Spring Seminars
DRP is organizing Spring Seminars to take place during Spring quarter 2025. Fourteen graduate students in our math department have created 11 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 8-12 students per seminar.
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 now open through Monday, March 31st (the start of Spring quarter). 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.
- "Comical" Linear Algebra and Google's Search Engine
led by Jeshu Dastidar Syllabus
Potential meeting times: (90 minutes) Mon/Wed/Fridays: 11am-5pm, Tuesdays: 1pm-3:30pm, Thursdays: 1pm-5pm
This seminar will be a gentle introduction to linear algebra, a branch of math that
studies linear equations and their properties; (part of) what makes this gentle is we will
be reading a book that is a manga, hence the "comical" in the title. Linear algebra is
essential in many areas of STEM fields and has many practical applications (even leading
to PhD theses, see the quote above). We will strive toward one such application and get
a glimpse into Google's search engine and how they rank the web pages! Prerequisites: curiosity! It will help to know about functions,
graphing, and some precalculus.
- Math in Nature and Art
led by Lisa Johnston, Timothy Paczynski Syllabus
Potential meeting times: Monday 3-4 or Monday 5-6
Math is deeply woven into both nature and art, often appearing in places we might not even
expect. Many people think that you have to be an expert in math to appreciate its beauty and complexity,
but that's not the case! In this seminar, we will explore the mathematical patterns and relationships that
shape the world around us. The major topics we will cover include symmetry, the golden ratio, Fibonacci
spirals, fractals, and the numerical patterns that appear in both nature and human creativity. Prerequisites: Must have thought at least one math concept was beautiful.
- Exploring Mathematics through Origami led by Evuilynn Nguyen Syllabus
Potential meeting times: Tuesdays or Thursdays between 11am - 3pm (flexible)
This seminar will explore mathematical concepts using the Japanese art of paper folding,
origami. We will demonstrate how paper folding can be used to visualize and solve geometric and algebraic
problems. Students will learn fundamental origami techniques, explore mathematical concepts, and discover
real world applications of origami in science and engineering. Each week combines theory with hands-on
activities, culminating in a final show and tell where students show off an origami model that interested
them mathematically. No prerequisites.
- Surreal Numbers led by David Tu Syllabus
Potential meeting times: 1 weekly 80 minute meeting either Tuesday or Thursday 12:10-1:30pm or 1:40-3:00pm
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.
- Social Choice Theory led by Alexia Dunker, Annette Belleman, Caleb Farrow Syllabus
Potential meeting times: 1 to 5 PM on Tuesdays, for one hour
Imagine you and your friends are planning a pizza night, and you are trying to find the best night
that works for everyone. Each person has their own complicated preferences: there are days you
love, days you can make it but would prefer other days, and days you simply cannot go. So how
do you choose a date that fairly takes into account everyone's preferences?
The answer, surprisingly, is that you cannot. Social choice theory is the study of these types
of situations and the best (and worst) ways to go about them. In this seminar, we will take a
beginner-friendly deep dive into voting theory, which analyzes what voting systems most accurately
represent the electorate. We will look at many different systems, including approval voting (similar
to a when2meet), ranked choice voting, and Condorcet voting (where you see which choice is
preferred most in head-to-head contests). We will see why each system has its flaws, and look at
various situations where there is no clear way to decide a winner. Most importantly, you will be
able to present on a specific voting theory concept, and become the expert in that topic. Prerequisites: None.
- Quandles: Tying Together Algebra and Knot Theory led by Ally Nagasawa-Hinck Syllabus
Potential meeting times: (90 minute sessions) Wednesdays between 3pm-5pm, Thursdays between 11:30am and 3:30pm
In this weekly seminar, we will explore the fascinating world of classical knots through
the emerging theory of quandles. Quandles provide us mathematicians with powerful algebraic tools to
study and classify knots using algebraic invariants.
During the first half of the quarter, we will build a strong foundation by familiarizing ourselves with
key concepts in classical knot theory and essential algebraic structures. With this shared
understanding, we will then dive into the study of quandles—exploring their properties, applications,
and computational aspects. Through hands-on examples and discussions, we will not only analyze
quandles but also experiment and play with them, gaining deeper insights into their role in knot
theory. Prerequisites: None.
- Symmetry led by Evan Ortiz Syllabus
Potential meeting times: Likely Tuesday or Thursday mornings
Symmetry is fundamental throughout the mathematical and physical worlds. In this seminar we will take a very hands on approach to understanding symmetry, and how to think about it mathematically, in particular as certain types of transformations. Most of our examples will come from geometric shapes in the xy-plane. The idea here is to be explorative, and build up our intuition for these transformation objects directly from the geometry in front of us. Prerequisites: None.
- Solving Differential Equations with MATLAB led by Michael Lewis Syllabus
Potential meeting times: (1 hour) Tuesdays or Thursday afternoons (1-4ish)
This seminar will be an introduction to numerical methods used to solve
differential equations. We will focus on implementing numerical methods in MATLAB (or using
built-in commands), and visualizing solutions to initial-value problems. Our goal is to cover the
most commonly used numerical methods and understand the
advantages and disadvantages of each method. Prerequisites: MAT 22B, basic MATLAB knowledge.
- Math Application Overview led by Kelli Gutierrez Syllabus
Potential meeting times: " (1 hour window) Mondays 2-4, Thursdays 1:30-4, Fridays 9:30-11:30
This seminar will be an exploratory introduction to different applications of math, from biology and physics
to image compression and disease modeling. If you have taken your lower division math courses and want to
learn about how different topics you've learned about are used in the real world, this is for you! Each week
we will focus on a different topic, and we will blend each meeting with lecture and group work style format. Prerequisites: Calculus sequence, 22A, 22B, some coding experience preferred but not required
- Numerical Methods -- What they didn't tell you led by Aidan Epperly Syllabus
Potential meeting times:
Numerical methods are the algorithms that we use to solve math problems using computers. If
you want to take a derivative, compute an integral, or solve a system of equations then there is
a numerical method out there for you! Unfortunately, many numerics classes are prevented from
getting to "the good stuff" due to a broad focus.
In this seminar, we will get straight to the heart of the subject by focusing on one and only
one question: how do we approximate functions on the interval [-1, 1]? Through this, a whole world
of practical algorithms for solving real-world problems will become available to us. Prerequisites: one programming language, linear algebra, calculus especially Taylor series, complex numbers.
- The Strongest Shape: Moduli theory through the lens of triangles led by Raymond Chan Syllabus
Potential meeting times: (90 minutes) Thursday 11-5pm
This seminar will focus on how to understand families of mathematical objects, focusing on the case where the objects are triangles. In the first few weeks, students will acquaint themselves with the concept of categories.
The language of categories is a beautiful invention allowing one to adequately package the
technical detail. After that, we will dive into the world of triangles, guided with a bunch of beautifully
drawn pictures in the reading. Prerequisites: MAT 150A and 127A.
