printer friendly pageMATH 272: Topics in Partial Differential Equations
Terms: Win
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Units: 3
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Repeatable for credit
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Grading: Letter or Credit/No Credit
Instructors: Liu, T.
MATH 282A: Low Dimensional Topology
The theory of surfaces and 3-manifolds. Curves on surfaces, the classification of diffeomorphisms of surfaces, and Teichmuller space. The mapping class group and the braid group. Knot theory, including knot invariants. Decomposition of 3-manifolds: triangulations, Heegaard splittings, Dehn surgery. Loop theorem, sphere theorem, incompressible surfaces. Geometric structures, particularly hyperbolic structures on surfaces and 3-manifolds.
Terms: Aut
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Units: 3
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Repeatable for credit
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Grading: Ltr-CR/NC
Instructors: Kerckhoff, S.
MATH 282B: Homotopy Theory
Homotopy groups, fibrations, spectral sequences, simplicial methods, Dold-Thom theorem, models for loop spaces, homotopy limits and colimits, stable homotopy theory.
Terms: Win
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Units: 3
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Repeatable for credit
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Grading: Ltr-CR/NC
Instructors: Galatius, S.
MATH 282C: Fiber Bundles and Cobordism
Possible topics: principal bundles, vector bundles, classifying spaces. Connections on bundles, curvature. Topology of gauge groups and gauge equivalence classes of connections. Characteristic classes and K-theory, including Bott periodicity, algebraic K-theory, and indices of elliptic operators. Spectral sequences of Atiyah-Hirzebruch, Serre, and Adams. Cobordism theory, Pontryagin-Thom theorem, calculation of unoriented and complex cobordism. May be repeated for credit.
Terms: Spr
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Units: 3
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Repeatable for credit
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Grading: Ltr-CR/NC
Instructors: Brumfiel, G.
MATH 284A: Geometry and Topology in Dimension 3
The Poincare conjecture and the uniformization of 3-manifolds. May be repeated for credit.
Terms: not given this year
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Units: 3
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Repeatable for credit
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Grading: Letter or Credit/No Credit
MATH 284B: Geometry and Topology in Dimension 3
The Poincare conjecture and the uniformization of 3-manifolds. May be repeated for credit.
Terms: not given this year
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Units: 3
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Repeatable for credit
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Grading: Letter or Credit/No Credit
MATH 286: Topics in Differential Geometry
May be repeated for credit.
Terms: Spr
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Units: 3
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Repeatable for credit
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Grading: Letter or Credit/No Credit
Instructors: Schoen, R.
MATH 290B: Model Theory B (PHIL 350B)
Decidable theories. Model-theoretic background. Arithmetic of addition, real closed and algebraically closed fields, weak second order arithmetic, theories of terms, theories of arrays, temporal logic. Combining decision procedures. May be repeated for credit. Prerequisite: 151,152 or equivalents.
Terms: Win
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Units: 1-3
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Repeatable for credit
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Grading: Letter or Credit/No Credit
Instructors: Mints, G.
MATH 292A: Set Theory (PHIL 352A)
The basics of axiomatic set theory; the systems of Zermelo-Fraenkel and Bernays-Gödel. Topics: cardinal and ordinal numbers, the cumulative hierarchy and the role of the axiom of choice. Models of set theory, including the constructible sets and models constructed by the method of forcing. Consistency and independence results for the axiom of choice, the continuum hypothesis, and other unsettled mathematical and set-theoretical problems. Prerequisites: PHIL160A,B, and MATH 161, or equivalents.
Terms: not given this year
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Units: 3
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Grading: Ltr-CR/NC
MATH 292B: Set Theory (PHIL 352B)
The basics of axiomatic set theory; the systems of Zermelo-Fraenkel and Bernays-Gödel. Topics: cardinal and ordinal numbers, the cumulative hierarchy and the role of the axiom of choice. Models of set theory, including the constructible sets and models constructed by the method of forcing. Consistency and independence results for the axiom of choice, the continuum hypothesis, and other unsettled mathematical and set-theoretical problems. Prerequisites: PHIL160A,B, and MATH 161, or equivalents.
Terms: not given this year
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Units: 3
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Grading: Ltr-CR/NC
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