printer friendly pageMATH 395: Classics in Geometry and Topology
Original papers in geometry and in algebraic and geometric topology. May be repeated for credit.
Terms: Win
| Units: 3
| Repeatable
for credit
Instructors:
Kerckhoff, S. (PI)
MATH 802: TGR Dissertation
Terms: Aut, Win, Spr, Sum
| Units: 0
| Repeatable
for credit
Instructors:
Bump, D. (PI)
;
Carlsson, G. (PI)
;
Cohen, R. (PI)
;
Diaconis, P. (PI)
;
Eliashberg, Y. (PI)
;
Ionel, E. (PI)
;
Kerckhoff, S. (PI)
;
Levy, D. (PI)
;
Li, J. (PI)
;
Liu, T. (PI)
;
Mazzeo, R. (PI)
;
Papanicolaou, G. (PI)
;
Schoen, R. (PI)
;
Simon, L. (PI)
;
Soundararajan, K. (PI)
;
Vakil, R. (PI)
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.
Instructors:
Kahle, M. (PI)
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 111: Computational Commutative Algebra
Introduction to the theory of commutative rings, ideals, and modules. Systems of polynomial equations in several variables from the algorithmic viewpoint. Groebner bases, Buchberger's algorithm, elimination theory. Applications to algebraic geometry and to geometric problems.
| UG Reqs: GER:DB-Math
MATH 118: Mathematics of Computation
Notions of analysis and algorithms central to modern scientific computing: continuous and discrete Fourier expansions, the fast Fourier transform, orthogonal polynomials, interpolation, quadrature, numerical differentiation, analysis and discretization of initial-value and boundary-value ODE, finite and spectral elements. Prerequisites:
MATH 51 and 53.
| 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 148: Algebraic Topology
Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots. Prerequisite: 109 or 120.
| UG Reqs: GER:DB-Math
MATH 154: Algebraic Number Theory
Properties of number fields and Dedekind domains, quadratic and cyclotomic fields, applications to some classical Diophantine equations; introduction to elliptic curves. Prerequisites: 120, 121.
| UG Reqs: GER:DB-Math
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