## MATH 78SI: Speedcubing: HIstory, Theory, and Practice

History of the Rubik's cube; the current cubing community; basic mathematical theory; concepts to improve speed solving skill. Prior ability to solve cube not required.

## MATH 88Q: The Mathematics of the Rubik's Cube

Preference to sophomores. Group theory through topics that can be illustrated with the Rubik's cube: subgroups, homomorphisms and quotient groups, the symmetric and alternating groups, conjugation, commutators, and Sylow subgroups.

## MATH 100: Mathematics for Elementary School Teachers

Mathematics and pedagogical strategies. Core mathematical content in grades K-6, classroom presentation, how to handle student errors, and mathematical issues that come up during instruction.

## MATH 132: Partial Differential Equations II

Laplace's equation and properties of harmonic functions. Green's functions. Distributions and Fourier transforms. Eigenvalue problems and generalized Fourier series. Numerical solutions. Prerequisite: 131P.

| UG Reqs: GER:DB-Math

## MATH 137: Mathematical Methods of Classical Mechanics

Newtonian mechanics. Lagrangian formalism. E. Noether's theorem. Oscillations. Rigid bodies. Introduction to symplectic geometry. Hamiltonian formalism. Legendre transform. Variational principles. Geometric optics. Introduction to the theory of integrable systems. Prerequisites: 51, 52, 53, or 51H, 52H, 53H.

| UG Reqs: GER:DB-Math

## MATH 138: Celestial Mechanics

Mathematically rigorous introduction to the classical N-body problem: the motion of N particles evolving according to Newton's law. Topics include: the Kepler problem and its symmetries; other central force problems; conservation theorems; variational methods; Hamilton-Jacobi theory; the role of equilibrium points and stability; and symplectic methods. Prerequisites: 53, and 115 or 171.

| UG Reqs: GER:DB-Math

## MATH 143: Differential Geometry

Geometry of curves and surfaces in three-space and higher dimensional manifolds. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces.

| UG Reqs: GER:DB-Math

## MATH 144: Riemannian Geometry

Smooth manifolds, tensor fields, geometry of Riemannian and Lorentz metrics, the Levi-Civita connection and curvature tensor, Ricci curvature, scalar curvature, and Einstein manifolds, spaces of constant curvature. Prerequisites:
Math 51, 52, and 53.

Instructors:
Schoen, R. (PI)

## MATH 145: Algebraic Geometry

Hilbert's nullstellensatz, complex affine and projective curves, Bezout's theorem, the degree/genus formula, blow-up, Riemann-Roch theorem. Prerequisites: 120, and 121 or knowledge of fraction fields. Recommended: familiarity with surfaces equivalent to 143, 146, 147, or 148.

| UG Reqs: GER:DB-Math

## MATH 146: Analysis on Manifolds

Differentiable manifolds, tangent space, submanifolds, implicit function theorem, differential forms, vector and tensor fields. Frobenius' theorem, DeRham theory. Prerequisite: 52 or 52H.

| UG Reqs: GER:DB-Math

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