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Topics from complex function theory, including contour integration and conformal mapping
Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n
Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices.
Sampling distributions, Normal, t, chi-square and F distributions. Moment generating function methods, Bayesian estimation and introduction to hypothesis testing
The fundamentals of graph theory: trees, connectivity, Euler torus, Hamilton cycles, matchings, colorings and Ramsey theory.
This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.
Elementary combinatorial techniques used in discrete problem solving: counting methods, solving linear recurrences, graph and network models, related algorithms, and combinatorial designs.
The second of a two course sequence of faculty-directed independent research culminating in the writing of a senior thesis and its presentation.
The first of a two course sequence of faculty-directed independent research culminating in the writing of a senior thesis and its presentation.
An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. (1st of two courses in sequence)