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:
Kimport, S. (PI)
;
Madnick, J. (PI)
;
Savvas, M. (PI)
...
more instructors for MATH 20 »
Instructors:
Kimport, S. (PI)
;
Madnick, J. (PI)
;
Savvas, M. (PI)
;
Wilson, J. (PI)
;
Zhu, X. (PI)
;
Cant, D. (TA)
;
Guijarro Ordonez, J. (TA)
;
Lolas, P. (TA)
;
Velcheva, K. (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:
Dhillon, G. (PI)
;
Kemeny, M. (PI)
;
Kimport, S. (PI)
...
more instructors for MATH 21 »
Instructors:
Dhillon, G. (PI)
;
Kemeny, M. (PI)
;
Kimport, S. (PI)
;
Mueller, S. (PI)
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Nguyen, D. (PI)
;
Schaeffer, G. (PI)
;
Solis, P. (PI)
;
Lim, B. (TA)
;
Wolf, A. (TA)
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 (ABCD/NP)
MATH 51: Linear Algebra and Differential Calculus of Several Variables
Geometry and algebra of vectors, matrices and linear transformations, eigenvalues of symmetric matrices, vectorvalued functions and functions of several variables, partial derivatives and gradients, derivative as a matrix, chain rule in several variables, critical points and Hessian, leastsquares, , constrained and unconstrained optimization in several variables, Lagrange multipliers. 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:
Cohen, R. (PI)
;
Datta, I. (PI)
;
Devadas, S. (PI)
;
Helfer, J. (PI)
;
Lim, B. (PI)
;
Lucianovic, M. (PI)
;
Ohrt, C. (PI)
;
Pan, D. (PI)
;
Perlmutter, N. (PI)
;
Szucs, G. (PI)
;
Tam, K. (PI)
;
Velcheva, K. (PI)
;
Wang, G. (PI)
;
White, B. (PI)
;
Wieczorek, W. (PI)
;
Zavyalov, B. (PI)
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Zhou, Y. (PI)
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Zhou, Z. (PI)
;
Zou, J. (PI)
MATH 51A: Linear Algebra and Differential Calculus of Several Variables, ACE
Students attend
MATH 51 lectures with different recitation sessions: three hours per week instead of two, emphasizing engineering applications. Prerequisite: application; see
https://web.stanford.edu/dept/soe/osa/ace.fb
Terms: Aut, Win, Spr

Units: 6

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
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
Instructors:
McConnell, S. (PI)
;
Mueller, S. (PI)
;
Starkston, L. (PI)
...
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Instructors:
McConnell, S. (PI)
;
Mueller, S. (PI)
;
Starkston, L. (PI)
;
Zaman, A. (PI)
;
Kraushar, N. (TA)
;
Szucs, G. (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 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
Instructors:
Dore, D. (PI)
;
Hershkovits, O. (PI)
;
Ljungberg, B. (PI)
...
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Instructors:
Dore, D. (PI)
;
Hershkovits, O. (PI)
;
Ljungberg, B. (PI)
;
Masullo, A. (PI)
;
Tokieda, T. (PI)
;
Wieczorek, W. (PI)
;
Zhang, S. (PI)
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:
Luk, J. (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

Grading: Letter (ABCD/NP)
Instructors:
Vondrak, J. (PI)
MATH 79SI: Proof Positive: Principles of Mathematics
What is a mathematical proof, and where do proofs come from? Students will become comfortable with fundamental techniques of mathematical proof through practice with interesting and accessible examples from many areas of math. Students will additionally hone their communication skills and develop their ability to formulate and answer precise mathematical questions. Topics include direct proof, proof by contrapositive, proof by contradiction, many applications of mathematical induction, constructing good definitions, and useful writing habits. The course is designed to prepare students who have completed or are concurrently enrolled in
MATH 51 to succeed in introductory proofbased math classes at the level of
MATH 115 or
MATH 120, or to simply appreciate the nature of proof at a deeper level than is seen in high school geometry. To be considered for enrollment, please email masonr@stanford.edu and attend the first class meeting on Tuesday, April 3 at 3PM in 300303.
Terms: Spr

Units: 1

Grading: Satisfactory/No Credit
Instructors:
Conrad, B. (PI)
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