## CME 307: Optimization (MS&E 311)

Applications, theories, and algorithms for finite-dimensional linear and nonlinear optimization problems with continuous variables. Elements of convex analysis, first- and second-order optimality conditions, sensitivity and duality. Algorithms for unconstrained optimization, and linearly and nonlinearly constrained problems. Modern applications in communication, game theory, auction, and economics. Prerequisites:
MATH 113, 115, or equivalent.

Terms: Win
| Units: 3

Instructors:
Ye, Y. (PI)

## CS 329M: Topics in Artificial Intelligence: Algorithms of Advanced Machine Learning

This advanced graduate course explores in depth several important classes of algorithms in modern machine learning. We will focus on understanding the mathematical properties of these algorithms in order to gain deeper insights on when and why they perform well. We will also study applications of each algorithm on interesting, real-world settings. Topics include: spectral clustering, tensor decomposition, Hamiltonian Monte Carlo, adversarial training, and variational approximation. Students will learn mathematical techniques for analyzing these algorithms and hands-on experience in using them. We will supplement the lectures with latest papers and there will be a significant research project component to the class. Prerequisites: Probability (
CS 109), linear algebra (
Math 113), machine learning (
CS 229), and some coding experience.

Last offered: Spring 2017

## ENGR 205: Introduction to Control Design Techniques

Review of root-locus and frequency response techniques for control system analysis and synthesis. State-space techniques for modeling, full-state feedback regulator design, pole placement, and observer design. Combined observer and regulator design. Lab experiments on computers connected to mechanical systems. Prerequisites: 105,
MATH 103, 113. Recommended: Matlab.

Terms: Aut
| Units: 3

## MATH 104: Applied Matrix Theory

Linear algebra for applications in science and engineering: orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares, the condition number of a matrix, algorithms for solving linear systems.
MATH 113 offers a more theoretical treatment of linear algebra.
MATH 104 and
EE 103/
CME 103 cover complementary topics in applied linear algebra. The focus of
MATH 104 is on algorithms and concepts; the focus of
EE 103 is on a few linear algebra concepts, and many applications. Prerequisites:
MATH 51 and programming experience on par with
CS 106.

Terms: Win, Spr
| Units: 3
| UG Reqs: GER:DB-Math

Instructors:
Kazeev, V. (PI)
;
Ying, L. (PI)
;
Datta, I. (TA)
;
McConnell, S. (TA)
;
Velcheva, K. (TA)
;
Zhang, S. (TA)

## MATH 113: Linear Algebra and Matrix Theory

Algebraic properties of matrices and their interpretation in geometric terms. The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization. (
Math 104 offers a more application-oriented treatment.)

Terms: Aut, Win, Spr, Sum
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Kazeev, V. (PI)
;
Kemeny, M. (PI)
;
Khoo, Y. (PI)
;
Manners, F. (PI)
;
Falcone, P. (TA)
;
Sherman, D. (TA)
;
Velcheva, K. (TA)
;
Wang, G. (TA)
;
Zhou, Y. (TA)

## MATH 121: Galois Theory

Field of fractions, splitting fields, separability, finite fields. Galois groups, Galois correspondence, examples and applications. Prerequisite:
Math 120 and (also recommended) 113.

Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math

Instructors:
Bump, D. (PI)
;
Stanton, C. (TA)

## MATH 122: Modules and Group Representations

Modules over PID. Tensor products over fields. Group representations and group rings. Maschke's theorem and character theory. Character tables, construction of representations. Prerequisite:
Math 120. Also recommended: 113.

Terms: Spr
| Units: 3

Instructors:
Wilson, J. (PI)
;
Kuhn, N. (TA)

## MATH 146: Analysis on Manifolds

Differentiable manifolds, tangent space, submanifolds, implicit function theorem, differential forms, vector and tensor fields. Frobenius' theorem, DeRham theory. Prerequisite: 62CM or 52 and familiarity with linear algebra and analysis arguments at the level of 113 and 115 respectively.

Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math

Instructors:
Starkston, L. (PI)
;
Fauteux-Chapleau, F. (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

Instructors:
Kerckhoff, S. (PI)
;
Arana Herrera, F. (TA)

## MS&E 310: Linear Programming

Formulation of standard linear programming models. Theory of polyhedral convex sets, linear inequalities, alternative theorems, and duality. Variants of the simplex method and the state of art interior-point algorithms. Sensitivity analyses, economic interpretations, and primal-dual methods. Relaxations of harder optimization problems and recent convex conic linear programs. Applications include game equilibrium facility location. Prerequisite:
MATH 113 or consent of instructor.

Terms: Aut
| Units: 3

Instructors:
Ye, Y. (PI)
;
Fu, R. (TA)

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