## CME 200: Linear Algebra with Application to Engineering Computations (ME 300A)

Computer based solution of systems of algebraic equations obtained from engineering problems and eigen-system analysis, Gaussian elimination, effect of round-off error, operation counts, banded matrices arising from discretization of differential equations, ill-conditioned matrices, matrix theory, least square solution of unsolvable systems, solution of non-linear algebraic equations, eigenvalues and eigenvectors, similar matrices, unitary and Hermitian matrices, positive definiteness, Cayley-Hamilton theory and function of a matrix and iterative methods. Prerequisite: familiarity with computer programming, and
MATH51.

Terms: Aut
| Units: 3

Instructors:
Moin, P. (PI)
;
Elnahhas, A. (TA)
;
Emeric, H. (TA)
;
Flint, T. (TA)
;
Gonzalez, C. (TA)
;
Gude, G. (TA)
;
Ha, B. (TA)
;
Romain, M. (TA)

## CS 229: Machine Learning (STATS 229)

Topics: statistical pattern recognition, linear and non-linear regression, non-parametric methods, exponential family, GLMs, support vector machines, kernel methods, deep learning, model/feature selection, learning theory, ML advice, clustering, density estimation, EM, dimensionality reduction, ICA, PCA, reinforcement learning and adaptive control, Markov decision processes, approximate dynamic programming, and policy search. Prerequisites: knowledge of basic computer science principles and skills at a level sufficient to write a reasonably non-trivial computer program in Python/numpy, familiarity with probability theory to the equivalency of CS109 or
STATS116, and familiarity with multivariable calculus and linear algebra to the equivalency of
MATH51.

Terms: Aut, Spr, Sum
| Units: 3-4

Instructors:
Avati, A. (PI)
;
Charikar, M. (PI)
;
Ma, T. (PI)
;
Ng, A. (PI)
;
Re, C. (PI)
;
Arad Hudson, D. (TA)
;
Caron, P. (TA)
;
Chen, E. (TA)
;
Chen, Y. (TA)
;
Ding, T. (TA)
;
Jia, Z. (TA)
;
Jiang, Q. (TA)
;
Jin, Y. (TA)
;
Khani, F. (TA)
;
Khosla, K. (TA)
;
Ko, M. (TA)
;
Kurenkov, A. (TA)
;
Li, J. (TA)
;
She, J. (TA)
;
Smit, A. (TA)
;
Steinberg, E. (TA)
;
Tlili, F. (TA)
;
Wang, G. (TA)
;
Xiong, Z. (TA)
;
Yang, J. (TA)
;
Zhang, K. (TA)
;
Zhang, V. (TA)
;
Zhu, M. (TA)

## MATH 51: Linear Algebra, Multivariable Calculus, and Modern Applications

This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course e-text connects the material to many fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion includes orthogonality, linear independence, matrix algebra, and eigenvalues with applications such as least squares, linear regression, and Markov chains (relevant to population dynamics, molecular chemistry, and PageRank); the singular value decomposition (essential in image compression, topic modeling, and data-intensive work in many fields) is introduced in the final chapter of the e-text. The multivariable calculus portion includes unconstrained optimization via gradients and Hessians (used for energy minimization), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning al
more »

This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course e-text connects the material to many fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion includes orthogonality, linear independence, matrix algebra, and eigenvalues with applications such as least squares, linear regression, and Markov chains (relevant to population dynamics, molecular chemistry, and PageRank); the singular value decomposition (essential in image compression, topic modeling, and data-intensive work in many fields) is introduced in the final chapter of the e-text. The multivariable calculus portion includes unconstrained optimization via gradients and Hessians (used for energy minimization), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning algorithms, such as backpropagation), and Newton's method (an ingredient in GPS and robotics). The course emphasizes computations alongside an intuitive understanding of key ideas. The widespread use of computers makes it important for users of math to understand concepts: novel users of quantitative tools in the future will be those who understand ideas and how they fit with examples and applications. This is the only course at Stanford whose syllabus includes nearly all the math background for
CS 229, which is why
CS 229 and
CS 230 specifically recommend it (or other courses resting on it). For frequently asked questions about the differences between
Math 51 and
CME 100, see the FAQ on the placement page on the Math Department website. Prerequisite:
Math 21,
Math 42, or the math placement diagnostic (offered through the Math Department website) in order to register for this course.

