MATH 197: Senior Honors Thesis
Honors math major working on senior honors thesis under an approved advisor carries out research and reading. Satisfactory written account of progress achieved during term must be submitted to advisor before term ends. May be repeated 3 times for a max of 9 units. Contact department student services specialist to enroll.
Terms: Aut, Win, Spr, Sum

Units: 16

Repeatable for credit

Grading: Letter (ABCD/NP)
Instructors:
Bump, D. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
;
Luk, J. (PI)
;
Reingold, O. (PI)
;
Ryzhik, L. (PI)
;
Savarese, S. (PI)
;
Vakil, R. (PI)
MATH 199: Independent Work
For math majors only. Undergraduates pursue a reading program; topics limited to those not in regular department course offerings. Credit can fulfill the elective requirement for math majors. Approval of Undergraduate Affairs Committee is required to use credit for honors majors area requirement. Contact department student services specialist to enroll.
Terms: Aut, Win, Spr, Sum

Units: 13

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
...
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Instructors:
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
;
Fredrickson, L. (PI)
;
Mazzeo, R. (PI)
;
Perlmutter, N. (PI)
;
Ryzhik, L. (PI)
;
Tsai, C. (PI)
MATH 210A: Modern Algebra I
Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, canonical forms and Jordan decomposition. Prerequisite: 122 or equivalent.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Church, T. (PI)
;
Dore, D. (TA)
MATH 215A: Algebraic Topology
Topics: fundamental group and covering spaces, basics of homotopy theory, homology and cohomology (simplicial, singular, cellular), products, introduction to topological manifolds, orientations, Poincare duality. Prerequisites: 113, 120, and 171.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Kerckhoff, S. (PI)
;
Arana Herrera, F. (TA)
MATH 216A: Introduction to Algebraic Geometry
Algebraic curves, algebraic varieties, sheaves, cohomology, RiemannRoch theorem. Classification of algebraic surfaces, moduli spaces, deformation theory and obstruction theory, the notion of schemes. May be repeated for credit. Prerequisites: 210ABC or equivalent.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Vakil, R. (PI)
MATH 220: Partial Differential Equations of Applied Mathematics (CME 303)
Firstorder partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: Basic coursework in multivariable calculus and ordinary differential equations, and some prior experience with a proofbased treatment of the material as in
Math 171 or
Math 61CM (formerly
Math 51H).
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ryzhik, L. (PI)
;
Liu, F. (TA)
MATH 230A: Theory of Probability I (STATS 310A)
Mathematical tools: sigma algebras, measure theory, connections between coin tossing and Lebesgue measure, basic convergence theorems. Probability: independence, BorelCantelli lemmas, almost sure and Lp convergence, weak and strong laws of large numbers. Large deviations. Weak convergence; central limit theorems; Poisson convergence; Stein's method. Prerequisites: 116,
MATH 171.
Terms: Aut

Units: 24

Grading: Letter or Credit/No Credit
MATH 244: Riemann Surfaces
Riemann surfaces and holomorphic maps, algebraic curves, maps to projective spaces. Calculus on Riemann surfaces. Elliptic functions and integrals. RiemannHurwitz formula. RiemannRoch theorem, AbelJacobi map. Uniformization theorem. Hyperbolic surfaces. (Suitable for advanced undergraduates.) Prerequisites:
MATH 106 or
MATH 116, and familiarity with surfaces equivalent to
MATH 143,
MATH 146, or
MATH 147.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Mazzeo, R. (PI)
MATH 249A: Topics in number theory
Topics of contemporary interest in number theory. May be repeated for credit.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Soundararajan, K. (PI)
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