## Graduate courses

### Standard graduate courses in geometry/topology

#### Pure Mathematics (PMATH) 665 Differential geometry

Some global aspects of surface theory, the Euler-Poincar characteristic, the global interpretation of Gaussian curvature via the Gauss-Bonnet formula. Submanifolds of n-space, induced Riemannian metrics, extrinsic and intrinsic curvatures, Gauss-Codazzi equations. Local Lie groups of transformations on n-space, infinitesimal generators, the Lie derivative. An introduction to differentiable manifolds, the tangent and cotangent bundels, affine connections and the Riemann curavture tensor. The above topics will be illustrated by applications to continuum mechanics and mathematical physics. Students without the required prerequisite may seek consent of the department.

Prerequisites: PMATH 365 or Applied mathematics (AM) 333 or consent of department

#### PMATH 667 Topology

Topics from algebraic, combinatorial and geometric topology. Students without the required prerequisite may seek consent of the department.

Prerequisite: PMATH 351 or consent of Department

#### PMATH 763 Lie groups and Lie algebras

An introduction to matrix Lie groups and their associated Lie algebra's: geometry of matrix Lie groups; relations between a matrix Lie group and its Lie algebra; representation theory of matrix Lie groups. Instructor Consent Required.

Prerequisite: PMATH 346, 351 and 365

#### PMATH 764 Algebraic curves

An introduction to the geometry of algebraic curves with applications to elliptic curves and computational algebraic geometry. Plane curves, affine varieties, the group law on the cubic, and applications. Instructor Consent Required

## Specialized topics courses

We typically offer one or two specialized topics courses in the Fall and Winter terms.

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