Math 390 Individual Study Opportunities
A.J. Hildebrand
About Math 390
Math 390 is a "Guided Individual Study" course on advanced topics that
are not covered in other courses. It is the undergraduate equivalent of
what at the graduate level would be called a "Reading Course" (Math 597).
The specific topic, number of credit
hours, and meeting format and times are arranged with the instructor.
The course will need to be approved by the Director of Undergraduate
Studies before a student can register for it.
A Math 390 arrangement can involve multiple students; most of my recent
Math 390 projects have been run in a small groups of 24 students each.
Sample Topics
Here are sample topics based on recent Math 390 courses I have given
that illustrate the range of possibilities:
 Game Theory: "The Iterated Prisoners Dilemma"
 Statistics: "Distinguishing Cause and Effect"
 Applied Mathematics: "Brownian Motion and PDEs"
 Pure Mathematics:
"Master Class on Selected Topics in Combinatorics, Analysis, and Probability"
 Math Contest Training: "Putnam Master Class"
Note that these are just examples of possible topics;
there are many other options. The main requirement on a Math 390 topic
is that (i) it is at an advanced level and (ii) not covered in
regular courses.
Text/course materials. For some topics there exists a single suitable
textbook, but more typically no such text is available. In those cases we will
use material from a variety of sources, such as chapters in textbooks,
original articles, and lecture notes. Usually, these materials are available
in electronic form, so there is no need to purchase texts.
Details

Format.
Math 390 is a "guided individual study" course: Instead of having formal
lectures, students enrolled in Math 390 study appropriate materials on
their own, with guidance by the instructor.
My recent Math 390 courses have all been carried out in minigroups of 24
students. I typically meet with the group once or twice a week for 12
hours each, depending on the number of credit hours that the students
have registered for. At these meetings, we will go over the material the
students have studied since the last last meeting, discuss any questions
that have come up, and assign new readings and exercises to be completed
by the next meeting.

Credit: Math 390 can be taken for up to 3 hours of credit
per course, and there is a maximum of 8 hours of Math 390 credit a student
can earn altogether. The number of credit hours should correspond to
the workload you plan to put into the course: 3 credit hours of Math
390 class should require a time investment equivalent to a regular 3
credit hour course; 1 credit hour should require about one third of the
time investment of a 3 hour regular course.
 Prerequisites.
While there are no absolute prerequisites, Math 390 is aimed at students
who already have a strong record in math courses and are interested in
learning topics beyond regular courses. For example, a student
interested in taking Math 390 on a probability/statistics topic should,
at a minimum, have taken Math 461 (or an equivalent course) with a grade
of A or A+.

Grading: Math 390 can be taken on a satisfactory/unsatisfactory basis
or graded by letter grade. Grading will be based on successful
completion of the readings and assignments.
 Math 390 versus regular classes. Aside from the different
formats (individual study versus lecture style classes), the main
difference to a regular class is in the nature of the topic covered,
which should be an "advanced topic not covered in regular classes."
In particular, Math 390 is not a substitute for taking regular classes.
 Math 390 (Individual Study) versus Math 492 (Undergraduate Research in
Math). These two courses are closely related and targeted at
similar audiences: students who have a strong record of math
courses (typically including honors courses) and who may be considering
graduate school in mathematics or a related field such as mathematical
finance, economics, statistics, computer science, etc. Math 390 can
lead to a Math 492 undergraduate research project, but can also be
taken independently of any Math 492 plans, and it is not a prerequisite
for Math 492. For more about Math 492 projects see my
Math 492 Page
and my
Undergraduate Research Page.
How to apply
If you are interested in doing a Math 390 type project with me, contact me at
ajh@illinois.edu, describing the general area(s) you are interested in for a
Math 390 topic. Attach your transcript (unofficial okay) so that I have an
idea of your mathematical background, your strengths and possible weaknesses.
The next step would be to meet with me to discuss possible topics. I
typically run Math 390 projects in small groups of 24 students, so whether a
project on a particular topic will run depends on the availability of students
with similar interests and backgrounds.
Once I have assembled a mini group of interested and qualified students, I
will submit the Math 390 proposal to the Director of Undergraduate Studies for
approval; once the approval is granted, you can register for the course. Note
that the usual registration deadlines apply; in particular, a course cannot
be added once the "Add" deadline has passed (usually during the second week of
the semester).
Last modified: Wed 08 May 2019 12:10:12 PM CDT
A.J. Hildebrand