## MATH 20: Calculus

The definite integral, Riemann sums, antiderivatives, the Fundamental Theorem of Calculus, and the Mean Value Theorem for integrals. Integration by substitution and by parts. Area between curves, and volume by slices, washers, and shells. Initial-value problems, exponential and logistic models, direction fields, and parametric curves. Prerequisite:
Math 19 or equivalent. If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

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

Instructors:
Grzegrzolka, P. (PI)
;
Lucianovic, M. (PI)
;
Schaeffer, G. (PI)
...
more instructors for MATH 20 »

Instructors:
Grzegrzolka, P. (PI)
;
Lucianovic, M. (PI)
;
Schaeffer, G. (PI)
;
Chen, S. (TA)
;
Fushida-Hardy, S. (TA)
;
Lim, B. (TA)
;
Mackey, W. (TA)
;
Marsden, M. (TA)
;
McConnell, S. (TA)
;
Ortiz, J. (TA)

## MATH 21: Calculus

Review of limit rules. Sequences, functions, limits at infinity, and comparison of growth of functions. Review of integration rules, integrating rational functions, and improper integrals. Infinite series, special examples, convergence and divergence tests (limit comparison and alternating series tests). Power series and interval of convergence, Taylor polynomials, Taylor series and applications. Prerequisite:
Math 20 or equivalent. If you have not previously taken a calculus course at Stanford then you must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

Terms: Aut, Win, Spr, Sum
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Datta, I. (PI)
;
Falcone, P. (PI)
;
Grzegrzolka, P. (PI)
...
more instructors for MATH 21 »

Instructors:
Datta, I. (PI)
;
Falcone, P. (PI)
;
Grzegrzolka, P. (PI)
;
Khu, D. (PI)
;
Kim, G. (PI)
;
Lim, B. (PI)
;
Schaeffer, G. (PI)
;
Zhang, S. (PI)
;
Zhou, Z. (PI)

## MATH 21A: Calculus, ACE

Students attend
MATH 21 lectures with different recitation sessions: two hours per week instead of one, emphasizing engineering applications. Prerequisite: application; see
https://web.stanford.edu/dept/soe/osa/ace.fb

Terms: Aut, Win, Spr
| Units: 5

Instructors:
Kim, G. (PI)
;
McConnell, S. (PI)
;
Schaeffer, G. (PI)
...
more instructors for MATH 21A »

Instructors:
Kim, G. (PI)
;
McConnell, S. (PI)
;
Schaeffer, G. (PI)
;
Velcheva, K. (PI)
;
Zhu, B. (PI)
;
Velcheva, K. (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)
;
Arana Herrera, F. (TA)
;
Cant, D. (TA)
;
Helfer, J. (TA)
;
Izzo, Z. (TA)
;
Libkind, S. (TA)
;
Sloman, L. (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)
;
Lucianovic, M. (PI)
;
Taylor, C. (PI)
...
more instructors for MATH 51A »

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

## MATH 52: Integral Calculus of Several Variables

Iterated integrals, line and surface integrals, vector analysis with applications to vector potentials and conservative vector fields, physical interpretations. Divergence theorem and the theorems of Green, Gauss, and Stokes. Prerequisite: 51 or equivalents.

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

Instructors:
Dimakis, P. (PI)
;
Grzegrzolka, P. (PI)
;
Nguyen, D. (PI)
...
more instructors for MATH 52 »

Instructors:
Dimakis, P. (PI)
;
Grzegrzolka, P. (PI)
;
Nguyen, D. (PI)
;
Ohrt, C. (PI)
;
Zhang, S. (PI)
;
Nguyen, D. (TA)

## MATH 53: Ordinary Differential Equations with Linear Algebra

Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of second-order equations to oscillations, matrix exponentials, Laplace transforms, stability of non-linear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.

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

Instructors:
Chodosh, O. (PI)
;
Ottolini, A. (PI)
;
Simper, M. (PI)
...
more instructors for MATH 53 »

Instructors:
Chodosh, O. (PI)
;
Ottolini, A. (PI)
;
Simper, M. (PI)
;
Varolgunes, U. (PI)
;
Wieczorek, W. (PI)

## MATH 62CM: Modern Mathematics: Continuous Methods

A proof-based introduction to manifolds and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology. Prerequisites:
Math 61CM and 63CM.

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

Instructors:
Cant, D. (PI)
;
Chodosh, O. (PI)

## MATH 63DM: Modern Mathematics: Discrete Methods

Third part of a proof-based sequence in discrete mathematics. The first half of the quarter gives a fast-paced coverage of probability and random processes with an intensive use of generating functions. The second half treats entropy, Shannon¿s coding theorem, game theory, probabilistic methods in solving non-probabilistic problems; some of these topics may vary from year to year. nnPrerequisite:
Math 61DM or 61CM

Terms: Spr
| Units: 5
| UG Reqs: WAY-FR

Instructors:
He, X. (PI)
;
Tokieda, T. (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)
;
Aboumrad, G. (TA)
;
Larson, M. (TA)
;
Li, H. (TA)
;
Love, J. (TA)
;
Pham, H. (TA)
;
Truong Vu, N. (TA)
;
Wang, G. (TA)
;
Zavyalov, B. (TA)
;
Zhou, Y. (TA)

Filter Results: