The math community at UT is vibrant and full of interesting, knowledgeable people. As such, there are a wealth of opportunities of which students can and should take advantage. Some of these opportunities are listed below, vaguely organized by category (click underlined words for links).

**Academic Opportunities**

**Freshman Research Initiative (FRI)**

FRI provides freshmen with a taste of what’s it like to go above and beyond the classroom in the STEM realm. Though most of the projects (called streams) are focused on laboratory science, there is one stream dedicated to math called Symmetry. The ideas of the Symmetry stream lead directly into pure math courses like M373K/L Algebraic Structures I/II and M367K Topology I and so the experience helps better prepare students for exploring those areas.

**Directed Reading Program (DRP)**

In their own words, “DRP pairs undergraduate students with graduate student mentors to undertake independent projects in mathematics. Any undergraduate student may apply for DRP and, if accepted, will be assigned an appropriate graduate mentor. The student and the mentor will agree on a project. It can be based on reading through a book or an article, but the project is not limited to such things. The program guidelines can be found here.”

Undergrads have the option to request a specific graduate student mentor, so we recommend that program applicants first partner with a grad student *before* applying (if possible) to ensure that mentors are a good match. Most grad students love math and are eager to lend a helping hand to someone not as far along in their mathematical journey, so you should reach out to them without reservations or worries. If you need specific pointers on approaching and getting to know the grad students then just ask someone in UT Math Club for help (we promise we don’t bite!).

The UT math department hosts a variety of seminars for grad students and more seasoned math faculty, with topics ranging across the mathematical spectrum. Students who have completed the core undergraduate pure math curriculum (M373K/L, M365C, and M367K) can benefit greatly from getting a picture of what lies on their mathematical horizon. For more information on seminars, check out this link. Note that most seminars operate on a volunteer basis and welcome competent undergrads.

**Conference Courses**

Have you ever wanted to take a course in representation theory or Riemann surfaces but the math department just never seems to offer it? Fret not: that’s what conference courses are for! Listed on the course schedule as M N75 Conference Course (where N is the number of hours), conference courses give small groups of students the opportunity to work closely with a professor on a topic of interest. As such, they require the approval of the overseeing professor as well as the chair of the undergraduate math department, both of whom must sign the required form that can be picked up in either the advising office on the 4th floor of RLM or the math department office on the 8th floor of RLM.

A few things to keep in mind. It is possible to change the focus of the conference course as the semester wears on — the course should be an organic, collaborative effort between you and your mentor. It is also possible to sign up for multiple conference courses in the same semester (just make sure you devote enough time to each!).

Example conference courses that undergrads have done at UT include:

- Algebraic geometry
- Analytic number theory
- Class field theory
- Commutative algebra
- Differential geometry
- Higher homotopy theory
- Homological algebra
- Representation theory
- Riemann surfaces

**Graduate Courses**

Every semester the course schedule features a variety of graduate courses. Prelim courses are offered regularly and help prepare graduate students for the qualifying exams they must take at the beginning of their PhD careers. Topics courses change every semester and may be rarely offered. Some topics courses are real gems — you should ask the graduate students to find out more.

Fall Prelim Courses:

- M380C Algebra I
- M381C Real Analysis
- M382C Algebraic Topology
- M383C Methods of Applied Mathematics I
- M385C Theory of Probability I
- M387C Numerical Analysis: Algebra and Approximation

Spring Prelim Courses:

- M380D Algebra II
- M381D Complex Analysis
- M382D Differential Topology
- M383D Methods of Applied Mathematics II
- M385D Theory of Probability II
- M387D Numerical Analysis: Differential Equations

It is common for advanced undergrads to enroll in prelim courses and even comprise a large portion of the class, so don’t be afraid of being the only undergrad in a class with a bunch of graduate students. That being said, you will probably have a better time if you can convince a buddy to tough things out with you from the start. Note that Methods of Applied Mathematics is actually a rigorous course in functional analysis, with the second half focusing on applications to partial differential equations (PDEs). Note also that a prelim course can be **VERY** different based on who is teaching.

**Outreach / Volunteer Opportunities**

**Saturday Morning Math Group (SMMG)**

SMMG meetings are held in RLM 4.102 on Saturday mornings (as the name suggests…). These meetings are totally free, require no pre-registration, and are typically led by guest speakers or UT faculty members. Check out SMMG if you are interested in getting some hands-on experience with junior/high schoolers, their teachers, and their parents.

In their own words, “MathHappens is dedicated to creating and supporting development of mathematical experiences outside of the classroom.” MathHappens is a not-for-profit educational outreach organization that has partnered with the UT math department on multiple occasions, most notably for H-E-B Free First Sundays at the Bullock Texas State History Museum. Students who work with MathHappens will receive compensation and be eligible to attend certain MathHappens social events (some of which have included knife throwers and actual fruit ninjas).

**Grader / Tutor / Learning Assistant (LA)**

Many undergrad math majors have benefited from grading for courses like M325K Discrete Mathematics, M328K Introduction to Number Theory, and M361 Theory of Functions of One Complex Variable. Graders work several hours per week in exchange for experience and compensation. If you are interested, a good person to contact is Prof. Michael Starbird.

**Other Opportunities**

STEMprov is a highly interactive experience that uses improv as a tool to teach people how to better navigate the STEM world. If you’re looking to stimulate your creative impulses, get out of your shell, or just have some plain old fun then STEMprov might be right for you.