Spring Seminars
DRP is organizing Spring Seminars to take place during Spring quarter 2024. Eleven graduate students and one post doc in our math department have created informal seminars to run weekly during the spring quarter. "Informal" here is indicating that these seminars will not count towards units or have any grade associated to them, and also hints that the group sizes will be small, about 10 students / seminar (except for Lattices and Polytopes, which will accept up to 18).
The goal of these seminars is to create a welcoming space for studying fun and exciting math with a small group under the guidance of a mentor. Participants will also gain experience communicating math and collaborating with their peers. Many of the seminars are well designed for calculus students, and will be nice demonstrations that not all mathematical thinking is computing derivatives and integrals. If you are interested in exploring some new mathematics by working with a small group and collaborating with a mentor, check out the descriptions below and consider applying.
Applications are open Monday, March 11th through close Monday, April 1st (the start of Spring quarter). Enrollment will be announced on Wednesday, April 3rd. 2024 Spring Seminar Application form for Undergraduates
Here are this year's spring seminar offerings. Seminars will typically meet once a week for 60-90 minutes. Exact times will be determined, but each seminar has listed a range of possible times.
- Gaming with system to game the system! led by Jake Quinn Syllabus
Potential meeting times: Mondays between 12-3pm, Wednesdays between 12-3pm, Fridays between 12-3pm or 4-5pm
As a kid, I often played games like Chopsticks or Tic-Tac-Toe. As I played them more, I started to discover ways to force draws. At the time, it was exciting to gradually come up with solutions to the games. In this seminar, we will try to revel in ways to unwind more complicated games. In these logic-based, two-player games, a famous game theoretic result (Zermelo's Theorem) tells us that if the game cannot end in a draw, a player has a winning strategy. We will explore the consequences of this theorem (when it applies) by playing and strategizing in several two-player games over the quarter. No prerequisites.
- Intro to Knot Theory led by Peyton Wood Syllabus
Potential meeting times: Tuesdays between 10am-1pm or Thursdays between 10am-1pm
Learn about the world of mathematical knots. In this seminar series we will learn the basics of knot theory through a weekly seminar that mixes traditional presentations with group discussions and small group time to work through examples. All participants will have the chance to research and present a knot theory related topic of their own later in the quarter. No mathematical background is required, only a willingness to learn. No prerequisites.
- Curiosities of Counting led by Mary Claire Simone Syllabus
Potential meeting times: Tuesdays between 9am-2pm or Thursdays between 9am-2pm
This seminar will be an exploratory introduction to combinatorics, the branch of math that studies fancy counting. We will learn and practice using essential counting techniques and strategies, and then apply them to problems involving discrete graphs (collections of dots and edges) and the symmetries of triangles, squares, cubes, and more. The end of the seminar will include some arts and crafts and appreciation of M.C. Escher's artwork. No prerequisites.
- Young Tableaux led by Stephanie Gaston Syllabus
Potential meeting times: Mondays or Wednesdays in the afternoon
This seminar will explore the combinatorics of tableaux. These combinatorial objects have numerous applications in combinatorics, representation theory, and algebraic geometry including in the study of symmetric functions and their bases and the representation theory of the Sn. To keep the seminar reachable, we will not be spending much time on these applications. We will focus on the objects themselves. No prerequisites.
- Surreal Numbers led by David Tu Syllabus
Potential meeting times: Tuesdays starting at 10:30am or 12:10pm or 1:40pm (meeting length 80 minutes)
Happiness, eternal friendship, and wealth beyond measure can all be yours even if you take this seminar. Surreal numbers are an extension of the real numbers that, among other weird properties, include infinity in a principled way. We will start from quite literally nothing, then use a couple simple rules to build up a number system that includes infinities, infinitesimals, and everything in between. Hopefully we'll also figure out how to do math with these numbers. This is the kind of seminar you should attend if it annoys you that infinity plus one is not a bigger number than infinity. Prerequisites: MAT 108 or similar familiarity with proof writing.
