# Featured REU projects

## Spring 2016

**Tyler McDaniel
Mentor: Braxton Osting**

Utah’s Pathways to Higher Education

** Olivia Dennis and Nathan Willis
Mentor: Owen Lewis**

Mathematical model of cell motility

# REU Symposium

These meetings are held at the end of semester and showcase the research that is being done by undergraduates in our department.**Spring 2017: Monday, May 1, 9:15-11:30 am. LCB 323**(Click here for schedule)

Archive of the symposium from Fall 2013 and here for pre Fall 2013.

# Current projects (Spring 2017)

Sarah Melancon and Dylan SollerMentor: Adam Boocher

Intro to research: Commutative Algebra

Weston Barton

Mentor: Tom Alberts

Sch\"{u}tzenberger Promotion Paths

Michael (Barrett) Williams

Mentor: Elena Cherkaev

A Computational Inverse Problem of the Diffusivity of Ice in Marginal Ice Zones

Willem Collier

Mentor; Arjun Krishnan

Shortest Paths on a Graph and Eigenvalue Distributions of Random Matrices

Max Carlson

Mentors: Christel Hohenegger, Braxton Osting

Improving the Numerical Method for Approximating Solutions to the Free Surface Sloshing Model

Peter Harpending

Mentor: Elena Cherkaev

Numerical fractional calculus

Rebecca Hardenbrook

Mentor: Ken Golden

Thermal Conductivity of Sea Ice in the Presence of Fluid Convection

# How to get involved

The Mathematics department provides the following research opportunities for undergraduate students.**Note:**You

*do not need to be*a Math major/minor to take advantage of these research opportunities!

## Math 4800 Undergraduate Research Topics

- These courses provide a research experience in a familiar course setting.
Topics vary every semester, but there is usually a Pure Mathematics and an
Applied Mathematics oriented course every academic year. Enrollment in this class is usually
*by permission of the instructor only*.

*Compensation:*$500 (Notice that this is a class, so regular tuition policies apply)

**Fall 2017: Representation Theory of Finite Groups**

**Instructor:**Adam Boocher

**When and Where:**Mondays and Wednesdays 1:25PM-2:45PM in AEB 306

**Class website**

**Description:**

Roughly speaking, group theory is the mathematical study of symmetry. Shapes in the plane may have rotational or reflectional symmetry; a collection of n objects can be permuted in n! different ways; a Rubik’s cube can be configured in roughly 43 quintillion different ways. Symmetries can be composed and in general the order of composition matters. The resulting mathematical objects - groups - have a rich structure. Understanding this structure can be quite challenging. In this course we’ll start with some down-to-earth examples of groups to build some intuition and the ability to do computations. Then we’ll dive into the basics of Representation Theory - a field that studies how to represent abstract groups as a collection of square matrices. We’ll see that the trace of these matrices is something very worthy of study - the character of the representation. Students should expect to work hard solving problems, doing computations, reading and presenting proofs in class. The course grade will be a combination of homework, class participation and an open-ended project.

**Prerequisites:**Permission of the instructor.

A solid background in Linear Algebra is essential, as is some exposure to group theory.

Depending on background, some self-study over the summer might be necessary. We will mostly follow the textbook Representations and Characters of Groups by James and Liebeck, though many topics will be supplemented with lecture notes, additional problems and other resources. Interested students should email boocher@math.utah.edu with their background and interest in the course.

**Math 4800 class archive**

## Introduction to Research projects

- The student works with a faculty mentor on exploring an area of
mathematics not usually taught in standard classes. Mentor and advisor meet
weekly throughout the semester to discuss topics from relevant text or journal
article readings. These projects may sometimes be appropriate as preludes to
independent projects, in cases where the ultimate research area requires a lot
of prerequisite knowledge. At the end of the semester, the REU student
produces a final expository paper on aspects of their research.

