# Research Related Courses

**Directed Study:**

You can take a course in which you engage in individual research under the supervision of a faculty member by registering for one of the three courses, MATH 4991, 4992, or 4993. This requires the agreement of a faculty member and strong preparation, often a 3.4 or above average in major courses and prerequisite courses for your topic. Feel free to contact a potential advisor, or an undergrad math research contact person if you are interested in this.

**Capstone:**

A Department of Mathematics Capstone can take the form of Research (pure Math 4020, or applied, Math 4020 or Math 4025), Modeling (Math 5131), or be a combination of the two (Math 4020 or 4025 or 5131). All capstones have a reflection component. In a pure math or applied research capstone the student will use or develop a theory to solve or contribute to the understanding of a mathematical problem. Math 5131 uses actual case studies which exclusively apply ordinary and differential equations. The case studies are a starting point for students’ own projects, which is the main focus of the course. The projects in Math 5131 may involve further research, or they may involve coming up with a good idea motivated by the case studies, and then doing the work to explore and explain them. In the Math 4020 or Math 4025 Capstones a student develops an original theory or application, new to the student.

**Junior/Senior Honors Project and graduation with Honors in Mathematics:**

Successful completion of a junior/senior honors project means that the mathematics major will graduate with Honors in Mathematics; no prior participation in the honors program is required. Students must complete at least 8 hours of supervised research resulting in a written thesis. The 8 hours may occur through a superior research project in Math 4020 or Math 4025 or Math 5131 followed by Math 4970 (Junior/Senior Honors Project 1). Another possibility for 8 hours of supervised research is Math 4970 followed by Math 4971 (Junior/Senior Honors Project 2). Directed study (Math 4991, 4992, or 4993) may also be used as the first 4 hours of supervised research. Supervision is by a Math Department faculty project advisor and the Undergraduate Research Committee of the Mathematics Department.

For general information about this program, see College Honors. The student must make a written proposal for a Junior-Senior honors thesis that is accepted by the Department of Mathematics Undergraduate Research Committee preferably before beginning the two course sequence, but at least before enrolling in the second course and before indicating intent to apply for College Honors in Mathematics online. For possible research topics, see Research Topics and Problems .