*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*

- General information.
**Teaching schedule for upcoming graduate courses**- Course combinations and
Spring-only courses.
- Suggested courses in other
departments.
- A variety of other information
and resources.

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 can__not__
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.

- The Mathematical Sciences CareerInformation page contains a lot of information about mathematical careers, including a number of career profiles of people working in non-academic settings.
- You may also find valuable information in the Science, Math and Engineering links at PhDs.Org.
- The Young Mathematician's Network
publishes an electronic newsletter (The
**Concerns of Young Mathematicians**) dedicated to issues of interest to graduate students and new Ph.D.s in mathematics. Some of the articles from past issues that I think are particularly worthwhile are collected below. Their web page also provides some links that may be worth looking at.

**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.

- Suggestions from the YMN board on choosing an advisor.
- Advice about getting started toward a career as an acutary, (April 19, 1995).
- There have been several articles addressing work in non-academic settings, like the interview with Jim Phillips at Boeing, or Tom Davis at SGI, and the article by C.E. Mannix.
- If you are considering a job at a four-year college, you might enjoy the article describing life at undergraduate schools, and the remarks about research vs. service at such institutions.
- If you are considering non-academic employment, you might appreciate reading about M. Sand's initial experiences working in industry.
- For those going on to a research position the article about making the transition to being responsible for your own research ought to be of interest.
- You might also be interested in some tips on the application and interview process.
- Even faculty might benefit from the article on how to give a good math talk!
- There is a brief article on grant writing basics by a former NSF program officer.
- The article on studying a research question might be useful for those starting a master's presentation.
- Gian-Carlo Rota's 10 lessons for lecturing, writing, and making a career of being a research mathematician.