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Course Criteria
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3.00 Credits
Studies semi-simple Artinian rings, the Jacobson radical, group rings, representations of finite groups, central simple algebras, division rings and the Brauer group. Prereq., MATH 6130, 6140.
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3.00 Credits
Focuses on differential geometric techniques in quantum field and string theories. Topics include spinors, Dirac operators, index theorem, anomalies, geometry of superspace, supersymmetric quantum mechanics and field theory, and nonperturbative aspects in field and string theories. Prereq., MATH 6230, PHYS 5250, or instructor consent. Recommended prereqs., MATH 6240 and PHYS 7280. Same as PHYS 6260.
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3.00 Credits
Studies nilpotent and solvable groups, simple linear groups, multiply transitive groups, extensions and cohomology, representations and character theory, and the transfer and its applications. Prereq., MATH 6130. Recommended prereq., MATH 6140.
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3.00 Credits
Covers homotopy theory, spectral sequences, vector bundles, characteristic classes, K-theory and applications to geometry and physics. Prereq., MATH 6220 or instructor consent.
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3.00 Credits
Presents the basic notions of analysis, e.g., limits, lim sup and lim inf, continuity, and the topology of the real line; develops the number theory of Lebesgue measure and the Lebesgue integral on the line, emphasizing the various notions of convergence and the standard convergence theorems. Applications are made to the classical L^p spaces. Prereq., MATH 4310 and 4320. Instructor consent required for undergraduates.
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3.00 Credits
Covers general metric spaces, the Baire Category Theorem, and general measure theory, including the Radon-Nikodym and Fubini theorems. Presents the general theory of differentiation on the real line and the Fundamental Theorem of Lebesgue Calculus. Prereq., Math 6310. Instructor consent required for undergraduates.
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3.00 Credits
Focuses on complex numbers and the complex plane. Includes Cauchy-Riemann equations, complex integration, Cauchy integral theory, infinite series and products, and residue theory. Prereq., MATH 4310. Undergraduates need instructor consent.
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3.00 Credits
Focuses on conformal mapping, analytic continuation, singularities, and elementary special functions. Prereq., MATH 6350. Instructor consent required for undergraduates.
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3.00 Credits
Focuses on mathematical theory of statistics covering distribution theory, estimation and testing of hypotheses, multivariate analysis, and nonparametric inference, all with emphasis on theory. Prereq., MATH 5520 or APPM 5520. Undergraduates must have approval of the instructor. Same as APPM 6520.
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3.00 Credits
Offers selected topics in probability such as sums of independent random variables, notions of convergence, characteristic functions, Central Limit Theorem, random walk, conditioning and martingales, Markov chains, and Brownian motion. Prereq., MATH 6310 or equivalent.
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