DRP

Project List

This is a list of topics proposed by current graduate students interested in mentoring this semester.

(Geometric Group Theory)
(Geometry: Euclid and Beyond by Hartshore ) Working through the text learn how geometry can be built up from the most basic of assumptions, various models of geometry beyond the typical plane and along the way see how alternative axioms can give rise to very distinct and nice geometries of their own, such as projective geometry

(Infinite Dimensional Linear Algebra)
(Geometric Group Theory)
(Homological Algebra (a more algebraic approach)) Roughly speaking, homology is a way of associating a sequence of abelian groups (or modules) called a complex to another object, for example a topological space. The homology of a topological space encodes topological information about the space in algebraic language. In this project, we will study complexes and their homology from a more abstract perspective. The interested students are required to have seen group theory. Also, a basic understanding on rings and modules would be appreciated but not required.

(Fuzzy logic and triangular norms) Fuzzy logic gives a mathematically rigorous way to talk about vagueness and concepts that are "fuzzy" by allowing logical statements to have more truth values than just "true" and "false". Triangular norms are algebraic, analytic objects that provide the basis for many fuzzy logics. Depending on the student's interest, we can focus more on the philosophical, logical, algebraic, or analytic areas of this field.
(Gödel's Theorems and Zermelo's Axioms) The text covers the foundations of mathematics, starting with formal logic, building up the machinery to talk rigorously about proofs and what theorems can be proven. Various results in formal logic, model theory and in arithmetic are proven in order to build towards Gödel's Completeness and Incompleteness theorems, along the way we also see non-standard models of arithmetic and other oddities.