## MATH 19: Calculus

Introduction to differential calculus of functions of one variable. Review of elementary functions (including exponentials and logarithms), limits, rates of change, the derivative and its properties, applications of the derivative. Prerequisites: trigonometry, advanced algebra, and analysis of elementary functions (including exponentials and logarithms). You must have taken the math placement diagnostic (offered through the Math Department website) in order to register for this course.

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

Instructors:
Chetard, B. (PI)
;
La, J. (PI)
;
Schaeffer, G. (PI)
;
Falcone, P. (TA)
;
Li, Z. (TA)
;
Marsden, M. (TA)
;
Stavrianidi, A. (TA)
;
Zhou, Y. (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)
;
Zhou, Z. (PI)
;
Hui, Y. (TA)
;
Izzo, Z. (TA)
;
Lim, B. (TA)
;
Truong Vu, N. (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 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)
;
Chaturvedi, S. (TA)
;
Lolas, P. (TA)

## 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, Sum
| 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)

## MATH 114: Introduction to Scientific Computing (CME 108)

Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).

Terms: Win, Sum
| Units: 3
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

## MATH 197: Senior Honors Thesis

Honors math major working on senior honors thesis under an approved advisor carries out research and reading. Satisfactory written account of progress achieved during term must be submitted to advisor before term ends. May be repeated 3 times for a max of 9 units. Contact department student services specialist to enroll.

Terms: Aut, Win, Spr, Sum
| Units: 1-6
| Repeatable for credit

Instructors:
Conrad, B. (PI)
;
Cook, N. (PI)
;
Dembo, A. (PI)
;
Eliashberg, Y. (PI)
;
Fox, J. (PI)
;
Kachru, S. (PI)
;
Luk, J. (PI)
;
Mazzeo, R. (PI)
;
Soundararajan, K. (PI)
;
Taylor, R. (PI)
;
Vasy, A. (PI)
;
Vondrak, J. (PI)

## 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 not in regular department course offerings. Credit can fulfill the elective requirement for Math majors. Departmental approval required; please contact the Student Services Specialist for the enrollment proposal form at least 2 weeks before the final study list deadline. May be repeated for credit. Enrollment beyond a third section requires additional approval.

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

Instructors:
Eliashberg, Y. (PI)
;
Taylor, R. (PI)
;
Tsai, C. (PI)
...
more instructors for MATH 199 »

Instructors:
Eliashberg, Y. (PI)
;
Taylor, R. (PI)
;
Tsai, C. (PI)
;
Vakil, R. (PI)
;
Vondrak, J. (PI)

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