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Course Criteria
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3.00 Credits
Systematic study of Markov chains and some of the simpler Markov processes, including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Prereqs., MATH 4310, MATH 4510 or APPM 3570, or APPM 4560, or instructor consent. Same as MATH 6550.
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3.00 Credits
Presents cardinal and ordinal arithmetic, and basic combinatorial concepts, including stationary sets, generalization of Ramsey's theorem, and ultrafilters, consisting of the axiom of choice and the generalized continuum hypothesis. Prereqs., MATH 4000 and 4730, or MATH 5000, or instructor consent. Undergraduates need instructor consent.
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3.00 Credits
Presents independence of the axiom of choice and the continuum hypothesis, Souslin's hypothesis, and other applications of the method of forcing. Introduces the theory of large cardinals. Prereq., MATH 6730. Undergraduates need instructor consent.
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1.00 - 3.00 Credits
Undergraduates must have approval of the instructor. May be repeated up to 6 total credit hours.
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1.00 - 6.00 Credits
This course is for students preparing for the no-thesis option for a master's degree. The content is set by the students' advisors.
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1.00 - 6.00 Credits
Master's Thesis
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3.00 Credits
Introduces the upper-half plane and its geometry, modular forms, congruence subgroups, cusps, Fourier expansions, Theta series, Poincare series, Hecke operators, and relations to Dirichlet series. Prereqs., MATH 6130 and 6350.
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3.00 Credits
May include the theory of automorphic forms, elliptic curves, or any of a variety of advanced topics in analytic and algebraic number theory. Prereq., MATH 6110.
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3.00 Credits
Prereqs., MATH 6130 and 6140.
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3.00 Credits
Focuses on Maxwell equations, Lorentz force, Minkowski space-time, Lorentz, Poincare, and conformal groups, metric manifolds, covariant differentiation, Einstein space-time, cosmologies, and unified field theories. Prereq., instructor consent. Undergraduates must have approval of the instructor.
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