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

This course provides unified coverage of linear algebra and multivariable differential calculus. It discusses applications connecting the material to many quantitative fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion of the course includes orthogonality, linear independence, matrix algebra, and eigenvalues as well as ubiquitious applications: least squares, linear regression, Markov chains (relevant to population dynamics, molecular chemistry, and PageRank), singular value decomposition (essential in image compression, topic modeling, and data-intensive work in the natural sciences), and more. The multivariable calculus material includes unconstrained optimization via gradients and Hessians (used for energy minimization in physics and chemistry), 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 (a crucial part of how GPS works). The course emphasizes computations alongside an intuitive understanding of key ideas, making students well-prepared for further study of mathematics and its applications to other fields. The widespread use of computers makes it more important, not less, for users of math to understand concepts: in all scientific fields, novel users of quantitative tools in the future will be those who understand ideas and how they fit with applications and examples. 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: 21, 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:
Church, T. (PI)
;
Conrad, B. (PI)
;
De Groote, C. (PI)
...
more instructors for MATH 51 »

Instructors:
Church, T. (PI)
;
Conrad, B. (PI)
;
De Groote, C. (PI)
;
Fayyazuddin Ljungberg, B. (PI)
;
He, J. (PI)
;
Kuhn, N. (PI)
;
Kuperberg, V. (PI)
;
Landesman, A. (PI)
;
Love, J. (PI)
;
Lucianovic, M. (PI)
;
Mazzeo, R. (PI)
;
McConnell, S. (PI)
;
Ohrt, C. (PI)
;
Sloman, L. (PI)
;
Stanton, C. (PI)
;
Taylor, C. (PI)
;
Wei, F. (PI)
;
Wieczorek, W. (PI)
;
Zhu, B. (PI)
;
Arana Herrera, F. (TA)
;
Cant, D. (TA)
;
Fayyazuddin Ljungberg, B. (TA)
;
Love, J. (TA)
;
Nguyen, D. (TA)
;
Stanton, C. (TA)
;
Ungemach, W. (TA)
;
Wei, F. (TA)
;
Zhang, S. (TA)
;
Zhou, Z. (TA)
;
Zou, J. (TA)

## MATH 199: Reading Topics

For math majors only. Undergraduates pursue a reading program under the direction of a math faculty member; topics limited to those topics not in regular department course offerings. Credit can fulfill the elective requirement for math majors. May be repeated for credit. Undergraduates may take this course at most 3 times, only enroll in one section per quarter, and complete up to 9 units total. Please contact the student services specialist for the enrollment proposal form at least 2 weeks before enrollment for the quarter closes.

Terms: Aut, Win, Spr, Sum
| Units: 1-3
| Repeatable for credit

Instructors:
Bump, D. (PI)
;
Candes, E. (PI)
;
Cohen, R. (PI)
;
Fox, J. (PI)
;
Mazzeo, R. (PI)
;
Soundararajan, K. (PI)
;
Taylor, R. (PI)
;
Tsai, C. (PI)
;
White, B. (PI)