Introduction to groups, rings, fields, vector spaces, and related concepts. Emphasis on development of careful mathematical reasoning. Prerequisites: MATH 235 or 236; MATH 300 or consent of instructor.

An introductory course in complex algebraic geometry. The basic techniques of Kahler geometry, Hodge theory, line and vector bundles which are needed for the study of the geometry and topology of complex projective algebraic varieties will be introduced and illustrated in basic examples.

This is an introductory course on symplectic topology along with its connections to differential, algebraic, complex and contact geometry and topology.

An introduction to the basic tools of algebraic topology, which studies topological spaces and continuous maps by producing associated algebraic structures (groups, vector spaces, rings, and homomorphism between them). Emphasis will be placed on being able to compute these invariants, not just on their definitions and associated theorems.

Satisfies Junior Year Writing requirement. Develops research and writing skills in mathematics through peer review and revision. Students write on mathematical subject areas, prominent mathematicians, and famous mathematical problems. Prerequisites: MATH 300 and completion of College Writing (CW) requirement.

Not available at this time.

Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications.

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis. Prerequisites: MATH 233 and 235, or consent of instructor, and knowledge of a scientific programming language.

This course is an introduction to differential geometry, where we apply theory and computational techniques from linear algebra, multivariable calculus and differential equations to study the geometry of curves, surfaces and (as time permits) higher dimensional objects.

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis. Prerequisites: MATH 233 and 235, or consent of instructor, and knowledge of a scientific programming language.