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)
;
Schaeffer, G. (PI)
;
Zhu, X. (PI)
...
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Instructors:
Kimport, S. (PI)
;
Schaeffer, G. (PI)
;
Zhu, X. (PI)
;
Bernard, C. (TA)
;
Datta, I. (TA)
;
Hui, Y. (TA)
;
Lim, B. (TA)
;
Silliman, J. (TA)
;
Zou, 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

Units: 4

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Acosta, J. (PI)
;
Cote, L. (PI)
;
Gao, J. (PI)
;
Kimport, S. (PI)
;
Lim, B. (PI)
;
Ljungberg, B. (PI)
;
Masullo, A. (PI)
;
Pan, D. (PI)
;
Schaeffer, G. (PI)
;
Ungemach, W. (PI)
;
Warner, E. (TA)
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

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Kemeny, M. (PI)
;
Lucianovic, M. (PI)
;
Manners, F. (PI)
...
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Instructors:
Kemeny, M. (PI)
;
Lucianovic, M. (PI)
;
Manners, F. (PI)
;
Schaeffer, G. (PI)
;
Stanton, C. (PI)
;
Velcheva, K. (PI)
;
Venkatesh, A. (PI)
;
Ward, A. (PI)
;
Wieczorek, W. (PI)
;
Wilson, J. (PI)
;
Zhang, S. (PI)
;
Zhou, Y. (PI)
;
Zhu, B. (PI)
;
Helfer, J. (TA)
;
Nguyen, D. (TA)
;
Stanton, C. (TA)
;
Wang, G. (TA)
;
Wolf, A. (TA)
;
Zhu, B. (TA)
MATH 51A: Linear Algebra and Differential Calculus of Several Variables, ACE
Students attend
MATH 51 lectures with different recitation sessions: four hours per week instead of two, emphasizing engineering applications. Prerequisite: application; see
http://soe.stanford.edu/edp/programs/ace.html.
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:
De Groote, C. (PI)
;
Entin, A. (PI)
;
Jafarov, J. (PI)
...
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Instructors:
De Groote, C. (PI)
;
Entin, A. (PI)
;
Jafarov, J. (PI)
;
Starkston, L. (PI)
;
Wieczorek, W. (PI)
;
Ljungberg, B. (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:
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
;
Hershkovits, O. (PI)
...
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Instructors:
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
;
Hershkovits, O. (PI)
;
Mantoulidis, C. (PI)
;
Tam, K. (PI)
;
Yang, T. (PI)
;
Madnick, J. (TA)
;
Silliman, J. (TA)
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)
;
Savvas, M. (TA)
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 or Credit/No Credit
Instructors:
Vondrak, J. (PI)
;
White, G. (TA)
MATH 106: Functions of a Complex Variable
Complex numbers, analytic functions, CauchyRiemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings. (
Math 116 offers a more theoretical treatment.) Prerequisite: 52.
Terms: Spr, Sum

Units: 3

UG Reqs: GER:DBMath

Grading: Letter or Credit/No Credit
Instructors:
Li, J. (PI)
;
Guijarro Ordonez, J. (TA)
MATH 109: Applied Group Theory
Applications of the theory of groups. Topics: elements of group theory, groups of symmetries, matrix groups, group actions, and applications to combinatorics and computing. Applications: rotational symmetry groups, the study of the Platonic solids, crystallographic groups and their applications in chemistry and physics. Honors math majors and students who intend to do graduate work in mathematics should take 120. WIM.
Terms: Spr

Units: 3

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Wieczorek, W. (PI)
;
Kraushar, N. (TA)
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