## 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.

Last offered: Winter 2018
| UG Reqs: WAY-FR, WAY-SMA

## 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.

Last offered: Winter 2020
| UG Reqs: WAY-FR

## 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. WIM

Terms: Sum
| Units: 3
| UG Reqs: WAY-FR

Instructors:
Fox, J. (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, least-squares, the condition number of a matrix, algorithms for solving linear systems.
MATH 113 offers a more theoretical treatment of linear algebra.
MATH 104 and
ENGR 108 cover complementary topics in applied linear algebra. The focus of
MATH 104 is on algorithms and concepts; the focus of
ENGR 108 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:DB-Math, WAY-FR

Instructors:
Kim, G. (PI)
;
Ma, C. (PI)
;
Taylor, C. (PI)
;
Ying, L. (PI)
;
Diaconu, S. (TA)
;
Guijarro Ordonez, J. (TA)
;
Li, H. (TA)
;
Marsden, M. (TA)

## 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.

Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Wieczorek, W. (PI)

## MATH 107: Graph Theory

An introductory course in graph theory establishing fundamental concepts and results in variety of topics. Topics include: basic notions, connectivity, cycles, matchings, planar graphs, graph coloring, matrix-tree theorem, conditions for hamiltonicity, Kuratowski's theorem, Ramsey and Turan-type theorem. Prerequisites: 51 or equivalent and some familiarity with proofs is required.

Terms: Win
| Units: 3
| UG Reqs: WAY-FR

Instructors:
Spink, H. (PI)
;
Pham, H. (TA)

## 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.

Terms: Spr, Sum
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Fox, J. (PI)
;
Kwan, M. (PI)

## 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. Prerequisite:
Math 51.

Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Angelo, R. (PI)
;
Trettel, S. (PI)

## MATH 110: Applied Number Theory and Field Theory

Number theory and its applications to modern cryptography. Topics: congruences, finite fields, primality testing and factorization, public key cryptography, error correcting codes, and elliptic curves, emphasizing algorithms. Includes an introduction to proof-writing. WIM. Prerequisite:
Math 51

Terms: Win
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Spink, H. (PI)
;
Xu, M. (TA)

## MATH 113: Linear Algebra and Matrix Theory

Algebraic properties of matrices and their interpretation in geometric terms. The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization. Includes an introduction to proof-writing. (
Math 104 offers a more application-oriented treatment.) Prerequisites:
Math 51

Terms: Aut, Win, Spr, Sum
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Varolgunes, U. (PI)
;
Venkatesh, S. (PI)
;
Vondrak, J. (PI)
...
more instructors for MATH 113 »

Instructors:
Varolgunes, U. (PI)
;
Venkatesh, S. (PI)
;
Vondrak, J. (PI)
;
Ye, L. (PI)
;
Falcone, P. (TA)
;
Love, J. (TA)

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