MATH 147: Differential Topology
Introduction to smooth methods in topology including tranvsersality, intersection number, fixed point theorems, as well as differential forms and integration. Prerequisites:
Math 144 or equivalent.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Chodosh, O. (PI)
MATH 158: Probability and Stochastic Differential Equations for Applications (CME 298)
Calculus of random variables and their distributions with applications. Review of limit theorems of probability and their application to statistical estimation and basic Monte Carlo methods. Introduction to Markov chains, random walks, Brownian motion and basic stochastic differential equations with some applications in science and/or engineering. Prerequisites:
Math 53 and introductory probability (such as
Stats 116 or
Math 151).
Terms: Spr
| Units: 4
| UG Reqs: WAY-FR
Instructors:
Adhikari, A. (PI)
MATH 171: Fundamental Concepts of Analysis
Recommended for Mathematics majors and required of honors Mathematics majors. A more advanced and general version of
Math 115, introducing and using metric spaces. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite:
Math 61CM, or 61DM, or
Math 51 and
Math 115. WIM
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
MATH 172: Lebesgue Integration and Fourier Analysis
Similar to 205A, but for undergraduate Math majors and graduate students in other disciplines. Topics include Lebesgue measure on Euclidean space, Lebesgue integration, L^p spaces, the Fourier transform, the Hardy-Littlewood maximal function and Lebesgue differentiation. Prerequisite: 171 or consent of instructor.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Sun, W. (PI)
MATH 173: Theory of Partial Differential Equations
A rigorous introduction to PDE accessible to advanced undergraduates. Elliptic, parabolic, and hyperbolic equations in many space dimensions including basic properties of solutions such as maximum principles, causality, and conservation laws. Methods include the Fourier transform as well as more classical methods. The Lebesgue integral will be used throughout, but a summary of its properties will be provided to make the course accessible to students who have not had 172 or 205A. In years when
Math 173 is not offered,
Math 220 is a recommended alternative (with similar content but a different emphasis). Prerequisite: 171 or equivalent.
Terms: Spr
| Units: 4
| UG Reqs: WAY-FR
Instructors:
Sussman, E. (PI)
MATH 197: Senior Honors Thesis
Honors math major working on senior honors thesis under an approved advisor carries out research and reading. Satisfactory written account of progress achieved during term must be submitted to advisor before term ends. May be repeated 3 times for a max of 9 units. Contact department student services specialist to enroll.
Terms: Aut, Win, Spr, Sum
| Units: 1-6
| Repeatable
3 times
(up to 9 units total)
Instructors:
Abouzaid, M. (PI)
;
Barrett, C. (PI)
;
Borga, J. (PI)
...
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Instructors:
Abouzaid, M. (PI)
;
Barrett, C. (PI)
;
Borga, J. (PI)
;
Charikar, M. (PI)
;
Chodosh, O. (PI)
;
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Icard, T. (PI)
;
Linderman, S. (PI)
;
Manolescu, C. (PI)
;
Montanari, A. (PI)
;
Reingold, O. (PI)
;
Rotskoff, G. (PI)
;
Ryzhik, L. (PI)
;
Schramm, T. (PI)
;
Schwarz, K. (PI)
;
Soundararajan, K. (PI)
;
Vondrak, J. (PI)
MATH 199: Reading Topics
For Math majors only. Undergraduates pursue a reading program under the direction of a Math faculty member; topics limited to those not in regular department course offerings. Credit can fulfill the elective requirement for Math majors. Departmental approval required; please contact the Student Services Specialist for the enrollment proposal form at least 2 weeks before the final study list deadline. May be repeated for credit. Enrollment beyond a third section requires additional approval.
Terms: Aut, Win, Spr, Sum
| Units: 3
| Repeatable
for credit
Instructors:
Borga, J. (PI)
;
Bump, D. (PI)
;
Chodosh, O. (PI)
;
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Ionel, E. (PI)
;
Luk, J. (PI)
;
Mazzeo, R. (PI)
;
Taylor, R. (PI)
MATH 205C: Topics in Harmonic Analysis
Topics of contemporary interest in Fourier, harmonic, and/or microlocal analysis. Prerequisite:
Math 205B.NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Chodosh, O. (PI)
MATH 210C: Lie Theory
Topics in Lie groups, Lie algebras, and/or representation theory. Prerequisite:
Math 210A and familiarity with the basics of finite group representations. When the course is on Lie groups, familiarity with tangent spaces and integration on manifolds is assumed. May be repeated for credit.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Bump, D. (PI)
MATH 215C: Differential Geometry
This course will be an introduction to Riemannian Geometry. Topics will include the Levi-Civita connection, Riemann curvature tensor, Ricci and scalar curvature, geodesics, parallel transport, completeness, geodesics and Jacobi fields, and comparison techniques. Prerequisites 147 or 215B. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.
Terms: Spr
| Units: 3
Instructors:
White, B. (PI)
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