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# 101 - 110 of 161 results for: MATH

## 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; Riemann-Roch 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 p-groups, regular and powerful groups, Sylow theorems, the Frattini argument, nilpotent groups, solvable groups, theorems of P. Hall, group cohomology, and the Schur-Zassenhaus 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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