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MATH 6550: Introduction to Stochastic Processes
3.00 Credits
University of Colorado Boulder
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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MATH 6550 - Introduction to Stochastic Processes
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MATH 6730: Set Theory
3.00 Credits
University of Colorado Boulder
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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MATH 6730 - Set Theory
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MATH 6740: Set Theory
3.00 Credits
University of Colorado Boulder
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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MATH 6740 - Set Theory
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MATH 6900: Independent Study
1.00 - 3.00 Credits
University of Colorado Boulder
Undergraduates must have approval of the instructor. May be repeated up to 6 total credit hours.
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MATH 6900 - Independent Study
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MATH 6940: Master's Degree Candidate
1.00 - 6.00 Credits
University of Colorado Boulder
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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MATH 6940 - Master's Degree Candidate
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MATH 6950: Master's Thesis
1.00 - 6.00 Credits
University of Colorado Boulder
Master's Thesis
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MATH 6950 - Master's Thesis
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MATH 8104: Modular Forms
3.00 Credits
University of Colorado Boulder
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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MATH 8104 - Modular Forms
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MATH 8114: Topics in Number Theory
3.00 Credits
University of Colorado Boulder
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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MATH 8114 - Topics in Number Theory
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MATH 8174: Topics in Algebra I
3.00 Credits
University of Colorado Boulder
Prereqs., MATH 6130 and 6140.
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MATH 8174 - Topics in Algebra I
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MATH 8250: Mathematical Theory of Relativity
3.00 Credits
University of Colorado Boulder
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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MATH 8250 - Mathematical Theory of Relativity
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