- Lattices and Polytopes led by Brittney Marsters and Anouk Brose Syllabus
Potential meeting times: Mondays after 4:15pm (meeting length 90 minutes) (preferred meeting time 5:15-6:45pm)
This seminar will be an introduction to the theory of lattices and polytopes. You can think of a polytope as what happens when you take points in space and snap a (dimension appropriate) rubber band around them. So polytopes are a generalization of forms like a triangle, cube, prism, pyramid, tetrahedron, etc. They are a geometric way to realize optimization problems from the real world and within mathematics, many other problems can be reformulated into the theory of polytopes. Prerequisites: Mathematical reasoning, vectors, R^n, functions and polynomials (MAT 108, MAT 22A).
- Categories for Beginning Mathematicians led by Raymond Chan Syllabus
Potential meeting times: Tuesdays before 2pm, Wednesdays between 12-3pm, Thursdays before 5pm
Category theory has been a fundamental language throughout modern mathematics, and this seminar aims to provide early exposure to relatively young mathematicians. In an arbitrary set, the only way to compare two elements is equality. This makes the notion of a set very simple, but it also implies (to some extent) that elements are disconnected/discrete in their own nature. However, in most cases, we will have ways other than equality to compare elements, like sizes of two real numbers. Very informally, a category is a general structure (or environment) where we can compare things in the way that we desire. While the categorical language will not be used extensively (or even at all) during any undergraduate classes, we hope the students can utilize the abstract thinking skill they develop during the seminar for their future mathematical endeavor. Prerequisites: Familiarity with sets and functions will be assumed (at the level of MAT 108). Familiarity with other mathematical objects (topological spaces, groups, rings, etc.) is useful but not strictly required.
- Representation Theory of Finite Groups led by Evuilynn Nguyen and Lisa Johnston Syllabus
Potential meeting times: Tuesdays or Thursdays in the morning
This seminar will be an introduction to representation theory. If you like group theory and linear algebra this is the perfect topic for you! Representation theory tells us how to write a group as a
group of matrices and is an essential tool for understanding groups better. We will use knowledge of finite groups and invertible matrices to understand how we can encode the action of a group element on a vector space in a matrix. Prerequisites: MAT 150A or equivalent group theory course, and familiarity with linear algebra.
- Finite Groups: Coprime Extensions and Hall Subgroups led by Ryan Pesak Syllabus
Potential meeting times: Tuesdays between 12-6pm (prefered meeting day), Mondays 2-3pm, Wednesdays 2-3pm or 4-6pm
While groups are covered in detail in the MAT 150 series, there are many theorems and techniques essential to the study of finite groups that students are not shown. In this seminar, we aim to learn such topics. In particular, our main goal will be to cover the Schur-Zassenhaus Theorem, which trivializes many group extension problems, and Hall pi-subgroups, which are a generalization of Sylow p-subgroups, but for multiple primes. This course will also be a presentation course, giving students the chance to develop their mathematical presentation skills in a consequence-free environment. Prerequisites: MAT 150A or equivalent knowledge of group theory. Experience with Sylow's theorems is encouraged but not required.
- Introduction to Simplicial Homology
led by Dr. Daniel Spiegel Syllabus
Potential meeting times: Thursdays between 9am-noon, Fridays between 9am-noon, Fridays between 2pm-5pm
Homology is a pillar of algebraic topology that roughly describes how many "holes" a topological space has and the dimensions of those holes. It provides algebraicinvariants that can help us differentiate between spaces. For example, if m and n are different natural numbers, then the spheres Sm and Sn are topologically distinct. The proof of this is surprisingly nontrivial but can be done using homology. More generally, the term homology refers to a certain method of associating algebraic invariants to various problems and has applications in many areas of mathematics and beyond, including in the classification of topological phases of matter. This seminar will be a gentle introduction to arguably the simplest type of homology: simplicial homology. The focus will be on understanding definitions and examples rather than proving difficult technical theorems. Prerequisites: MAT 150A, and ideally MAT 147.