Terms: Aut, Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Cant, D. (PI)
;
Chen, D. (PI)
;
Chetard, B. (PI)
;
Dore, D. (PI)
;
Helfer, J. (PI)
;
Izzo, Z. (PI)
;
Kim, G. (PI)
;
Kraushar, N. (PI)
;
Larson, H. (PI)
;
Lucianovic, M. (PI)
;
Perlman, M. (PI)
;
Sloman, L. (PI)
;
Taylor, C. (PI)
;
Trettel, S. (PI)
;
Wang, G. (PI)
;
White, B. (PI)
;
Wieczorek, W. (PI)
;
Ying, L. (PI)
;
Zavyalov, B. (PI)
;
Angelo, R. (TA)
;
Arana Herrera, F. (TA)
;
Cant, D. (TA)
;
Guijarro Ordonez, J. (TA)
;
Helfer, J. (TA)
;
Izzo, Z. (TA)
;
Libkind, S. (TA)
;
Mackey, W. (TA)
;
Sloman, L. (TA)
;
Wang, G. (TA)
;
Zachos, E. (TA)
;
Zhang, S. (TA)

## MATH 51A: Linear Algebra, Multivariable Calculus, and Modern Applications, ACE

Students attend
MATH 51 lectures with different recitation sessions: four hours per week instead of two, emphasizing engineering applications. Prerequisite: application; see
https://engineering.stanford.edu/students-academics/engineering-diversity-programs/additional-calculus-engineers-ace

Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Cotner, S. (PI)
;
Kim, G. (PI)
;
Lucianovic, M. (PI)
...
more instructors for MATH 51A »

Instructors:
Cotner, S. (PI)
;
Kim, G. (PI)
;
Lucianovic, M. (PI)
;
Taylor, C. (PI)
;
Wieczorek, W. (PI)
;
Yang, K. (TA)
;
Zachos, E. (TA)

## ME 300A: Linear Algebra with Application to Engineering Computations (CME 200)

Computer based solution of systems of algebraic equations obtained from engineering problems and eigen-system analysis, Gaussian elimination, effect of round-off error, operation counts, banded matrices arising from discretization of differential equations, ill-conditioned matrices, matrix theory, least square solution of unsolvable systems, solution of non-linear algebraic equations, eigenvalues and eigenvectors, similar matrices, unitary and Hermitian matrices, positive definiteness, Cayley-Hamilton theory and function of a matrix and iterative methods. Prerequisite: familiarity with computer programming, and
MATH51.

Terms: Aut
| Units: 3

Instructors:
Moin, P. (PI)
;
Elnahhas, A. (TA)
;
Emeric, H. (TA)
;
Flint, T. (TA)
;
Gonzalez, C. (TA)
;
Gude, G. (TA)
;
Ha, B. (TA)
;
Romain, M. (TA)

## STATS 229: Machine Learning (CS 229)

Topics: statistical pattern recognition, linear and non-linear regression, non-parametric methods, exponential family, GLMs, support vector machines, kernel methods, deep learning, model/feature selection, learning theory, ML advice, clustering, density estimation, EM, dimensionality reduction, ICA, PCA, reinforcement learning and adaptive control, Markov decision processes, approximate dynamic programming, and policy search. Prerequisites: knowledge of basic computer science principles and skills at a level sufficient to write a reasonably non-trivial computer program in Python/numpy, familiarity with probability theory to the equivalency of CS109 or
STATS116, and familiarity with multivariable calculus and linear algebra to the equivalency of
MATH51.

Terms: Aut, Spr, Sum
| Units: 3-4

Instructors:
Avati, A. (PI)
;
Charikar, M. (PI)
;
Ma, T. (PI)
;
Ng, A. (PI)
;
Re, C. (PI)
;
Arad Hudson, D. (TA)
;
Caron, P. (TA)
;
Chen, E. (TA)
;
Chen, Y. (TA)
;
Ding, T. (TA)
;
Jia, Z. (TA)
;
Jiang, Q. (TA)
;
Jin, Y. (TA)
;
Khani, F. (TA)
;
Khosla, K. (TA)
;
Ko, M. (TA)
;
Kurenkov, A. (TA)
;
Li, J. (TA)
;
She, J. (TA)
;
Smit, A. (TA)
;
Steinberg, E. (TA)
;
Tlili, F. (TA)
;
Wang, G. (TA)
;
Xiong, Z. (TA)
;
Yang, J. (TA)
;
Zhang, K. (TA)
;
Zhang, V. (TA)
;
Zhu, M. (TA)

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