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## Numerical Methods in Finance

This course contains the basic numerical and simulation techniques for the pricing of derivative securities.

## Differential Geometry I

Core topics in differential and Riemannian geometry including Lie groups, curvature, relations with topology.

## Real Analysis I

Lebesgue measure and integration, differentiation, abstract measure theory.

This course is equivalent to MATH 6579. Students should not be able to obtain credit for both MATH 6579 and MATH 6337.

## Complex Analysis

Complex integration, including Goursat's theorem; classification of singularities, the argument principle, the maximum principle; Riemann Mapping theorem; analytic continuation and Riemann surfaces; range of an analytic function, including Picard's theorem.

## Multivariate Statistical Analysis

Multivariate normal distribution theory, correlation and dependence analysis, regression and prediction, dimension-reduction methods, sampling distributions and related inference problems, selected applications in classification theory, multivariate process control, and pattern recognition.

## Statistical Estimation

Basic theories of statistical estimation, including optimal estimation in finite samples and asymptotically optimal estimation. A careful mathematical treatment of the primary techniques of estimation utilized by statisticians.

## Probability II

Develops the probability basis requisite in modern statistical theories and stochastic processes. (2nd of two courses)

## Algebra II

Graduate level linear and abstract algebra including rings, fields, modules, some algebraic number theory and Galois theory. (2nd of two courses)

## Survey of Calculus

Functions, the derivative, applications of the derivative, techniques of differentiation, integration, applications of integration to probability and statistics, multidimensional calculus.

## Finite Mathematics

Linear equations, matrices, linear programming, sets and counting, probability and statistics.