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

# Current projects (Fall 2016)

Kira ParkerMentor: Braxton Osting

Ranking methods and competitive climbing

Noble Williamson

Mentor: Gordan Savin

Quadratic Forms and the Geometry of Numbers

Olivia Dennis

Mentor: Braxton Osting

Information Theory

Michael Zhao

Mentor: Gordan Savin

Binary integral hermitian forms and quaternion algebras

Jacob Madrid

Mentor: Sean Lawley

An Improved Numerical Method for the Stochastic Simulation of the Diffusion Process with a Partially Absorbing Boundary

Max Carlson

Mentors: Christel Hohenegger, Braxton Osting

Numerical Solution to Sloshing Free Surface

Peter Harpending

Mentor: Elena Cherkaev

Eigenvalue Solution Methods of Fractional Differential Equations

Caleb Webb

Mentor: Maxence Cassier, Aaron Welters (Florida Tech)

Spectral Analysis of Periodic, Nonreciprocal Systems Consisting of High-loss and Lossless Components

Dietrich Geisler

Mentor: Aaron Bertram

Construction of Lie Groups from Associated Lie Algebras and Root Systems

Rebecca Hardenbrook

Mentor: Jon Chaika (funded by NSF)

Interval exchanges

# 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 2016 Math 4800: Random Walks with Algebraic Combinatorics**

**Instructor:**Tom Alberts

**When and Where:**TBA

**Description:**If you have ever found yourself in an unknown city then likely you performed some version of a random walk: not knowing which street to take next you randomly chose among the available options and then repeated. Although it’s a simple mechanism, the statistics of the walk produced in this way turn out to be ubiquitous across mathematics. If the geometry of the city has an underlying “group structure” then from a mathematical point of view the random walk process is particularly interesting. Commonly the statistical properties of the random walker are studied by simple counting arguments, and if one exploits the underlying group structure to do so then the tools of algebraic combinatorics become available. The course will start with the basics of simple random walk on integer lattices, with an emphasis on studying it through combinatorial ideas. Many simple and cute, but powerful, methods of counting will be used. We will then move into the study of random walks on graphs and groups and along the way encounter many interesting objects such as Young tableaux, the RSK algorithm, and the matrixtree theorem. We will also briefly discuss the deep connections to probability, statistics, differential equations, geometry, and number theory.

**Prerequisites:**Permission of the instructor. Linear Algebra is a must. Calculus will be assumed. Basic knowledge of groups and group theory would be helpful but is not required. Basic familiarity with programming is helpful as computer simulations will be part of the projects.

**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**

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

*Expectations:*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**!). During the semester meet regularly with mentor, and generate an evaluation and a report, give a talk with slides

*Application for Fall 2016 are now open with the deadline of September 2.*

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).

**Applications for the Fall 2016 are now open with the deadline of September 2, 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**