## Where to begin?

There are numerous research and internship options available in addition to other avenues for gaining experience inside and outside the classroom. Among the more popular programs is the network of Research Experience for Undergraduates (REUs) sites hosted by universities across the U.S. Typically each site supports 4 – 8 students who visit it during summer and work there with a mentor on a research project. An REU lasts about 8 weeks. Travel, room and board are covered and you get paid $2000 – $6000. Most deadlines are in **February**.

#### Department Research Opportunities

Interested in doing research with a local Math faculty member? **You should start by reviewing the research areas of the Math Department and faculty involved in those areas, and you can find that information here. **You do not have to wait until a faculty member has a position available, and you are encouraged to discuss Math research with any faculty member. Many research projects will require the completion of MATH 309, MATH 310, or MATH 325 with an excellent grade.

Below, you will find some current projects that faculty members have proposed. If you are interested in one of these, you are encouraged to first contact Alex Zupan, the math department's undergraduate chair, to set up a meeting to discuss possible projects.

Name |
Project Type |
Time Period |
Project Title |
Project Description |
Preferred Prerequisites |

Kristen Amman | UCARE | Summer 24, AY 24-25 | Understanding student experiences retaking calculus: Linking cognitive and behavioral outcomes | This project aims to understand student experiences retaking Calculus by characterizing how the experience of relearning Calculus differs from the experience of learning Calculus for the first time. The goal of such a characterization is to explain differences in course outcomes for students who have taken a calculus course in high school, students who have taken a college calculus course before but need to take calculus again, and students who have never seen calculus before. Undergraduate researchers will have the opportunity to learn a variety of educational research techniques. | MATH 106 or MATH 103 with prior teaching experience |

Román Aranda | FYRE | AY 24-25 | Computing the genus of a matrix | The goal of this project is to build examples of multicurves in a surface with prescribed intersection numbers. The student would spend the first part of the semester learning about the topology of surfaces and combinatorics of filling curves. During this project, the student can explore low-dimensional topology and introduce themselves to the world of mapping class groups. | MATH 106 |

Morgen Bills | Volunteer | Summer 24 | Brauer Algebra module study | Some problems in the non-semisimple cases for Brauer Algebra modules remain unresolved. This project would look for any additions to the existing theory. | MATH 310, MATH 314 |

Huijing Du | UCARE, FYRE, Grant funded, Volunteer | Summer 24, AY 24-25 | Data-driven mathematical modeling of pancreatic cancer growth and treatments | Pancreatic cancer is one of the most deadly types of cancer and has extremely poor prognosis. In this project we aim to develop a mathematical model of pancreatic cancer, and use it to qualitatively explain a variety of biomedical and clinical data. | MATH 221 |

Yu Jin | UCARE, FYRE, Volunteer | AY 24-25 | Dynamics of the zebra mussel population | Mathematical modeling on dynamics of the zebra mussel population can help develop control strategies on the mussel population in rivers. The student will work on deriving a suitable mathematical model to describe the dynamics of the zebra mussel population with stage structures (e.g. larva, Juvenile and adult stages), fitting the model with zebra mussel data in a particular river, and predicting whether the zebra mussel population will be persistent or extinct there. We will work on linear or nonlinear difference models. Numerical calculations will be involved. |
MATH 314 |

Yu Jin | UCARE, Volunteer | AY 24-25 | Effects of pandemic-influenced population dispersal on disease transmission | During a pandemic or disease outbreak, a population's dispersal may be highly influenced by the current pandemic situation. The susceptible population may be hesitated to move to a new place where there is a large amount of infectious individuals. We would like to develop an ordinary differential equation system to study how such pandemic-influenced population dispersal affects disease transmission among multiple patches. | MATH 221, experience with Matlab |

Tri Lai | UCARE, Volunteer | Summer 2024 | Enumeration of tilings | We enumerate the tilings of certain regions and investigate possible connections to other math topics, e.g., symmetric functions and cluster algebras. | MATH 309, MATH 310, or MATH 325 |

Yvonne Lai | Grant funded | AY 24-25 | What can online chat data about algebra tell us about teaching and learning mathematics? | I'm looking for someone to join a team to analyze online chat data of high school students discussing how they would solve some algebra problems involving the idea of a function, and also potentially analyze interviews of high school algebra teachers. | Interest in teaching, strong writing skills. |

Yvonne Lai | Independent study, Volunteer | AY 24-25 | Math Wars: What is the cost? | In the 1990s and 2000s, there were loud and sometimes vicious debates about what mathematics should be taught in high schools and how it should be taught. These debates were sometimes so rhetorically violent that some call this period the "Math Wars". There are echos of these debates now, and this project will look at interviews of professionals who are "veterans" of the Math Wars and their perception of the cost of the Math Wars. This would be a great project for anyone interested in history, policy, or politics around education. | Strong writing skills. |

Petronela Radu | UCARE, FYRE, Grant funded | Summer 24, AY 24-25 | Nonlocal models | Nonlocal models basically allow us to approximate derivatives with integrals. Sounds crazy, but there is a lot to discover, theoretically, numerically, and from a modeling point of view. | MATH 107, MATH 221 |

Alexandra Seceleanu | UCARE, Grant funded, Volunteer | Summer 24, AY 24-25 | Polynomials | One possible project could be very computationally-intensive, using the super computer to gather specific information about some collection of polynomials. This requires no background. Other projects can be more theoretical; they would involve determining information about some collection of polynomials using abstract reasoning. For the latter Math 310 is a good pre-requisite. | MATH 310 |

