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.
Terms: not given this year

Units: 1

Grading: Satisfactory/No Credit
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.
Terms: not given this year

Units: 3

Grading: Letter (ABCD/NP)
MATH 100: Mathematics for Elementary School Teachers
Mathematics and pedagogical strategies. Core mathematical content in grades K6, classroom presentation, how to handle student errors, and mathematical issues that come up during instruction.
Terms: not given this year

Units: 4

Grading: Letter or Credit/No Credit
MATH 108: Introduction to Combinatorics and Its Applications
Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics. Prerequisites: 51 or equivalent.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Hicks, A. (PI)
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.
Terms: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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.
Terms: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
MATH 138: Celestial Mechanics
Mathematically rigorous introduction to the classical Nbody 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; HamiltonJacobi theory; the role of equilibrium points and stability; and symplectic methods. Prerequisites: 53, and 115 or 171.
Terms: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
MATH 143: Differential Geometry
Geometry of curves and surfaces in threespace and higher dimensional manifolds. Parallel transport, curvature, and geodesics. Surfaces with constant curvature. Minimal surfaces.
Terms: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
MATH 144: Riemannian Geometry
Smooth manifolds, tensor fields, geometry of Riemannian and Lorentz metrics, the LeviCivita connection and curvature tensor, Ricci curvature, scalar curvature, and Einstein manifolds, spaces of constant curvature. Prerequisites:
Math 51, 52, and 53.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Schoen, R. (PI)
MATH 145: Algebraic Geometry
Hilbert's nullstellensatz, complex affine and projective curves, Bezout's theorem, the degree/genus formula, blowup, RiemannRoch theorem. Prerequisites: 120, and 121 or knowledge of fraction fields. Recommended: familiarity with surfaces equivalent to 143, 146, 147, or 148.
Terms: not given this year

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
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