# Student Research

Undergraduate research is an inquiry or investigation conducted by an undergraduate student with faculty collaboration that makes an original intellectual or creative contribution to the discipline. The Mathematics Department often has opportunities for students to engage in research projects in mathematics. Within the Department, we introduce students to the world of mathematical research in many ways.

**Individual Research**- We support**individual research projects**that students complete working with individual faculty members. These are often done in the form of a directed study. Click here for how to get started.**Honors in Mathematics**- A student project often grows into an honors thesis that is submitted to earn the designation**Honors in Mathematics**. Past projects have investigated questions in algebra, geometry, differential equations, linear algebra, combinatorics, and many others. Students who show outstanding promise are asked by faculty members to participate. Click here for more details. Students can also use this as their Capstone Experience for the Edgar Fellows Honors Program.**BioMathematics**- We have a**Research Group in BioMathematics**that has ongoing projects in applications of mathematics to Biology.**Research Weekend**- We sponsor a**weekend symposium in the Spring semester**, where we invite an accomplished mathematician to campus to give a colloquium and to lead a two-day research experience in mathematics to a select group of students (more details).**Summer Research and Study Abroad**- We encourage our students to apply for and participate in NSF-supported REUs, attend special summer programs at other institutions, or to study abroad at one of the many universities offering research programs each summer. Recently, our students have participated in programs at Iowa State, NC State, Cal State San Bernardino, Valparaiso, Virginia Tech, Penn State, UC Fresno, the Texas A&M pre-REU, and PCMI.

Geneseo Students have many internal and external forums in which to share and present their research. Here are a few examples of where our mathematics students have presented their research:

**G.R.E.A.T. Day**(Geneseo Recognizing Excellence, Achievement, and Talent) is a forum for all students at Geneseo to present results from projects, directed studies, or research. Each spring students have the option of presenting their results orally or in the form of a poster. Click here for more details.**Hudson River Undergraduate Conference**for undergraduate students interested in mathematics. It was started in 1994 by a group of schools, primarily in eastern New York and New England with the intent of providing undergraduates with the experience of attending and/or presenting at a professional mathematics meeting designed primarily with the student in mind. The focus is on student presentations with several faculty presentations, all aimed at a student audience. There is an invited speaker who is a prestigious mathematician. These have included Benoit Mandelbrot, John Koch, Joseph Gallian, and Peter Hilton.- Students can have opportunities to present their research projects in MAA, ASA, NCTM or other professional meetings. MAA Seaway Section Meetings are semiannual meetings. Undergraduate students give talks at each of the meetings. Other meetings involve various activities, such as a poster competition, a game show, an ice cream social, or a scavenger hunt.
**UP-STAT**is annual joint conference of the Upstate Chapters of the American Statistical Association. Students present their statistics research projects, and participate in Predictive Data Analytics Competition in group.- SURC is SUNY Undergraduate Research Conference. This brings together undergraduate researchers as well as their faculty mentors throughout the SUNY and CUNY system for a full day of activities.

#### Why do research?

Research projects are valuable experiences for undergraduate students. For instance, a research project:

- Allows us to discover fresh, novel and attractive mathematical solutions,
- Improves our creativity and problem solving abilities,
- Allows us to apply classroom knowledge to unsolved mathematical problems,
- Allows us to solve real life problems,
- Provides a taste of what graduate school is like.
- Helps our chances of being accepted into Ph.D. programs (not exclusively in mathematics,) and
- Helps us become better qualified for internships.

Please click here for characteristics of excellence in undergraduate research.

**How to get started?**

1. Ask a professor. Some professors have ideas for research projects or directed studies, so visit office hours and ask around. However, advising a student in research takes a lot of time, so be respectful when they decline. Take a look at each professor’s website to get an idea of what topics they are interested in. Some professors have sites specific to working with students, and we may list some links here. Others have specific semesters in which they get many students involved in research.

