# Undergraduate Research in Mathematics

We encourage students to pursue undergraduate research projects with faculty mentors. Projects can be based around any mathematical idea or problem that interests you, and faculty often have a few good ideas of their own for research projects. If you are interested in research, contact a faculty member and we'll get things started.

In the mathematics department, we view undergraduate research as a collaborative effort on a problem whose solution is unknown, often even to the faculty mentor. Ideally, the research process involves literature review, original discoveries by the student, and ultimately, the public communication of results such as a journal publication or a presentation at a professional meeting.

Committing to a research project is a valuable experience as it allows you to take the tools developed in class and apply them to real problems. Research demands equal parts perseverance and creativity, but the reward of finding something new on your own is great. Taking part in a research project is a privilege - many schools do not encourage undergraduate research the way that Shippensburg does.

General information on student research at Shippensburg is also available.

#### Examples of research projects in the Mathematics Department

Below are some faculty members who have conducted research projects with students. If you see a topic that interest you, feel free to contact that faculty member about the possibility of conducting similar research. Many research projects result in papers and/or presentations at national conferences.

- Lance Bryant
*Commutative algebra, semigroup properties, data science*- L. Nicklas, "Identification and Classification of Breast Cancer Through Machine Learning and Computer Vision Models." With funding from an SU Undergraduate Research grant.
- (With J. Hamblin) A. Garibay, G. Sigado, and M. Carlin, "Numerical Semigroups and the Game Chomp."
- (With D. Ensley) T. Biondino, H. Jones, and L. Lawyer, "Predicting Student Success at Shippensburg University." With funding from Dean of the College of Arts and Sciences.
- J. Joseph, A. Koederitz, and L. Lawyer, "Data Analysis for Shippensburg University’s New Student Orientation Program." With funding from an SU Student/Faculty Research Engagement (SFRE) grant.
- (With J. Hamblin) D. Eschbach, "Minimal Communication Networks: Connecting Graph Theory and Algebra." With funding from an SU Summer Undergraduate Research Experiences (SURE) grant.
- Ryan Long, “Apery Diagrams of Numerical Semigroups”
- Kellie Bresz, "Quotients of Numerical Semigroups with Maximal Embedding Dimension"

- Ji Young Choi
*Enumerative Combinatorics/Sequences, Elementary Number Theory*- Justin Baker, "Graph pebbling numbers of the ycles attached an edge"
- Kelly Toppin, "Minimum Pk-total Weights"
- Ibrahim Abdurrahman, "Possible counterexamples on Collatz Conjecture"
- Conner Oldt, "Optimization of cooking pizzas"

- Doug Ensley
*Technology in teaching mathematics, algebra, algorithms, data science*- (With L. Bryant) T. Biondino, H. Jones, and L. Lawyer, "Predicting Student Success at Shippensburg University." With funding from Dean of the College of Arts and Sciences grant.
- Nick Bilchak Stroughair, "A Genetic Algorithm Approach to the 2048 Puzzle"
- Ryan Long, “Sliding Tile Puzzles”
- Josh Ide, “An Extension of the Google PageRank Algorithm to College Football Rankings”

- Ben Galluzzo
*Mathematical modeling*- Leah Fleming, "Chambersburg Borough’s Municipal Electric Utilities: A Look at Alternative Energy Sources." Presented in the Honors Symposium at the annual SU Minds@Work conference.
- Crystal Evans, Conner Chapman, and Rebecca Feaser, "Chambersburg Area Senior High School Basketball Analytics: Data Mining and Application of Team Performance." Presented at the annual SU Minds@Work conference.
- Jesse Helman, Levi Nicklas, and Julienne Nicklas, "Population Dynamics of Oysters: An Exploratory Approach." Presented at the annual SU Minds@Work conference.

- Debbie Gochenaur
*Mathematics education*- Sara Gherardi, "Error Patterns in Solving Unit Circle Problems Video Analysis."
- Ethan Clever, "Active Learning in the Middle School." With funding from an SU Undergraduate Research grant.
- Brendan Weiser, "Math Monologues: Middle school math videos for parents." With funding from an SU Undergraduate Research grant.
- Andrew Geesaman, "Bridging the Gap: High Impact Techniques for Students with Asperger's." Andy presented his research at the National Council of Teachers of Mathematics Conferences in Denver & in New Orleans.
- Brenna DeShong, "Becoming Teacher-Leaders: Supporting and Empowering Students with Learning Disabilities." Brenna presented her research at the National Council of Supervisors of Mathematics Conference in New Orleans.
- Linzy Hull, "Around the world: How eight countries have progressed in serving students with disabilities." Linzy presented her research at the West Virginia Council of Teachers of Mathematics Annual Conference.

