MATH 224: Topics in Mathematical Biology
Mathematical models for biological processes based on ordinary and partial differential equations. Topics: population and infectious diseases dynamics, biological oscillators, reaction diffusion models, biological waves, and pattern formation. Prerequisites: 53 and 131, or equivalents.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MATH 226: Numerical Solution of Partial Differential Equations (CME 306)
Hyperbolic partial differential equations: stability, convergence and qualitative properties; nonlinear hyperbolic equations and systems; combined solution methods from elliptic, parabolic, and hyperbolic problems. Examples include: Burger's equation, Euler equations for compressible flow, NavierStokes equations for incompressible flow. Prerequisites:
MATH 220A or
CME 302.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ying, L. (PI)
MATH 227: Partial Differential Equations and Diffusion Processes
Parabolic and elliptic partial differential equations and their relation to diffusion processes. First order equations and optimal control. Emphasis is on applications to mathematical finance. Prerequisites:
MATH 131 and
MATH 136/
STATS 219, or equivalents.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MATH 230B: Theory of Probability (STATS 310B)
Conditional expectations, discrete time martingales, stopping times, uniform integrability, applications to 01 laws, RadonNikodym Theorem, ruin problems, etc. Other topics as time allows selected from (i) local limit theorems, (ii) renewal theory, (iii) discrete time Markov chains, (iv) random walk theory,nn(v) ergodic theory. Prerequisite: 310A or
MATH 230A.
Terms: Win

Units: 23

Grading: Letter or Credit/No Credit
Instructors:
Montanari, A. (PI)
MATH 230C: Theory of Probability (STATS 310C)
Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or
MATH 230B.
Terms: Spr

Units: 24

Grading: Letter or Credit/No Credit
Instructors:
Chatterjee, S. (PI)
MATH 231A: An Introduction to Random Matrix Theory (STATS 351A)
Patterns in the eigenvalue distribution of typical large matrices, which also show up in physics (energy distribution in scattering experiments), combinatorics (length of longest increasing subsequence), first passage percolation and number theory (zeros of the zeta function). Classical compact ensembles (random orthogonal matrices). The tools of determinental point processes.
Terms: not given this year

Units: 3

Grading: Letter (ABCD/NP)
MATH 231C: Free Probability
Background from operator theory, addition and multiplication theorems for operators, spectral properties of infinitedimensional operators, the free additive and multiplicative convolutions of probability measures and their classical counterparts, asymptotic freeness of large random matrices, and free entropy and free dimension. Prerequisite:
STATS 310B or equivalent.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MATH 232: Topics in Probability: Percolation Theory
An introduction to some of the most important theorems and open problems in percolation theory. Topics include some of the difficult early breakthroughs of Kesten, Menshikov, Aizenman and others, and recent fieldsmedal winning works of Schramm, Lawler, Werner and Smirnov. Prerequisites: graduatelevel probability.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 233: Probabilistic Methods in Analysis
Proofs and constructions in analysis obtained from basic results in Probability Theory and a 'probabilistic way of thinking.' Topics: Rademacher functions, Gaussian processes, entropy.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 234: Large Deviations Theory (STATS 374)
Combinatorial estimates and the method of types. Large deviation probabilities for partial sums and for empirical distributions, Cramer's and Sanov's theorems and their Markov extensions. Applications in statistics, information theory, and statistical mechanics. Prerequisite:
MATH 230A or
STATS 310.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
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