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Course Criteria
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3.00 Credits
YairMinsky. mwf 11.35-12.25 QR Meets RP (34) Hilbert, normed, and Banach spaces; geometry of Hilbert space, Riesz-Fischer theorem; dual space; Hahn-Banach theorem; Riesz representation theorems; linear operators; Baire category theorem; uniform boundedness, open mapping, and closed graph theorems. After math 320a.
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3.00 Credits
Staff. For description see under Statistics.
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3.00 Credits
Andrew Casson. mwf 10.30-11.20 QR (33) Group theory, structure of Abelian groups, and applications to number theory. Symmetric groups and linear groups including orthogonal and unitary groups; properties of Euclidean and Hermitian spaces. Some examples of group representations. Modules over Euclidean rings, Jordan and rational canonical forms of a linear transformation. After math 222a or b or equivalent.
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3.00 Credits
aG ,Introduction to Representation Theory
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3.00 Credits
Dennis Borisov. tth1-2.15 QR (26) Prime numbers; quadratic reciprocity law, Gauss sums; finite fields, equations over finite fields; zeta-functions. After math 350a.
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3.00 Credits
Roger Howe. mw 2.30-3.45 QR (37) Study of fundamental ideas of Lie groups and Lie algebras such as the exponential map. Connections with geometry and physics. After math 230 or 250a or equivalent. math 300b or 301a and math 350a recommended.
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3.00 Credits
Marketa Havlickova. tth11.35-12.50 QR (24) Mathematics 455 Rings, with emphasis on integral domains and polynomial rings. The theory of fields and Galois theory, including finite fields, solvability of equations by radicals, and the fundamental theorem of algebra. Quadratic forms. After math 350a.
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3.00 Credits
Corina Calinescu. mw 2.30-3.45 QR Meets RP (37) A survey of algebraic constructions and theories at a sophisticated level. Topics include categorical language, free groups and other free objects in categories, general theory of rings and modules, artinian rings, and introduction to homo-logical algebra. After math 350a and 370b.
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3.00 Credits
Dennis Borisov. tth 2.30-3.45 QR Meets RP (27) Topics in commutative algebra: general extension of fields; Noetherian, local, and Dedekind rings. Introduction to valuation theory. Rudiments of algebraic geometry. After math 380a.
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3.00 Credits
Vincent Moncrief mwf 11.35-12.25 (34) Newton's equations and the Galilean group; the Euler-Lagrange equations and Noether's theorem; the Kepler problem and rigid body motion; symplectic manifolds and Hamiltonian mechanics . Afte r math 120 a o r b , an d 222 a o r b o r 225 a orb, or equivalents. math 430b, Introduction to Algebraic Topology. TulliaDymarz. mwf 1.30-2.20 QR (36) The theory of fundamental groups and covering spaces, with particular reference to two-dimensional manifolds. Aftermath 350a, and 301a or 300b, or equivalents.
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