2. Attend math colloquia. Sometimes questions discussed in colloquia can lead to interesting projects, and since many professors are present, it can also lead to a natural person to work with.

#### Some recent student research projects:

2015, *Applications of Nonparametric Estimators in Fuzzy and Cellular Automata Algorithms*(supervised by Bilgic)**Herbert Sussmann,****2014,***Computational techniques for the statistical analysis of “big data” in R*(supervised by Bilgic)**Wilson Cheung, <2012,***On uniform bounds for rational points on quadratic rational curves and thin sets.*(supervised by Rault)**Bennett, Mike; Lazebnik, Kirill Y; Singer, Jeffrey A., 2012,***On invariant area formulas and lattice point bounds for the intersection of hyperbolic and elliptic regions.*(supervised by Rault)**Kaitlyn Gayvert**, 2012,*Mathematical Model Creation for Tumor Growth in Advanced Neuroendocrine Pancreatic Cancer*(supervised by Leary)**Dan Rossi**, 2012,*Numerical range of some doubly stochastic matrices.*(supervised by Rault)**Kevin Palmowski**, 2011,*Topics in Numerical Linear Algebra: Numerical Methods for Eigenvalue Approximation*(supervised by Haddad)**Tyler Massaro**, 2011,*Stability Analysis of Fitzhugh-Nagumo with Smooth Periodic Forcing*(supervised by Esham)**Nicholas Devin**, 2009,*Exploring the Jones Polynomial*(supervised by Heap and Johannes)**Arunima Ray**, 2009,*Exploring the connections between Fourier analysis and wavelets*(supervised by Nicodemi)

**Expectations of the student:**

**Expectations of the student:**

a. Professionalism. A high level of professionalism is required: do not wait until the last moment to finish tasks, don’t be afraid to ask questions or look things up, come prepared to meetings, don’t waste time, give forewarning if you are going to cancel a meeting, and be sure to dress and act professionally at conferences.

b. Meetings. Most research progress takes place outside of meeting times. However, it is expected that a faculty adviser may ask you to meet for 1 to 3 hours per week. If one week you are unprepared or overwhelmed with exams, then be sure to cancel the meeting in advance: remember to avoid wasting time. Conversely, it is expected that the student leave extra time aside at high stress times like conference presentations - expect to meet extra.

c. Agreement to disseminate. Faculty receive credit for doing research when talks or publications arise as a result. Therefore, it is an expectation that, if the faculty adviser deems the project a success, the student (i) apply for SUNY Geneseo travel funds to attend a conference, (ii) create a talk using LaTeX and practice it under supervision of the faculty adviser, and (iii) help in writing any requested proof details for a paper for publication.

**Suggested pre-requisites:**

Students should be above average, usually with more than a 3.0 GPA in mathematics.

- It is recommended that students have completed Math 239: Introduction to Mathematical Proof, before seeking out research projects.
- In addition, many projects may require knowledge of advanced 300-level courses in mathematics, computer programming and writing skills.

**Can I get credit?**

Yes, students often enroll in Math 399, or sometimes Math 393 [an additional offering is in the process of being added to the course listing: “Math 398: Directed Research]. However, this may increase the expectations of you in the project.** **

**Can I get paid?**

Payment in mathematics research is rare, unless you attend a summer Research Experience for Undergraduates. The college does offer some support for students doing research, but it is designed for lab workers in the sciences and thus under-used in mathematics. If your participation in the project is contingent on not working in a job, then consider applying for a stipend here: https://www.geneseo.edu/undergraduate_research/student-research-assistantships.

**Resources **

**Resources**

**Council on Undergraduate Research****MAA PIC Math (Preparation for Industrial Careers in Mathematical Sciences)****Professor Caroline Haddad's REU links and more****NSF REU SITES****MAA Undergraduate Research Page****AMS REU Sites****NSA REU and Internships****Annual Nebraska Conference for Undergraduate Women in Mathematics**