Special Topics in Mathematics

MATH 290

01: History of Mathematics

Spring 2022

Instructor:  Lillian Pierce

Have you ever wondered where the numerical shapes 0, 1, 2, 3... come from? Who came up with using the symbol pi? Would we think about math differently if we used different symbols? How did people ever start thinking about solving equations? Why are people so interested in triangles, circles, and squares? Why are there infinitely many prime numbers? What does it mean for an infinite set to be countable or uncountable? Why do people sometimes say math is beautiful?

What do we learn by looking at the mathematics of the past? What mathematical concepts or notation could we invent now to make the mathematics of the future easier? What do we learn when we look at who has engaged in mathematics in the past? Who can engage in mathematics now? Everyone! You, in particular! Come join us for Math 290, Special Topics in the History of Mathematics.

Math 290 will include a mix of lecture/discussions, guest lectures from scholars around the country, student presentations, problem sets, and informational essays written by students. The textbooks will include “Journey through Genius” by William Dunham, which has a European perspective, and “The Crest of the Peacock” by George Gheverghese Joseph, which has a worldwide perspective. Additional readings will be distributed throughout the semester, and chosen by students as they develop independent projects. 

02: Fourier Series and Beyond

Spring 2022
Fourier analysis

Instructor:  Jim Nolen

This special-topics course will introduce students to important and fascinating topics in mathematical analysis that have played a fundamental role in many applications.  This semester, the course will focus on Fourier analysis and its application to partial differential equations (PDEs) and to imaging.  The course will be divided into three modules: (1) Fourier series and analysis (2) PDEs for diffusion and reaction (3) application to Computed Tomography (CT).  Prior experience with analysis or differential equations or imaging is not required.  The course is designed to build student literacy in mathematics and to expose students to salient ideas before they have taken more advanced analysis courses.  Specific topics to be covered in the three modules include: Fourier series and transforms, function spaces, orthogonality, Plancherel theorem; heat equation, linear reaction-diffusion systems, Turing instability and pattern formation; X-ray and Radon transform, Fourier Slice Theorem for Radon transform, filtered back projection for computed tomography (CT).

Topics vary by semester. Instructor: Staff
Old Map with words "Mathematica Quia Omi" written across
Typically Offered
Occasionally