L11 Econ 501
Macroeconomics I (3 units)
The first of a two semester sequence on graduate macro theory. The focus is on determination of aggregate income, employment, and prices with emphasis on static theory and the microfoundations of macroeconomics, including consumption and investment behavior, static models of income and price determination, problems of unemployment and inflation, and alternative theories of the roles of fiscal and monetary policy.

L11 Econ 503
Microeconomics I (3 units)
The first of a two-semester graduate sequence in microeconomic theory. First semester considers production and costs, supply of output and demand for inputs, demands for final products, choice under uncertainty, introduction to market structure and game theory, and time and capital. Prerequisite: Econ 508 (taught in August prior to the Fall term) and Econ 511 (to be taken concurrently), or with permission of instructor.

L11 Econ 511
Quantitative Methods I (3 units)
Study of those topics of mathematics of special usefulness in economic research. Selection and ordering of topics will vary with level of student preparation but will usually include the following: vectors, matrices, lines mappings; their manipulation and elementary properties; elementary topology, and elements of multidimensional calculus.

L11 Econ 512
Quantitative Methods in Economics II (3 units)
Introduction to mathematical statistics designed to provide a background for the study of econometrics. Selection of topics will usually include the following: probability introduction to distribution theory, including limiting distributions and distributions of quadratic terms, Bayes Theorem, and hypothesis testing.

L11 Econ 513
Introduction to Econometrics (3 units)
Classical multiple regression analysis and an introduction to generalizations useful in empirical research in economics, including a framework for dealing with problems of multicollinearity, specification error, heteroskedasticity, serial and contemporaneous correlation, identification and consistent estimation in simultaneous equation models.

ESE 520
Probability and Stochastic Processes (3 units)
Review of probability theory, models for random signals and noise, calculus of random processes, noise in linear and nonlinear systems, representation of random signals by sampling and orthonormal expansions. Poisson, Gaussian, and Markov processes as models for engineering problems. Prerequiste: ESE 326.

ESE 521
Random Variables and Stochastic Processes I (3 units)
Mathematical foundations of probability theory, including constructions of measures, Lebesque-measure, Lebesque-integral, Banach space property of Lp, basic Hilbert-space theory, conditional expectation, Kolmogorov's theorems on existence and sample-path continuity of stochastic processes. An in-depth look at the Wiener process, filtrations and stopping times, Markov processes and diffusions, including semigroup properties and the Kolmogorov forward and backward equations. Prerequisites: ESE 520 or equivalent, Math 411.

ESE 403
Operations Research (3 units)
Introduction to the mathematical aspects of various areas of operations research, with additional emphasis on problem formulation. This is a course of broad scope, emphasizing both the fundamental mathematical concepts involved, and also aspects of the translation of real-world problems to an appropriate mathematical model. Subjects to be covered include linear and integer programming, network problems, and dynamic programming. Prerequisites: Math 217 and familiarity with matrix or linear algebra or permission of instructor.