Mentor: James Warta 

Area: Topology 

Prerequisites: Basic set theory, introductory real analysis, knowledge of groups and group actions will help, but is not strictly necessary 

Text: Using the Borsuk-Ulam Theorem 

Mentor: Arun Suresh 

Area: Algebra and Algebraic Geometry

Prerequisites: Exposure to introductory abstract algebra, some (minimal) level of comfort with rings, quotients and homomorphisms. 

Text: Some ring theory from Dummit and Foote (to rehash the pre-reqs), The rising sea, foundations of algebraic geometry (focus on Chapters 1,3) 

Mentor: Paul Simanjuntak

Area: Analysis

Prerequisites:  A (very) basic programming experience (any language) is needed, but we won't use anything really advanced. Knowing something about probability is helpful (e.g. what is expected value, normal distribution, very basic stats).

Text: Vershynin's "High Dimensional Probability", Chapter 1 and 2.

Mentor: Derek Sparrius

Area: Analysis

Prerequisites:  Have completed the full 3 semester calculus sequence. Ideally have completed a course on ordinary differential equations but I am willing/prepared to spend time covering that topic as we need it. Having exposure to proof based mathematics can be helpful but not necessary.

Text: A First Course in the Calculus of Variations by Mark Kot

Mentor: Brent Koogler

Area: Analysis

Prerequisites:  Know how to write proofs. Familiarity with a programming language (any).

Text: N/A (Depends on student's interest.)

Mentor: Srishti Singh

Area: Algebra

Prerequisites:  Really just a GOOD understanding of proof techniques

Text: N/A

Mentor: Stephen Landsittel

Area: Algebra

Prerequisites:  Had at least one abstract math course (a 4000 level math or a set theory for instance) and knows some abstract algebra (some theory of groups and rings).

Text: I propose (at least the first half of) the modules chapter in Hungerford (it is a GTM book, but doesn’t really assume anything and is fairly accessible) with a potential goal of the student presenting a (elementary and concrete module-theoretic) proof of the nine lemma. If the student makes fast progress then the goal can be moved to instead completing a chosen exercise later in chapter 4.

Mentor: Luis Flores

Area: Algebra

Prerequisites:  Good understanding of linear algebra, and abstract algebra. More specifically, we will be working with vector spaces, modules, algebras and their corresponding morphisms.

Text: An Introduction to Quiver Representations by Derksen and Weyman & Quiver Representations by Ralf Schiffler.

Mentor: Mitchell Ray 

Area: Mathematical Finance

Prerequisites:  Math 2300 and some statistics background (Stat 2500 would be sufficient). 

Text: Derivatives Markets by Robert Mcdonald 3rd Edition, focusing on parts 3 and 5.