# 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 2018 Symposium will take place on April 26, 2:30 to 4:30 in LCB 215**

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

# Current projects (Spring 2018)

Charlotte BlakeMentor: Andrej Cherkaev

Approximation of a chain of vibrating bistable spring-mass links with one stable nonlinear spring

Hannah Choi

Mentor: Sean Lawley

First Passage Time and its Ecological Applications

Jack Garzella

Mentor: Fernando Guevara-Vasquez

Using Spring and Mass Networks to Model an Elastic Body

Han Le

Mentor: Tom Alberts

Statistical properties of large sample covariance matrix

Delaney Mosier

Mentor: Ken Golden

Poisson Equation Model for Sea Ice Concentration Fields in a Changing Climate

Katelyn Queen

Fred Adler

Dynamic Modelling of Subclones in Patients with Late-Stage Breast and Ovarian Cancers

Hannah Waddell

Fred Adler

The Community Ecology of the Music Canon

# 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 2018: Elliptic curves**

**Instructor:**Gil Moss

**When and Where:**Tuesday and Thursday, 2:00-3:20, location TBD

**Description:**

The study of diophantine equations forms an ancient branch of number theory whose goal is to count solutions of polynomial equations in the integers or rational numbers. Fermat's last theorem is a famous example. Whereas linear and quadratic equations are well understood, much is unknown when the equations have degree 3. What little is known was proven using elegant combinations of algebra, number theory, and algebraic geometry. This course will focus in depth on cubic equations in two variables, that is, elliptic curves. We will begin by briefly covering some concepts in algebraic geometry, we will then shift to exploring the interplay of geometry and number theory in the setting of elliptic curves. In the first portion of the course, we will explore the interplay of geometry and number theory in the setting of elliptic curves. Examples of topics include finding rational points of finite order, counting points over finite fields, and the group properties of the set of rational points. The second portion of the course will shift to a broader discussion of some major developments that have taken place in the subject over the last century.

For more details, please consult the syllabus.

**Prerequisites:**Permission of the instructor.

There are no formal prerequisites, besides having experience writing proofs. However, the course will focus on the interplay of algebra, geometry, analysis, and number theory, so it is recommended that students have some familiarity with the basic notions in these areas (e.g. linear algebra, groups, rings, fields, polynomials, infinite series, complex numbers, factorization and primes in the integers). As one example, Math 4400 would provide a good background; or taking Math 5310 concurrently.

**Interested students should email the instructor at moss@math.utah.edu**

**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 2018 will open May 10*

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 Summer 2018 will open May 10*

See application instructions below

Individual faculty members or research groups may also sponsor undergraduate research through grants. Current department wide grants that provide support for undergraduate research are:

## 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**

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