Structural properties of basic algebraic systems such as groups, rings and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization and symmetric polynomials. Time permitting, such topics as group representations or algebras over a field may be included. Prerequisite: MATH 3351 or 4651, or instructor permission.

This course will cover the representation theory of finite groups and other interactions between linear and abstract algebra. Topics include: bilinear and sesquilinear forms and inner product spaces; important classes of linear operators on inner product spaces; the notion of group representations; complete reducibility of complex representations of finite groups; character theory; some applications of representation theory.

Prerequisite: MATH 3351 (or 4651) and MATH 3354 (or 4652) 

Geometric study of curves/surfaces/their higher-dimensional analogues. Topics vary and may include curvature/vector fields and the Euler characteristic/the Frenet theory of curves in 3-space/geodesics/the Gauss-Bonnet theorem/and/or an introduction to Riemannian geometry on manifolds. Prerequisites: MATH 2310 and MATH 3351 or instructor permission.

Introduces abstract topological spaces. Topics include topological spaces & continuous functions/connectedness/compactness/countability/separation axioms. Rigorous proofs emphasized. Covers myriad examples, i.e., function spaces/projective spaces/quotient spaces/Cantor sets/compactifications. May include intro to aspects of algebraic topology, i.e., the fundamental group. Prerequisites: MATH 2310, MATH 3351, and MATH 3310.