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91 - 100 of 126 results for: MATH

MATH 243: Functions of Several Complex Variables

Holomorphic functions in several variables, Hartogs phenomenon, d-bar complex, Cousin problem. Domains of holomorphy. Plurisubharmonic functions and pseudo-convexity. Stein manifolds. Coherent sheaves, Cartan Theorems A&B. Levi problem and its solution. Grauert¿s Oka principle. nPrerequisites: MATH 215A and experience with manifolds.
Last offered: Winter 2011 | Repeatable for credit

MATH 244: Riemann Surfaces

Riemann surfaces and holomorphic maps, algebraic curves, maps to projective spaces. Calculus on Riemann surfaces. Elliptic functions and integrals. Riemann-Hurwitz formula. Riemann-Roch theorem, Abel-Jacobi map. Uniformization theorem. Hyperbolic surfaces. (Suitable for advanced undergraduates.) Prerequisites: MATH 106 or MATH 116, and familiarity with surfaces equivalent to MATH 143, MATH 146, or MATH 147.
Last offered: Autumn 2017 | Repeatable for credit

MATH 245A: Topics in Algebraic Geometry

Topics of contemporary interest in algebraic geometry. May be repeated for credit.
Terms: Aut | Units: 3 | Repeatable 3 times (up to 9 units total)
Instructors: Vakil, R. (PI)

MATH 245B: Topics in Algebraic Geometry

May be repeated for credit.
Terms: Win | Units: 3 | Repeatable 3 times (up to 9 units total)
Instructors: Li, J. (PI)

MATH 245C: Topics in Algebraic Geometry

May be repeated for credit.
Last offered: Spring 2017 | Repeatable for credit

MATH 249A: Topics in number theory

Topics of contemporary interest in number theory. May be repeated for credit.
Terms: Aut | Units: 3 | Repeatable 3 times (up to 9 units total)
Instructors: Taylor, R. (PI)

MATH 249B: Topics in Number Theory

Last offered: Winter 2018 | Repeatable 3 times (up to 9 units total)

MATH 249C: Topics in Number Theory

Last offered: Spring 2017 | Repeatable for credit

MATH 256A: Partial Differential Equations

The theory of linear and nonlinear partial differential equations, beginning with linear theory involving use of Fourier transform and Sobolev spaces. Topics: Schauder and L2 estimates for elliptic and parabolic equations; De Giorgi-Nash-Moser theory for elliptic equations; nonlinear equations such as the minimal surface equation, geometric flow problems, and nonlinear hyperbolic equations.
Terms: Aut | Units: 3
Instructors: Luk, J. (PI)

MATH 256B: Partial Differential Equations

Continuation of 256A.
Terms: Win | Units: 3 | Repeatable for credit
Instructors: Ryzhik, L. (PI)
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