- Lenny Jones
*Number theory, algebra*- Dan White, “Appending Digits to Generate an Infinite Sequence of Composite Numbers.” Paper appears in The Journal of Integer Sequences.
- Maria Elena Markovich, "Generating Composites by Appending Digits to Certain Types of Integer." Maria presented her research at the Joint Mathematics Meetings 2013 in San Diego, CA in the AMS special session on
*Coverings of the Integers.* - Alicia Lamarche, "Representing Integers as the Sum of Two Squares in the Ring Zn"
- Kellie Bresz, Alicia Lamarche, and Maria Markovich, "Extending a Theorem of Sierpinski to Powers of 2 Plus a Fibonacci Number"

- Dave Kennedy
*Mathematics education*- Lynne Dettra and Jeremy Eastman, "Totally Mental: Mental Math Techniques in Elementary Students" Students presented work at the PA Council of Teachers of Mathematics & WV Council of Teachers of Mathematics annual conferences

- Luis Melara
*Applied mathematics*- Blake Burkett, “A Mathematical Approach to the Cavendish Banana”

- Marc Renault
*Number theory, combinatorics, the Fibonacci sequence*- Rebekkah Stanko, "The Generalized Game of 21"
- Josh Ide, “Power Fibonacci Sequences.” Joint paper produced, and published in the Fibonacci Quarterly.
- Josh Updike and Patrick Flanagan, "Symmetries of Fibonacci Points, Modulo M". This resulted in a paper that appears in the Fibonacci Quarterly.
- Alex Dishong, "Calculating the Moduli that Produce a Given Period of the Fibonacci Sequence"

#### Research funding

**Undergraduate Research Grants -**At the beginning of the fall semester, a call goes out for students to apply for research funding. Each student (or student group) that applies must have a faculty sponsor, and grant funding can cover expenses like travel to conferences and poster printing. Applications are due at the beginning of October.**SFRE Grants -**Faculty in the College of Arts and science can apply for these grants at the end of each semester. Funds from these grants can be used to support student research, so make sure your faculty mentor is aware of these grants.**SURE Grants (Summer Undergraduate Research Experience) -**Near the start of the spring semester, a call goes out for faculty/student research pairs to apply for SURE grants. These grants will pay students $750 over the summer to conduct research with a faculty member. Free, on-campus housing is available to students in the SURE program. The deadline is in mid-March.**The Math Department Research Fund -**The math department maintains a small amount of money to help with expenses like regional conference registration and poster printing, if not already covered by an undergraduate research grant. Talk to your research mentor or the math department chair to request these funds.**The Dean's Office -**If you have a large expense (like airfare to a national conference) that is not covered by an undergraduate research grant, the Office of the Dean*might*be able to help. Talk to your research mentor about applying for funding from the Dean.

#### Conferences where undergraduates can present

**Minds@Work Conference -**Here at Ship, this takes place near the end of April each year. Registration opens near the beginning of the spring semester.**EPaDel -**This is the local regional meeting of the MAA. There is a fall meeting and a spring meeting.**PCTM -**The PA Council of Teachers of Mathematics. Yearly conference in the fall semester.**NCTM -**The National Council of Teachers of Mathematics. Yearly conference in April.**MathFest -**The annual national meeting of the MAA. This takes place at the beginning of August each year.**The Joint Mathematics Meetings -**The largest annual mathematics conference in the world! Each year we have several faculty attend this meeting. Occurs in January, before classes resume.**The SIAM Annual Meeting -**The Society for Industrial and Applied Mathematics. Yearly national meeting in July. There is also an annual student conference for the mid-Atlantic region.**NIMBioS -**An annual undergraduate research conference at the interface of biology and mathematics. Runs each fall.

#### Creating a poster

#### Journals that publish undergraduate research

**Involve - A Journal of Mathematics**: Involve publishes original, scholarly papers written by students at any level.**The Pentagon**: This is the journal of Kappa Mu Epsilon that publishes "outstanding" papers by undergraduate students.**Pi Mu Epsilon Journal**: Papers available here are written by or for undergraduates.**SIAM**: This is a online journal that publishes undergraduate research in all areas of applied and computational mathematics.