## 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, the four fundamental subspaces of a matrix, 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.) Prerequisites:
MATH 51 and
MATH 52 or 53.

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

Instructors:
Hicks, A. (PI)
;
Greverath, D. (TA)
;
Li, C. (TA)
;
Masullo, A. (TA)
;
Silliman, J. (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
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Chatterjee, S. (PI)
;
Church, T. (PI)
;
Kerckhoff, S. (PI)
...
more instructors for MATH 113 »

Instructors:
Chatterjee, S. (PI)
;
Church, T. (PI)
;
Kerckhoff, S. (PI)
;
Helfer, J. (TA)
;
Sun, Q. (TA)
;
Wang, G. (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:
Yun, Z. (PI)
;
Rosengarten, Z. (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)
;
Wolf, A. (TA)

## 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

Instructors:
Cohen, R. (PI)
;
Alvarez-Gavela, D. (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)

## MS&E 311: Optimization

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

## MS&E 321: Stochastic Systems

Topics in stochastic processes, emphasizing applications. Markov chains in discrete and continuous time; Markov processes in general state space; Lyapunov functions; regenerative process theory; renewal theory; martingales, Brownian motion, and diffusion processes. Application to queueing theory, storage theory, reliability, and finance. Prerequisites: 221 or
STATS 217;
MATH 113, 115. (Glynn)

Terms: Spr
| Units: 3

Instructors:
Glynn, P. (PI)

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