APPLIED MATHEMATICS COURSES, FALL TERM 2007/SPRING TERM 2008

. AMTH 110a, "Introduction to Quantitative Thinking: The Pleasures of Counting." Staff.

Methods of quantitative inference and modeling are introduced via applications from a variety of different fields. Possible topics include data encryption, codes, scaling phenomena, traffic flow, warfare, and population growth. Some use of computing software such as Mathematica or MATLAB. No prior acquaintance with calculus or computing assumed.

. AMTH 125b/MATH 125b/OPRS 125b, "Introduction to Management Science: Probabilistic Models." Eric Denardo.

A problem-based introduction to models of decision making in an unpredictable environment. Real-world applications motivate the study of objective and subjective probability, decision analysis, utility theory, production and inventory control, queueing theory, and computer simulation. Spreadsheets are introduced. Prerequisite: MATH 222a or b or 225a or b or equivilent.

. AMTH 222a or b/MATH 222a or b, "Linear Algebra with Applications." Mikhail Kapranov [F], Peter Schultheiss [Sp].

Matrix representation of linear equations. Gauss elimination. Vector spaces. Linear independence, basis, and dimension. Orthogonality, projection, least squares approximation; orthogonalization and orthogonal bases. Extension to function spaces. Determinants. Eigenvalues and eigenvectors. Diagonalization. Difference equation and matrix differential equations. Symmetric and Hermitian matrices. Orthogonal and unitary transformations; similarity transformations. May not be taken after MATH 225a or b.

. AMTH 235a/OPRS 235a, "Optimization I." Eric Denardo.

Linear programming, a resource-allocation method widely used by engineers, managers, economists, and social scientists. The theory of linear programming (the simplex method, sensitivity analysis, prices, duality, and geometry) is coupled with a survey of its principal uses. Prerequisite: MATH 222a or b or equivalent.

. AMTH 237a, "Optimization and Convexity." Staff.

Fundamental theory and algorithms of optimization, emphasizing convex optimization, with applications to a wide range of fields. The geometry of convex sets, basic covex analysis, optimality conditions, duality. Numerical algorithms: steepest descent, Newton's method, interior point methods. Applications from statistics, communications, control, signal processing, physics, and economics. Prerequisites: linear algebra and differential calculus.

. AMTH 244a/MATH 244a, "Discrete Mathematics." Dennis Borisov.

Basic concepts and results in discrete mathematics: graphs, trees, connectivity, Ramsey theorem, enumeration, binomial coefficients, Stirling numbers. Properties of finite set systems. Recommended preparationtours@rvdestinations.com: MATH 115a or b or equivalent.

. AMTH 260a/MATH260a, "Basic Analysis in Function Spaces." Ronald Coifman.

The standard basic functional analytic tools needed by scientists and users of mathematics. MATH 260a is a natural continuation of PHYS 301a.

. AMTH 342a/EENG442a, "Linear Systems." A. Stephen Morse.

Introduction to finite-dimensional, continuous, and discrete-time linear dynamical systems. Exploration of the basic properties and mathematical structure of the linears systems used for modeling dynamical processes in robotics, signal and image processing, economics, statistics, environmental and biomedical entineering, and control theory. Prerequisite: MATH 222a or b or permission of instructor.

. AMTH 361a/STAT 361a, "Data Analysis." Lisha Chen.

Through analysis of data sets using the S statistical computing language, study of a selection of statistical topics such as linear and nonlinear models, maximum likelihood, resampling methods, curve estimation, model selection, classification, and clustering. Weekly sessions in the Statistical Computing laboratory. After STAT 242b and MATH 222a or b, or equivalents.

. AMTH 364b/EENG 454b/STAT 364b, "Information Theory." Andrew Barron.

Foundations of information theory in communications, statistical inference, statistical mechanics, probability, and algorithmic complexity. Quantities of information and their properties: entropy, conditional entropy, divergence, mutual information, channel capacity. Basic theorems of data compression and coding for noisy channels. Applications in statistics, communication networks, and finance. After STAT 241a.

AMTH 462a/CPSC 462a, "Graphs and Networks." Daniel Spielman.

A mathematical examination of graphs and their applications in the sciences. Families of graphs include social networks, small-world graphs, Internet graphs, planar graphs, well-shaped meshes, power-law graphs, and classic random graphs. Phenomena include connectivity, clustering, communication, ranking, and iterative processes. Prerequisites: linear algebra and discrete methematics; a course in probability is recommended.

AMTH 464a/664a, "Topics in Computational Biology." Director: Steven Zucker. Lecturers: Thierry Emonet, Michael Krauthammer, Xiao-Jing Wang, Gunter Wagner.

An overview of basic topics in computational biology spanning scales from molecules through cells to networks. It is intended for students with mathematical and/or computational background to learn selected topics in computational biology, and for students in biology with some background in mathematics or physics to learn selected topics in mathematical modeling and computation.s

AMTH 490b, "Senior Seminar and Project." Andrew Barron.

AMTH 511a/CPSC 465a/565a, "Topics in Algorithms." Maxim Sviridenko.

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