sp21

Archived: 

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)

Numerical Methods for Dynamical Systems

Approximation of the dynamical structure of a differential equation and preservation of dynamical structure under discretization.

Numerical Approximation Theory

Theoretical and computational aspects of polynomial, rational, trigonometric, spline and wavelet approximation.

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.

Differential Equations

Methods for obtaining numerical and analytic solutions of elementary differential equations. Applications are also discussed with an emphasis on modeling.

Multivariable Calculus

Linear approximation and Taylor’s theorems, Lagrange multiples and constrained optimization, multiple integration and vector analysis including the theorems of Green, Gauss, and Stokes.

Introduction to Multivariable Calculus

An introduction to multivariable calculus through vectors in 3D, curves, functions of several variables, partial derivatives, min/max problems, multiple integration. Vector Calculus not covered.

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