Kazuo Yamazaki | UCARE, FYRE | Summer 24 | Deterministic and Stochastic PDEs of Fluid Mechanics, Mathematical Physics, and Mathematical Biology | Opportunities to understand mathematical problems that arise in analysis on PDEs of fluid mechanics (e.g., Navier-Stokes equations), Mathematical Physics (e.g., Phi4 model from quantum field theory), or Mathematical Biology (e.g., infectious diseases) in both deterministic and stochastic case (i.e., forced by random noise). | MATH 208, MATH 221, and MATH 314 |

Alex Zupan | UCARE, FYRE | Summer 24, AY 24-25 | Fusion numbers of ribbon knots | A "knot" is a simple closed curve in 3-dimensional space, considered up to smooth deformations that can bend and stretch, but don't break, the curve. Distinguishing knots is, in general, a very difficult problem, and so we often pass to "knot invariants", tools to help us distinguish different knots. In this project, we will study and catalogue a particular geometric invariant, the "fusion number" of a ribbon knot. | MATH 208, MATH 221, or MATH 314 |

#### Nation-wide Research and Internships Opportunities

**MathPrograms.org**: A very convenient (free!) online application system and a perfect place to start. It features a large and constantly updated database of various math-related opportunities for students. You can create an account, store application materials, manage reference letters, and apply to multiple programs right from this website.**MathJobs.org**: Another very convenient (free!) online application system. After registration and data entry, applicants can apply for jobs, keep track of applications, print out paper coversheets, and invite their reference writers to submit letters into the system.- Database of REUs and REUs in Mathematics from the
**National Science Foundation**. - List of REU programs compiled by the
**American Mathematical Society (AMS)** - List of Internships and Co-ops compiled by the
**AMS** - List of Internships compiled by the
**Society for Industrial and Applied Mathematics (SIAM)** - Semester and Summer programs compiled by the
**Mathematical Association of America (MAA)** - List of Research Opportunities and Other Programs for Women (and everyone) compiled by the
**Women in Math Project** - Pathways to Science: A website of information about REUs, scholarships, and travel and research opportunities for Undergraduate students in STEM.
- American Mathematical Society's Mathematical Opportunities
- Society for Industrial and Applied Mathematics Career Resources
- International Association of Quantitative Finance Job Board
- The Institute for Operations Research and the Management Sciences (INFORMS) Career Center
- National Council of Teachers of Mathematics Career Center
- Society of Actuaries Career Development
- Casualty Actuarial Society Career Center
- American Statistical Association Career Center

#### Federal Research and Internship Programs

**National Aeronautics and Space Administration (NASA)**- Internships
- NASA Nebraska Space Grant
**Department of Energy (DoE)**- Internships
- Sample: Oak Ridge National Laboratory
**Department of Defense (DoD)**- Student internships and summer programs
- USSTRATCOM Programs (part of DoD in Omaha, NE)
**Department of Homeland Security (DHS)**- Internships for current students
**National Security Agency (NSA)Programs**- The NSA offers summer programs very similar to the REU's. Citizenship or permanent residency required. Highly competitive. Application deadlines
**vary by program!** **Central Intelligence Agency (CIA)Programs**- The CIA offers programs that start several times a year and can be for multiple years.
**Other Federal Agencies**(some require US citizenship or residency)- Federal Bureau of Investigation (FBI)
- Los Alamos National Laboratory Student Programs
- Oak Ridge Institute for Science and Education (ORISE) Opportunity Catalog
- National Institute of Standards and Technology
- National Oceanic and Atmospheric Administration (NOAA)
- Sandia National Lab
- United States Census Bureau
- USAJOBS - Government website information about jobs open to students and recent graduates.

#### Academic Programs Outside of UNL

**Summer Undergraduate Applied Mathematics Institute**- Held at the Center for Nonlinear Analysis at Carnegie Mellon University, in addition to a stipend participants receive credit from Carnegie Mellon for this 7-week learning and research experience.
**Quantitative Research in the Life and Social Sciences Program (QRLSSP)**- The Quantitative Research in the Life and Social Sciences Program (QRLSSP) is an intensive summer research experience that prepares undergraduate students for the rigors of graduate level research at the interface of mathematics, statistics, and the natural and social sciences.
**Mathematics Advanced Study Semesters (MASS) at Penn State**- MASS is held during the fall semester of each year at Penn State University.
**Institute for Pure and Applied Mathematics at UCLA**- Offers summer schools, research programs, and more at UCLA.
**Budapest Semesters in Mathematics**and**Budapest Semesters in Mathematics Education**- Education Abroad in Hungry!
**The Peace Corps**- The Peace Corps is often in need of Math teachers, which is an exciting way to get Math teaching experience without a teaching degree or teaching certificate!

#### Opportunities and Resources At UNL

**Undergraduate Creative Activities and Research Experiences (UCARE)**- This UNL program is designed to promote undergraduate research by having students work on a research project with a faculty mentor.
**Honors Thesis**- Many students in the UNL Honors Program do their senior theses under the direction of math faculty.
**Senior Thesis**- Many students also complete a senior thesis under the direction of math faculty. Completion of a senior thesis can qualify you for a degree with Distinction!
**Handshake**- Handshake is the place for students of the University of Nebraska-Lincoln to search and apply for internships, co-ops, part-time and full-time jobs.
**University Career Services' Ways to Gain Experience**- University Career Services has an excellent guide to ways to gain experience.
**College of Arts & Sciences Career Coaches**- Our Career Coaches have both appointments and drop-ins available to help you reach your career goals!

#### Questions?

**Have questions about where to start, what to do, or who to talk to?**- Don't hesitate to contact Professor Alex Zupan, Undergraduate Chair for Mathematics, or Doug Pellatz, Assigned Advisor for Mathematics.