**MATH 391 Section PW1: Knot Theory REU (Intro to Math Research)****Spring 2024 Pre-Session Course**

Dr. Alexander Zupan will be teaching MATH 391 Section PW1: Knot Theory REU (Intro to Math Research) during the Spring 2024 Pre-Session. **Enroll now as this course is in danger of being cancelled due to low enrollment!** This 2 credit hour course will count has an Advanced Math course for the Math major or minor.**In this course, you will undertake an original, collaborative research project in mathematics**. The main objective is for you to gain an in-depth understanding of and experience doing research in pure or applied mathematics. In a typical mathematics class, the exercises you are asked to complete are pointed and concise, your professor already knows and understands the solutions, and they expect you to solve the problems in a more or less straightforward way. In contrast, when you are doing mathematical research, the problems can be vague and open-ended, and no one has ever found a solution to these problems. This new experience can be intensely frustrating, but it can also be incredibly rewarding.**During the three week of January pre-session, you will attempt to make progress on unanswered questions within the field of knot theory, the study of the mathematical properties of closed loops in 3-dimensional space**. In particular, you will consider problems related to invariants of knots, including their ribbon numbers and fusion numbers. You will learn what these concepts mean and develop a foundational understanding of the field of knot theory. You will also gain understanding of the logistics of mathematical research, and at the end of the course, you will know how to find and read mathematical research papers, you will understand what goes into a good research presentation, and you will write professionally and mathematically using the LaTex package. A possible (but certainly not guaranteed) outcome is that you may coauthor a research paper to be submitted for peer review and publication at the end of this course. **Finally, this course will prepare you to do further research in mathematics, with a goal of being able to funnel your experience into a successful UCARE or external REU application**.*This course satisfies UNL's Experiential Learning requirement and counts toward the minor in mathematics.***Class Time:** 10:00 – 12:00 NOON

Jan 02 – Jan 19, Web Conferencing**Please contact Dr. Zupan at zupan@unl.edu if you have questions!**