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. Initialvalue 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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Kemeny, M. (PI)
;
Kimport, S. (PI)
;
Lucianovic, M. (PI)
...
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Instructors:
Kemeny, M. (PI)
;
Kimport, S. (PI)
;
Lucianovic, M. (PI)
;
Schaeffer, G. (PI)
;
Solis, P. (PI)
;
Chen, D. (TA)
;
Hui, Y. (TA)
;
McConnell, S. (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

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Datta, I. (PI)
;
Dore, D. (PI)
;
Falcone, P. (PI)
;
Howe, S. (PI)
;
Hui, Y. (PI)
;
Izzo, Z. (PI)
;
Kimport, S. (PI)
;
Lim, B. (PI)
;
Schaeffer, G. (PI)
;
Taylor, C. (PI)
;
Wang, G. (PI)
;
Wieczorek, W. (PI)
;
Zavyalov, B. (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

Grading: Letter or Credit/No Credit
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, datadriven, 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 dataintensive 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 underl
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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, datadriven, 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 dataintensive 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 wellprepared 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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Church, T. (PI)
;
Conrad, B. (PI)
;
De Groote, C. (PI)
...
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Instructors:
Church, T. (PI)
;
Conrad, B. (PI)
;
De Groote, C. (PI)
;
Fayyazuddin Ljungberg, B. (PI)
;
He, J. (PI)
;
Kuperberg, V. (PI)
;
Love, J. (PI)
;
Lucianovic, M. (PI)
;
Mazzeo, R. (PI)
;
McConnell, S. (PI)
;
Ohrt, C. (PI)
;
Sloman, L. (PI)
;
Taylor, C. (PI)
;
Wei, F. (PI)
;
Wieczorek, W. (PI)
;
Zhu, B. (PI)
;
Cant, D. (TA)
;
Fayyazuddin Ljungberg, B. (TA)
;
Love, J. (TA)
;
Wei, F. (TA)
;
Zou, J. (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/studentsacademics/engineeringdiversityprograms/additionalcalculusengineersace
Terms: Aut, Win, Spr

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Conrad, B. (PI)
;
Lucianovic, M. (PI)
;
Ungemach, W. (PI)
...
more instructors for MATH 51A »
Instructors:
Conrad, B. (PI)
;
Lucianovic, M. (PI)
;
Ungemach, W. (PI)
;
Wieczorek, W. (PI)
;
Stanton, C. (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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
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 secondorder equations to oscillations, matrix exponentials, Laplace transforms, stability of nonlinear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
MATH 63CM: Modern Mathematics: Continuous Methods
A proofbased course on ordinary differential equations, continuing themes from
Math 61CM and
Math 62CM. Topics include linear systems of differential equations and necessary tools from linear algebra, stability and asymptotic properties of solutions to linear systems, existence and uniqueness theorems for nonlinear differential equations with some applications to manifolds, behavior of solutions near an equilibrium point, and SturmLiouville theory. Prerequisites:
Math 61CM and
Math 62CM.
Terms: Spr

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
Instructors:
White, B. (PI)
MATH 63DM: Modern Mathematics: Discrete Methods
Third part of a proofbased sequence in discrete mathematics. This course covers several topics in probability (random variables, independence and correlation, concentration bounds, the central limit theorem) and topology (metric spaces, pointset topology, continuous maps, compactness, Brouwer's fixed point and the BorsukUlam theorem), with some applications in combinatorics. Prerequisites: 61DM or 61CM
Terms: Spr

Units: 5

UG Reqs: WAYFR

Grading: Letter (ABCD/NP)
Instructors:
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, leastsquares, 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:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Kazeev, V. (PI)
;
Taylor, C. (PI)
;
Ying, L. (PI)
;
Guijarro Ordonez, J. (TA)
;
Liu, Y. (TA)
;
Luo, S. (TA)
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