## 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 and 42 or equivalents.

| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Lin, Y. (PI)
;
Wieczorek, W. (PI)
;
Yang, T. (PI)
;
Katsnelson, V. (TA)
;
Zhou, Y. (TA)

## MATH 52H: Honors Multivariable Mathematics

Continuation of 51H. Prerequisite: 51H.

| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Eliashberg, Y. (PI)

## 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 and 42 or equivalents.

| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Brendle, S. (PI)
;
Ho, K. (PI)
;
Jafari, A. (PI)
;
Wieczorek, W. (PI)
;
Yang, T. (PI)
;
Booher, J. (TA)
;
Cheng, D. (TA)
;
Liu, B. (TA)
;
Nariman, S. (TA)
;
Pan, D. (TA)
;
Shabani, B. (TA)
;
Tsai, L. (TA)
;
Yang, H. (TA)

## MATH 53H: Honors Multivariable Mathematics

Continuation of 52H. Prerequisite: 52H.

| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Li, 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.

| UG Reqs: WAY-FR, WAY-SMA

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.

| UG Reqs: WAY-FR

Instructors:
Wieczorek, W. (PI)

## MATH 101: Math Discovery Lab

MDL is a discovery-based project course in mathematics. Students work independently in small groups to explore open-ended mathematical problems and discover original mathematics. Students formulate conjectures and hypotheses; test predictions by computation, simulation, or pure thought; and present their results to classmates. No lecture component; in-class meetings reserved for student presentations, attendance mandatory. Admission is by application:
http://math101.stanford.edu. Motivated students with any level of mathematical background are encouraged to apply.

| UG Reqs: WAY-FR

Instructors:
Church, T. (PI)

## MATH 104: Applied Matrix Theory

Linear algebra for applications in science and engineering: orthogonality, projections, the four fundamental subspaces of a matrix, 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.) Prerequisites:
MATH 51 and
MATH 52 or 53.

| UG Reqs: GER:DB-Math

Instructors:
Ying, L. (PI)
;
Zheng, T. (PI)

## MATH 106: Functions of a Complex Variable

Complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings. (
Math 116 offers a more theoretical treatment.) Prerequisite: 52.

| UG Reqs: GER:DB-Math

Instructors:
Gu, Y. (PI)

## MATH 108: Introduction to Combinatorics and Its Applications

Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics. Prerequisites: 51 or equivalent.

| UG Reqs: GER:DB-Math

Instructors:
Lemke Oliver, R. (PI)

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