MATH 234: Large Deviations Theory (STATS 374)
Combinatorial estimates and the method of types. Large deviation probabilities for partial sums and for empirical distributions, Cramer's and Sanov's theorems and their Markov extensions. Applications in statistics, information theory, and statistical mechanics. Prerequisite:
MATH 230A or
STATS 310.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MATH 239: Computation and Simulation in Finance
Monte Carlo, finite difference, tree, and transform methods for the numerical solution of partial differential equations in finance. Emphasis is on derivative security pricing. Prerequisite: 238 or equivalent.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MATH 243: Functions of Several Complex Variables
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 244: Riemann Surfaces
Compact Riemann surfaces and algebraic curves; cohomology of sheaves; Serre duality; RiemannRoch theorem and application; Jacobians; Abel's theorem. May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 245A: Topics in Algebraic Geometry: Moduli Theory
Topics in the study of moduli spaces: Basic of algebraic surfaces, Hodge structure of surfaces, moduli of K3 surfaces, cycles and rational curves in K3 surfaces, Torelli for K3 surfaces.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Li, J. (PI)
MATH 245B: Topics in Algebraic Geometry: Intersection Theory
Topics such as intersection theory on surfaces, toric varieties, and homogeneous spaces; numerical criteria for positivity; Chow groups and rings. May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 245C: Topics in Algebraic Geometry: Alterations
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 247: Topics in Group Theory
Topics include the Burnside basis theorem, classification of pgroups, regular and powerful groups, Sylow theorems, the Frattini argument, nilpotent groups, solvable groups, theorems of P. Hall, group cohomology, and the SchurZassenhaus theorem. The classical groups and introduction to the classification of finite simple groups and its applications. May be repeated for credit.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 248: Ergodic Theory and Szemeredi's Theorem
An introduction to ergodic theory leading to (and proving) Szemeredi's theorem and its multidimensional extension. Prerequisite: 205a and some knowledge of Hilbert spaces.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 248A: Algebraic Number Theory
Structure theory and Galois theory of local and global fields, finiteness theorems for class numbers and units, adelic techniques. Prerequisites:
MATH 210A,B.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
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