printer friendly pageMATH 231C: Free Probability
Background from operator theory, addition and multiplication theorems for operators, spectral properties of infinite-dimensional operators, the free additive and multiplicative convolutions of probability measures and their classical counterparts, asymptotic freeness of large random matrices, and free entropy and free dimension. Prerequisite:
STATS 310B or equivalent.
MATH 233: Probabilistic Methods in Analysis
Proofs and constructions in analysis obtained from basic results in Probability Theory and a 'probabilistic way of thinking.' Topics: Rademacher functions, Gaussian processes, entropy.
| Repeatable
2 times
(up to 6 units total)
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.
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.
MATH 243: Functions of Several Complex Variables
| Repeatable
for 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.
| Repeatable
for credit
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.
| Repeatable
3 times
(up to 9 units total)
MATH 245C: Topics in Algebraic Geometry: Alterations
| Repeatable
for 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.
| Repeatable
for 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.
| Repeatable
for credit
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