# UNDERGRADUATE RESEARCH

# OPPORTUNITIES FOR RESEARCH

**NOTE:**You

**to be a Math major/minor to take advantage of these research opportunities):**

*do not need**by permission of the instructor only*.

### MATH 4800 - Undergraduate Research Topics

Fall 2022: |
Introduction to Algebraic and Tropical Curves |

Instructor: |
Tommaso de Fernex (defernex@math.utah.edu) |

Day(s)/Time: |
MoWe / 03:00PM-04:20PM |

Location: |
LCB 121 |

Course Credit: |
3 credits |

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

Description: |
The course introduces basic concepts in algebraic and tropical geometry. Algebraic geometry studies zero sets of polynomials; in tropical algebra, the sum of two numbers is their minimum and the product is their sum. Rather than giving a rigorous, abstract treatment of the theory, we will discuss many examples focusing on the case of plane curves and explore some of the connections between algebra, geometry, topology, and other fields. |

Prerequisites: |
Enrollment in this class is by permission of the instructor only. While there are no fixed prerequisites, given the advanced level of the course students will be expected to have a some familiarity with the basics notions in algebra (rings, fields, polynomials), topology (open and closed sets, continuity, compact surfaces), and complex analysis (holomorphic functions, power series). Having taken or taking concurrently one or more of Math 4200, 4400, 5310, 5510 is recommended. |

*Applications for Fall 2022 are due Tuesday, August 16th.*

*Applications for Fall 2022 are due Tuesday, August 16th.*

*See below for instructions.*

*See below for instructions.*

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 student produces a final expository paper on aspects of their research.

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, which is usually held on the Reading Day before final exams begin. |

Course Credit: |
You may take Introduction to Research as a class (up to 3 credit hours). Please specify that in your application. (The course number will be 5910. Normal tuition policies apply. You can count this course towards university
Upper Division Hour 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!). |

### Application Instructions:

See this file for instructions.

*Applications for Fall 2022 are due Tuesday, August 16th.*

*Applications for Fall 2022 are due Tuesday, August 16th.*

*See below for instructions.*

*See below for instructions.*

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.

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, write a report, and submit an evaluation. Your work, presentation, and report will be evaluated by Mathematics faculty. |

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

### Application Instructions:

See this file for instructions.

Science Research Initiative (SRI)

**Within the College of Science**

The SRI is a program for first- and second-year students that enables them to start working in an SRI stream, or research experience, at the beginning of their journey at the University of Utah. This program assumes incoming students will not have any college-level research experience; instead, you will learn alongside your fellow students to gain research skills, technical experience, and the unique opportunity to learn from faculty.

Click Here for More Information

## 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.

### 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.

**RESEARCH RELATED LINKS**

### 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 (URSD) 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.

Questions?

**OR**

JWB 325

801-585-1628