printer friendly pageMATH 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. WIM. Admission is by application: Please email jacobfox@stanford.edu for application information. Motivated students with any level of mathematical background are encouraged to apply.
Terms: Sum
| Units: 3
| UG Reqs: WAY-FR
Instructors:
Fox, J. (PI)
;
Angelo, R. (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
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)
;
Perlman, M. (TA)
;
Raksit, A. (TA)
;
Wu, Y. (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
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)
...
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Instructors:
Varolgunes, U. (PI)
;
Venkatesh, S. (PI)
;
Vondrak, J. (PI)
;
Ye, L. (PI)
;
Dore, D. (TA)
;
Falcone, P. (TA)
;
Love, J. (TA)
;
Miagkov, K. (TA)
MATH 114: Introduction to Scientific Computing (CME 108)
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).
Terms: Win, Sum
| Units: 3
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR
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