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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.
Theory of linear operators on Hilbert space; spectral theory of bounded and unbounded operators; applications
An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. (2nd of two courses in sequence)
Applications of probabilistic techniques in discrete mathematics, including classical ideas using expectation and variance as well as modern tools, such as martingale and correlation inequalities.
Selection of topics vary with each offering.
Description, institutional features, and mathematical modeling of fixed income securities. Use of both deterministic and stochastic models. Crosslisted with ISYE 6769.
Fundamentals of statistical inference are presented and developed for models used in the modern analysis of financial data. Techniques are motivated by examples and developed in the context of applications. Crosslisted with ISYE 6783.
The fundamental group, covering spaces, core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality.