Project List
This is a list of topics proposed by current graduate students interested in mentoring this semester.
Topology
- (Problems in knot theory (and/or) Topics in topology)
Analysis
- (Dynamical Systems - Introduction to chaotic systems)
Algebra
- (Finite Group Theory (and/or) Basic Character Theory)
- (Differential Graded (DG) algebras/modules/categories) For a student more interested in category theory, we can have more of an emphasis on dg categories after introducing dg modules/algebras first as a kind of motivation. For those with (slightly) less of a tolerance for abstract nonsense, we can have more of an emphasis on studying dg algebras/modules in a direction that sounds most compelling to the student, perhaps ending with introducing the notion of a dg category.
- (Category Theory) The topics covered includes the very basics to various examples, adjoints, limits and colimits, and then various other topics largely directed by student interest as time permits.
Math Education
- (Undergraduate math education—proofs (or) What kinds of studies exist in mathematics education?) Have you ever wondered if there are ways to better teach (or learn) proofs-based mathematics? Or if there are ways that are particularly bad? We can read about it! (or) We will look at different types of study design and try to figure out how, depending on what question(s) you are asking, a certain study design might be better or worse for your purposes.
Logic
- (Multi-valued and fuzzy logics) Multi-valued logic is a mathematically rigorous way to talk about logical statements that are neither true nor false (perhaps their truth value is unknown). Fuzzy logic extends multi-valued logic, allowing us to reason about vauge and "fuzzy" concepts by using an infinite number of truth values.
