## 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:DB-Math, WAY-FR

Instructors:
Fredrickson, L. (PI)
;
De Groote, C. (TA)

## MATH 62DM: Modern Mathematics: Discrete Methods

This is the second part of a proof-based sequence in discrete mathematics. This course covers topics in elementary number theory, group theory, and discrete Fourier analysis. For example, we'll discuss the basic examples of abelian groups arising from congruences in elementary number theory, as well as the non-abelian symmetric group of permutations. Prerequisites: 61DM or 61CM.

Terms: Win
| Units: 5

Instructors:
Soundararajan, K. (PI)
;
Love, J. (TA)

## MATH 63CM: Modern Mathematics: Continuous Methods

A proof-based 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 Sturm-Liouville theory. Prerequisites:
Math 61CM and
Math 62CM.

Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Luk, J. (PI)
;
Reinhold, J. (TA)

## MATH 63DM: Modern Mathematics: Discrete Methods

Third part of a proof-based 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, point-set topology, continuous maps, compactness, Brouwer's fixed point and the Borsuk-Ulam theorem), with some applications in combinatorics. Prerequisites: 61DM or 61CM

Terms: Spr
| Units: 5

Instructors:
Vondrak, J. (PI)
;
Wei, F. (TA)

## MATH 70SI: The Game of Go: Strategy, Theory, and History

Strategy and mathematical theories of the game of Go, with guest appearance by a professional Go player.

Last offered: Autumn 2014

## 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 proof-based 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 300-303.

Terms: Spr
| Units: 1

Instructors:
Conrad, B. (PI)

## 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: 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.

Terms: Spr
| Units: 3
| 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. WIM

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

Instructors:
Church, T. (PI)
;
Silliman, J. (TA)

## 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
EE 103/
CME 103 cover complementary topics in applied linear algebra. The focus of
MATH 104 is on algorithms and concepts; the focus of
EE 103 is on a few linear algebra concepts, and many applications. Prerequisites:
MATH 51 and programming experience on par with
CS 106.

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

Instructors:
Kazeev, V. (PI)
;
Ying, L. (PI)
;
Datta, I. (TA)
;
McConnell, S. (TA)
;
Velcheva, K. (TA)
;
Zhang, S. (TA)

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