# Senior Seminar Information (Class of 2022)

For the 2021-2022 academic year, the senior seminar topics are Chaotic Dynamical Systems or Infinite Series.

To ensure the senior seminar experience is an enriching experience it is necessary to keep class sizes relatively small and even. To help the department place students into seminars, each major who plans to take a senior seminar submits a proposal by NOON on the last day of classes of the winter semester of the junior year. Some details:

- The proposal is a LaTeX document, a template, to be filled out carefully by the student. The proposal should be approximately one page. It should describe which senior seminar you prefer to take, and why. For help with LaTeX, visit the What is LaTeX page.
- As a hypothetical example, here is a sample completed proposal in PDF format as Bernhard Riemann would have submitted it.
- By noon on the due date, the completed proposal is to be uploaded as a single PDF to the Senior Capstone Project Google form.
- The PDF file should have a useful, descriptive name. Riemann would’ve named his “BernhardRiemannSeminarProposal.pdf”, for example.
- It is a good idea for juniors to discuss the choice between thesis and seminar with faculty members before writing a proposal.
- The Department meets to consider all thesis and seminar proposals. The Department Chair will notify students of the results of the meeting by the middle of the short-term.
- The course descriptions for the Winter 2022 senior seminars are below.

**MATH 495D. Chaotic Dynamical Systems.**

One of the major scientific accomplishments of the last twenty-five years was the discovery of chaos and the recognition that sensitive dependence on initial conditions is exhibited by so many natural and man-made processes. To really understand chaos, one needs to learn the mathematics behind it. This seminar considers mathematical models of real-world processes and studies how these models behave as they demonstrate chaos and its surprising order. Prerequisite(s): MATH 301. Instructor permission is required. [W3] S. Ross.

**Math 495M Infinite Series.**

An infinite series is the sum of the terms of an infinite sequence. In calculus we encounter infinite series of real numbers, for example, the geometric series. This course focuses on infinite series of functions, beginning with an introduction to function series and convergence. Students explore power series, Laurent series, and trigonometric series, culminating with an in-depth examination of Fourier series. Fourier series have numerous applications to areas such as partial differential equations, signal and image processing, acoustics and econometrics, to name only a few. Based on student interests, they investigate one or more of the aforementioned applications of Fourier series using current research papers and texts in mathematics and computer software. Prerequisite(s): MATH 301. Instructor permission is required. [W3] K. Ott.