MATH 171: Fundamental Concepts of Analysis
Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 115 but altered content and more theoretical orientation. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite: 51H or 115 or consent of the instructor. WIM
Terms: Aut, Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Schoen, R. (PI)
;
Soundararajan, K. (PI)
MATH 175: Elementary Functional Analysis
Linear operators on Hilbert space. Spectral theory of compact operators; applications to integral equations. Elements of Banach space theory. Prerequisite: 115 or 171.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Menz, G. (PI)
MATH 193: Polya Problem Solving Seminar
Topics in mathematics and problem solving strategies with an eye towards the Putnam Competition. Topics may include parity, the pigeonhole principle, number theory, recurrence, generating functions, and probability. Students present solutions to the class. Open to anyone with an interest in mathematics.
Terms: Aut

Units: 1

Repeatable for credit

Grading: Satisfactory/No Credit
Instructors:
Soundararajan, K. (PI)
MATH 210A: Modern Algebra I
Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, introduction to representation theory. Prerequisite: 122 or equivalent.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Yun, Z. (PI)
MATH 215B: Complex Analysis, Geometry, and Topology
Topics: fundamental group and covering spaces, homology, cohomology, products, basic homotopy theory, and applications. Prerequisites: 113, 120, and 171, or equivalent; 215A is not a prerequisite for 215B.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Galatius, S. (PI)
MATH 215C: Complex Analysis, Geometry, and Topology
Differentiable manifolds, transversality, degree of a mapping, vector fields, intersection theory, and Poincare duality. Differential forms and the DeRham theorem. Prerequisite: 215B or equivalent.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Carlsson, G. (PI)
MATH 228: Stochastic Methods in Engineering (CME 308)
Review of basic probability; Monte Carlo simulation; state space models and time series; parameter estimation, prediction, and filtering; Markov chains and processes; stochastic control; and stochastic differential equations. Examples from various engineering disciplines. Prerequisites: exposure to probability; background in real variables and analysis.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Papanicolaou, G. (PI)
MATH 230A: Theory of Probability (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
Instructors:
Diaconis, P. (PI)
MATH 236: Introduction to Stochastic Differential Equations
Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Random walk approximation of diffusions. Prerequisite: 136 or equivalent and differential equations.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Papanicolaou, G. (PI)
MATH 238: Mathematical Finance (STATS 250)
Stochastic models of financial markets. Forward and futures contracts. European options and equivalent martingale measures. Hedging strategies and management of risk. Term structure models and interest rate derivatives. Optimal stopping and American options. Corequisites:
MATH 236 and 227 or equivalent.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Papanicolaou, G. (PI)
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