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# 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 (Spring 2019)

Yuhui Yao
Mentor: Karl Schwede
Polynomial evaluation over finite and rational fields through matrices in Macaulay2

Charlotte Blake
Mentor: Yekaterina Epshteyn
Efficient Numerical Algorithms for Automatically Processing Data with Application to Materials Science

Gabrielle Legaspi
Mentor: Yekaterina Epshteyn
Coarsening Models

Camille Humphries
Mentor: Yekaterina Epshteyn
Fast Numerical Algorithms for Models with Nonlinear Diffusion

Justin Baker
Mentor: Elena Cherkaev
Optimal Transportation Networks

Cassidy Buhler
Mathematical Modeling of Adaptive Therapy in Prostate Cancer

Thomas White
Mentor: Christopher Janjigian
Simulating stochastic processes with new methods of modeling

# 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!

## Summer Program 2019 - RTG Pre_REU in Number Theory

Are you interested in learning about deeper mathematical concepts, but don't yet have the background to take more advanced classes? Are you interested in learning more about mathematical research, but think there is a lot more you need to learn for now? Then this program may be for you!

This program is intended for enthusiastic (budding) math majors who are looking for an intensive summer of mathematics, even though they do not have the mathematical experience to be ready to do a research project. Our subject is NUMBER THEORY, the study of the integers, whose basic questions have stimulated mathematics research for thousands of years. Today number theory lies at the nexus of many areas of theoretical mathematics, and it also plays a basic role in applications to cryptography.

Participants will work closely throughout the day with one another and with the program staff, exploring a series of challenging problem sets that gradually develop many of the great ideas of classical number theory. Rather than having material presented to them in lectures, students will be asked to experiment with the subject, formulating conjectures about what they believe to be true, and then to justify their claims rigorously. They will discover the excitement of being the origin rather than the receptacle of mathematical ideas; and they will prepare themselves to take advantage of the many remarkable possibilities open to mathematics majors at the U.

The program will run from June 17-July 12, from 9:15-3:30 each weekday. Participants will be PAID a $2,000 stipend for their enthusiastic participation. To apply, please fill out the application form by following the link below. Please send any questions to patrikis@math.utah.edu. The application deadline is April 15. Application form ## 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 2019: Polynomials
Instructor: Thomas Polstra
Polynomials are central to the study mathematics. For example, we learn in Calculus that Taylor polynomials are used to approximate exponential, logarithmic, and trigonometric functions. Behind these simple mathematical objects is a rich theory which unites many branches of mathematics. In this course we will explore analytic, algebraic, geometric, and number theoretic properties of polynomials in hopes of connecting the dots between seemingly different branches of mathematics.

Time and place: TuTh, 2:00PM-03:20PM, JWB 308 For more information or to register please contact the instructor.

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.

Students are strongly encouraged to take Intro to Research first, before doing an individual project. If you would like an exception, please ask your mentor to comment on your previous experience relevant for your project, in the letter of support.

You may take Intro to Research as a class, up to 3 credit hours. Please specify that in your application
(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 2019 is now open. The deadline is may 17
However, if you are taking this for credit, please contact the undergraduate director as soon as possible!

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 $1,500 (for Fall and Spring semesters. For the Summer the amounts are multiplied by 3/4). Continued funding depends on the student's performance in the previously funded REU activities. 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 1-2 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 Spring 2019 is now open The deadline is May 17 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