## 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 205L: Continuous Mathematical Methods with an Emphasis on Machine Learning

A survey of numerical approaches to the continuous mathematics with emphasis on machine and deep learning. Although motivated from the standpoint of machine learning, the course will focus on the underlying mathematical methods including computational linear algebra and optimization, as well as special topics related to training/using neural networks including automatic differentiation via backward propagation, steepest/gradient decent, momentum methods and adaptive time stepping for ordinary differential equations, etc. Students have the option of doing written homework and either a take-home or in class exams with no programming required, or may skip the exams and instead do a programming project. (Replaces
CS205A, and satisfies all similar requirements.) Prerequisites:
Math 51;
Math 104 or 113 or equivalent or comfortable with the associated material.

Terms: Win
| Units: 3

Instructors:
Fedkiw, R. (PI)

## CS 229T: Statistical Learning Theory (STATS 231)

How do we formalize what it means for an algorithm to learn from data? How do we use mathematical thinking to design better machine learning methods? This course focuses on developing mathematical tools for answering these questions. We will present various learning algorithms and prove theoretical guarantees about them. Topics include generalization bounds, implicit regularization, the theory of deep learning, spectral methods, and online learning and bandits problems. Prerequisites: A solid background in linear algebra (
Math 104,
Math 113 or
CS205) and probability theory (CS109 or STAT 116), statistics and machine learning (
STATS 315A,
CS 229 or
STATS 216).

Last offered: Autumn 2018

## 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

Instructors:
Rock, S. (PI)

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

Instructors:
Candes, E. (PI)
;
Taylor, C. (PI)
;
Velcheva, K. (PI)
...
more instructors for MATH 104 »

Instructors:
Candes, E. (PI)
;
Taylor, C. (PI)
;
Velcheva, K. (PI)
;
Larson, M. (TA)
;
Li, H. (TA)
;
Pham, H. (TA)
;
Truong Vu, N. (TA)
;
Wang, G. (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.) Prerequisites:
Math 51

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

## 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, WAY-FR

Instructors:
Tsai, C. (PI)
;
Cotner, S. (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:
Bump, D. (PI)

## 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: Spr
| Units: 3
| UG Reqs: GER:DB-Math

Instructors:
Hershkovits, O. (PI)

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