**New for Summer 2016: course registration is no longer required, but you can register for a class, up to 3 credit hours. Please specify that in your application**

You may register for a course (up to 3 credit hours) (The course number may be: Math 5910, 5960, 4999, depending on your case. If you register, this would be a course, so normal tuition policies apply. You can count this course towards university upper course requirements, but not as an elective for your math/applied math major. Note that a section needs to be created for you and your mentor, so**please apply early**!).

*Compensation:*up to $1000 in Fall or Spring. Up to$750 in the Summer.

*Expectations:*During the semester meet regularly with mentor (at least weekly), and generate an expository paper summarizing what you learned. You are also encouraged to give a presentation in our symposium.

Deadline: Usually Tuesday on the second week of classes (first week of classes in the Summer).

*Application for Summer 2017 is now being accepted! Deadline: May 16 at noon.*

See application instructions below ## Independent REU projects

- Work on a research project in Mathematics under the mentorship of a faculty member.
You must have a member of the Mathematics faculty who is willing to serve as your mentor. Discuss with the prospective mentor the scope and design of your project and prepare a project description.

*Time Commitment:*10 hours per week, on average

*Compensation:*up to $2000 first semester, up to $1000 afterwards (for Fall and Spring semesters. For the Summer the amounts are multiplied by 3/4).

*Expectations:*Meet regularly with mentor, give a talk with slides, and generate an evaluation and a report. Your work, presentation and report will be evaluated by faculty members and 2-3 best projects will be featured on our department website.

*Deadline:*Usually Tuesday on the second week of classes (first week of classes in the Summer).

**Application for Summer 2017 is now being accepted! Deadline: May 16 at noon.**

See application instructions below

## Application for Intro to Research or Independent REU project

Complete the online application form. You also need to submit before the deadline to ugrad_director(AT) math (DOT) utah [DOT] edu the following supplementary material:- A
**letter of support**from your mentor (usually sent to the email above directly by your mentor). - A
**current unofficial transcript**(generated on CIS). If you have a considerable amount of transfer credits (especially for Math classes), please include an unofficial transcript from your previous institution(s). (If sent by email, please use the**PDF format.**) - A
**project proposal**prepared with your mentor. (If sent by email, please use the**PDF format.**) - If this is a continuing award: your
**report from previous semester**, approved by your mentor.

## Other funding sources

The Undergraduate Research Opportunity Program (UROP) which is sponsored by the University of Utah Office of Undergraduate Studies also supports undergraduate research. The support you get is $1200 for the first semester and $600 for a renewal (as of Fall 2015). The deadlines are usually mid July (for Fall support) and mid November (for Spring support), so plan accordingly.Individual faculty members or research groups may also sponsor undergraduate research through grants. Current department wide grants that provide support for undergraduate research are:

## Undergraduate Research Scholar Designation

Students fulfilling certain qualifications may have the designation of "Undergraduate Research Scholar" appear in the awards section of their transcript. For more information visit the Undergraduate Research Scholar Designation webpage.**Why?**
An independent research project is excellent preparation for graduate school,
teaching, research, or a job in industry. It is also fun and challenging.
You will learn things in a completely new way when you work independently, but
with the help of a faculty mentor.

**How?** Choose an undergraduate research advisor (a faculty member) and
a problem or topic to work on. If you desire, you may apply for funding,
either through the Mathematics department REU program (see above)
or the Office of Undergraduate Studies' UROP program.

**What?** Whatever you do --- solve a problem, prove a theorem, develop a
computer model, find a new way of teaching or explaining a topic -- you will
write up the results in a paper accessible to other undergraduate students.

**When?** Usually during the junior or senior year.

**For more information about research opportunities**: consult with a faculty member you would be interested in working with, or the Undergraduate Research Coordinator/Director of Undergraduate Studies:

Alla Borisyuk

LCB 303

801-585-1639

ugrad_director(AT)math.utah.edu

**Research Related Links**