schedule, even though they are not numbered as sequences. If you are looking for something to fill a spot on your Spring schedule, some of the following may be what you are looking for.
4124 Algebra is sometimes offered in Spring or Summer, but generally available in the Fall.
5114 Topics in Algebra is offered in the Spring as a follow-up for students taking 4124 in the Fall. As a topics course it's content changes from year to year. Contact the scheduled faculty member to find out about the planned content.
5524 Matrix Theory is usually offered in the Summer and either Fall or Spring. In the Spring it provides an alternate follow-up to 4124, and might also be good for those warming up for 5465 (Numerical Analysis) in the future.
4324 Elementary Topology is offered in the Fall. Although a 4000-levelcourse, many entering students have never seen this material and stand to benefit from the perspective it provides.
5344 Topics in Topology and Geometry is offered in the Spring. As a topics course the content will change from year to year. Contact the scheduled faculty member to find out about the planned content.
5454 Graph Theory, 5464 Combinatorics - these can be taken in either order. Graph Theory is usually available in the Summer.
5474 Finite Difference Methods, 5484 Finite Element Methods are another regular Fall, Spring combination.
Some 4000-level courses that you may also want to consider are Number Theory (4134), Complex Analysis (4234), Fourier Series and PDE (4425), Dynamical Systems (4254)
The point has been made over and over, both by our alumni now well into their careers and by national studies of graduate education, that it is very valuable for mathematics graduate students to get some exposure to other disciplines. Whatever you do with the rest of your career, you will probably be working with colleagues who were trained in different subjects. Learning to bridge the "jargon gap" to other subjects, and appreciate the issues that are important to nonmathematical professionals is very valuable. You will benefit greatly if you can take a couple courses in mathematically related subjects from different departments while you are a graduate student. Here are some ideas. Please let me know of other appropriate suggestions or additional information.
AEO 5244 has been mentioned. 5224, 5234 certainly look appropriate, as well.
The Economics Dept. has indicated to us that the following of their courses should suit mathematically inclined students. Many of these courses all incorporate a mathematical game theory point of view I (M. Day) have course syllabi, if you want to see them.
ECON 4424: Game Theory with economic Applications
ECON 5005,6: Prices, Markets and resource Allocation. "The corequisite for 5005 should read 5125. I would think that a second year math graduate student should be able to cover his/her gaps very fast by self-studying the textbook. But of course it is up the instructors and administrators to determine whether a waiver is appropriate. Roughly speaking, 5125 covers50% of material that should be known by your students and 50% optimization techniques used in economics, but also in many other fields and, perhaps, also of some interest for math students who see their future in applications. Many of our first year students taking 5005 do have an economics background, but some don't and it is not a requirement." - Hans Haller.
ECON 5125,6,7: Empirical Research Methods in Economics. "Roughly speaking, 5125 covers 50% of material that should be known by your students and 50% optimization techniques used in economics, but also in many other fields and, perhaps, also of some interest for math students who see their future in applications." (H. Haller) Generally (based on the catalogue description) this looks like a lot of practical techniques that may be of value to some of our students.
ECON 6404: Industry Structure. "This course is relatively low tech. But it relies on basic knowledge in microeconomics and game theory as covered in 5005. On the other hand, the more difficult concepts will be furnished or repeated, if the need arises. Thus it is hard, but not impossible to follow the course without having taken 5005. (It is hopelessto try without some advanced undergraduate microeconomics.)" - Hans Haller
Several ISE courses are good possibilities. In addition to the following two you might also consider 5124, 5424, 5464.
ISE 5405,6: Optimization. Shiralli's course covering linear and nonlinear programming. It has been taken by a number of our graduate students.
ISE 5414: Random Processes. Stochastic processes for operations research applications. Some undergraduate probability and statistics is the prerequisite.
STAT 5104: Probability and Distribution Theory, and STAT5114: Statistical Inference. This pair of courses is the best foundation for students who want to take further course work in statistics. An undergraduate advanced calculus course which includes functions of several variables(or our 4225,6) should be adequate preparation.
STAT 5615,6: Statistics in Research. This is a "service course "for students from other departments. It emphasizes applied techniques and includes an introduction to basic probability. It might be the best choice for those students who just need some basic statistics technique under their belt before starting their first job. Prerequisites are minimal: calculus and some computer experience.
Several of the ESM courses would be very good choices, for instance 5304, 5314, 5414, 5754, 6314.
There are probably some CS courses on combinatorial algorithms- perhaps a good companion/follow-up to our Graph Theory, Combinatorics. A good data structures course is probably important for anyone who might find themselves doing program development. Talk to Cal Ribbens to get some leads on these and other possibilites in CS.
Various essays and readings. The following articles were taken mostly from Concerns of Young Mathematicians. (Back issues are available from their web site above.) The essays below are ones I thought would be of particular interest to graduate students. I do not necessarily endorse everything that is said in these articles, but these "editorials" written by or for graduate students or new Ph.D.s at least address important issues.