## Mathematics Comps (priority given to Mathematics majors)

### Algebraic Curves and Dedekind Domains

Advisor: Alex Barrios

Terms: Fall/Winter

Prerequisites: Math 342

### Orbits of Noncrossing Tree Partitions

Video

Advisor: Al Garver

Terms: Winter Spring

Prerequisites: It would be useful to have taken Math 342 (Abstract Algebra I) or Math 333 (Combinatorial Theory), but these are not required. Topics studied in Math 342 will be especially useful if students are interested in learning about the related representation theory.

### Heights and Dynamics

Advisor: Rafe Jones

Terms: Fall/Winter

Prerequisites: Math 236 or the equivalent. Some experience with number theory is helpful but not required.

### Directed Reading in Elliptic Functions and Modular Forms or Directed Reading in Algebraic Geometry

Advisor: Mark Krusemeyer

Terms: Winter/Spring

Elliptic Project Prerequisites: (Required) Math 361 or 261; (highly recommended) Math 342. Some background in number theory may be helpful, but is not required.

Algebraic Geometry Project Prerequisites: Math 342. Additional background in algebra may be helpful, but Math 352 is not required; in particular, we are not likely to use anything substantial from either Galois theory or representation theory (the most frequent topics in Math 352 in recent years).

### Transient Dynamics in Ecological ODE Models

Video

Advisor: Kate Meyer

Terms: Winter/Spring

Prerequisites: To participate in this comps group you will need to have a background in ODEs (Math 241) and interest in mathematical modeling. You will use MATLAB or Python to carry out numerical simulations, but you can learn as you go and previous experience is not required.

### Directed Reading in Geometric Group Theory

Advisor: MurphyKate Montee

Terms: Winter/Spring

Prerequisites: Suggested (but not required) prior knowledge: Familiarity with groups, like you would have from Math 342 (Abstract Algebra).

### Topology of Graph Configuration Spaces

Video

Advisor: Steve Scheirer

Terms: Winter/Spring

Prerequisites: None, but if you’ve taken Topology or Abstract Algebra, you might find this particularly attractive.

### Bernoulli Numbers and Irregular Primes

Advisor: Caroline Turnage-Butterbaugh

Terms: Fall/Winter

Prerequisites: We have a lot of flexibility in this project. The only required prerequisite is Math 312 (Elementary Number Theory) or Math 342 (Abstract Algebra I). Certain background will lead the project in different directions, but those directions will be decided upon after the group is formed. (For example, if the group members have seen Math 261/Math 361 (Complex Analysis), then there are certain directions we can take.)

## Mathematics and Statistics Comps (both Mathematics and Statistics majors accepted)

### Jigsaw Puzzles and Broken Bones

Advisor: Rob Thompson

Terms: Fall/Winter

Prerequisites: There are no specific prerequisites. I recommend having taken at least one CS course or equivalent computing experience.

## Statistics Comps (priority given to Statistics majors)

### Statistical Models of Infectious Disease

Advisor: Tom Madsen

Terms: Fall/Winter

Prerequisites: Math 245 and 275. Math 241 is helpful but not at all required.

### Quantile Regression

Video

Advisor: Andy Poppick

Terms: Winter/Spring

Prerequisites: Statistical Inference (Math 275) and Applied Regression Analysis (Math 245)

### Statistical Analysis of Networks

Advisor: Katie St. Clair

Terms: Fall/Winter

Prerequisites: Math 275 and either Math 245 or a CS course beyond CS 111.