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This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.
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.
The fundamentals of graph theory: trees, connectivity, Euler torus, Hamilton cycles, matchings, colorings and Ramsey theory.
The topics covered parallel those of MATH 3215, with a more rigorous and intensive treatment. Credit is not allowed for both MATH 3215 and 3225.
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.
Fourier analysis in Euclidean space. Basic topics including L^1 and L^2 theory; advanced topics such as distribution theory, uncertainty, Littlewood-Paley theory
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)
Fundamental methods of enumeration and asymptotic analysis, including the use of inclusion/exclusion, generating functions, and recurrence relations. Applications to strings over a finite alphabet and graphs.
Georgia Institute of TechnologyNorth Avenue, Atlanta, GA 30332Phone: 404-894-2000