printer friendly pageMATH 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: Win
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Vasy, A. (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. Prerequisite: 171 or equivalent.
Terms: Spr
| Units: 3
Instructors:
Maximo, D. (PI)
MATH 175: Elementary Functional Analysis
Linear operators on Hilbert space. Spectral theory of compact operators; applications to integral equations. Elements of Banach space theory. Prerequisite: 115 or 171.
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Ford, A. (PI)
MATH 177: Geometric Methods in the Theory of Ordinary Differential Equations
Hamiltonian systems and their geometry. First order PDE and Hamilton-Jacobi equation. Structural stability and hyperbolic dynamical systems. Completely integrable systems. Perturbation theory.
Terms: Spr
| Units: 3
Instructors:
Eliashberg, Y. (PI)
MATH 180: Introduction to Financial Mathematics
Financial derivatives: contracts and options. Hedging and risk management. Arbitrage, interest rate, and discounted value. Geometric random walk and Brownian motion as models of risky assets. Initial boundary value problems for the heat and related partial differential equations. Self-financing replicating portfolio. Black-Scholes pricing of European options. Dividends. Implied volatility. Optimal stopping and American options. Prerequisite: 53. Corequisites: 131, 151 or
STATS 116.
Terms: Spr
| Units: 3
| UG Reqs: GER:DB-Math
Instructors:
Menz, G. (PI)
MATH 193: Polya Problem Solving Seminar
Topics in mathematics and problem solving strategies with an eye towards the Putnam Competition. Topics may include parity, the pigeonhole principle, number theory, recurrence, generating functions, and probability. Students present solutions to the class. Open to anyone with an interest in mathematics.
Terms: Aut
| Units: 1
| Repeatable
5 times
(up to 5 units total)
Instructors:
Soundararajan, K. (PI)
MATH 196: Undergraduate Colloquium
Weekly lectures by different experts on topics in pure and applied mathematics that go beyond the standard curriculum. May be repeated for credit for up to 3 units. Does not count toward the math major or minor.
Terms: Aut, Win, Spr
| Units: 1
| Repeatable
3 times
(up to 3 units total)
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
| Units: 1-6
| Repeatable
3 times
(up to 9 units total)
Instructors:
Bump, D. (PI)
;
Conrad, B. (PI)
;
Mazzeo, R. (PI)
;
Soundararajan, K. (PI)
;
Venkatesh, A. (PI)
;
Ying, L. (PI)
MATH 198: Practical Training
Only for students majoring in mathematics. Students obtain employment in a relevant industrial or research activity to enhance their professional experience. Students submit a concise report detailing work activities, problems worked on, and key results. May be repeated for credit up to 3 units. Prerequisite: qualified offer of employment and consent of department. Prior approval by Math Department is required; you must contact the Math Department's Student Services staff for instructions before being granted permission to enroll.
Terms: Aut, Win, Spr, Sum
| Units: 1
| Repeatable
3 times
(up to 3 units total)
Instructors:
Conrad, B. (PI)
MATH 199: Independent Work
For math majors only. Undergraduates pursue a reading program; topics limited to those not in regular department course offerings. Credit can fulfill the elective requirement for math majors. Approval of Undergraduate Affairs Committee is required to use credit for honors majors area requirement. Contact department student services specialist to enroll.
Terms: Aut, Win, Spr, Sum
| Units: 1-3
| Repeatable
3 times
(up to 9 units total)
Instructors:
Bump, D. (PI)
;
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
...
more instructors for MATH 199 »
Instructors:
Bump, D. (PI)
;
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Soundararajan, K. (PI)
;
Vakil, R. (PI)
;
Vasy, A. (PI)
;
White, B. (PI)
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