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)
;
Makisumi, S. (PI)
...
more instructors for MATH 51 »
Instructors:
Kemeny, M. (PI)
;
Lucianovic, M. (PI)
;
Makisumi, S. (PI)
;
Manners, F. (PI)
;
Pan, D. (PI)
;
Schaeffer, G. (PI)
;
Stanton, C. (PI)
;
Velcheva, K. (PI)
;
Venkatesh, A. (PI)
;
Ward, A. (PI)
;
Wieczorek, W. (PI)
;
Wilson, J. (PI)
;
Wolf, A. (PI)
;
Zhai, L. (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:
Bernard, C. (PI)
;
De Groote, C. (PI)
;
Entin, A. (PI)
...
more instructors for MATH 52 »
Instructors:
Bernard, C. (PI)
;
De Groote, C. (PI)
;
Entin, A. (PI)
;
Jafarov, J. (PI)
;
Starkston, L. (PI)
;
Wieczorek, W. (PI)
;
Fayyazuddin 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:
De Groote, C. (PI)
;
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
...
more instructors for MATH 53 »
Instructors:
De Groote, C. (PI)
;
Eliashberg, Y. (PI)
;
Fredrickson, L. (PI)
;
Hershkovits, O. (PI)
;
Love, J. (PI)
;
Mantoulidis, C. (PI)
;
Raju, C. (PI)
;
Tam, K. (PI)
;
Yang, T. (PI)
;
Madnick, J. (TA)
;
Silliman, J. (TA)
;
Ungemach, W. (TA)
MATH 61CM: Modern Mathematics: Continuous Methods
This is the first part of a theoretical (i.e., proofbased) sequence in multivariable calculus and linear algebra, providing a unified treatment of these topics. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, metric spaces, differentiation in Euclidean space, submanifolds of Euclidean space, inverse and implicit function theorems, and many examples. Part of the linear algebra content is covered jointly with
Math 61DM. Students should know 1variable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BClevel Advanced Placement calculus exam, or consent of the instructor.
Terms: Aut

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Vasy, A. (PI)
;
Zachos, E. (TA)
MATH 61DM: Modern Mathematics: Discrete Methods
This is the first part of a theoretical (i.e., proofbased) sequence in discrete mathematics and linear algebra. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and linear algebra methods in discrete mathematics including spectral graph theory and dimension arguments. Part of the linear algebra content is covered jointly with
Math 61CM. Students should have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BClevel Advanced Placement calculus exam, or consent of the instructor.nnThis sequence is not appropriate for students planning to major in natural sciences, economics, or engineering, but is suitable for majors in any other field (such as MCS ("data science"), computer science, and mathematics).
Terms: Aut

Units: 5

UG Reqs: WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Fox, J. (PI)
;
Sauermann, L. (TA)
MATH 62CM: Modern Mathematics: Continuous Methods
A continuation of themes from
Math 61CM, centered around: manifolds, multivariable integration, and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space and an introduction to general manifolds (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology. Prerequisite:
Math 61CM.
Terms: Win

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Mazzeo, R. (PI)
;
Masullo, A. (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 80Q: Capillary Surfaces: Explored and Unexplored Territory
Preference to sophomores. Capillary surfaces: the interfaces between fluids that are adjacent to each other and do not mix. Recently discovered phenomena, predicted mathematically and subsequently confirmed by experiments, some done in space shuttles. Interested students may participate in ongoing investigations with affinity between mathematics and physics.
Terms: Win

Units: 3

UG Reqs: WAYFR, WAYSMA

Grading: Letter (ABCD/NP)
Instructors:
Finn, R. (PI)
MATH 87Q: Mathematics of Knots, Braids, Links, and Tangles
Preference to sophomores. Types of knots and how knots can be distinguished from one another by means of numerical or polynomial invariants. The geometry and algebra of braids, including their relationships to knots. Topology of surfaces. Brief summary of applications to biology, chemistry, and physics.
Terms: Win

Units: 3

UG Reqs: WAYFR

Grading: Letter (ABCD/NP)
Instructors:
Wieczorek, W. (PI)
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