## 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.

Last offered: Spring 2015
| UG Reqs: GER:DB-Math

## 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 for credit

Instructors:
Soundararajan, K. (PI)
;
Vakil, R. (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
| Units: 1-6
| Repeatable for credit

Instructors:
Boyd, S. (PI)
;
Cohen, R. (PI)
;
Conrad, B. (PI)
;
Eliashberg, Y. (PI)
;
Vasy, A. (PI)
;
Venkatesh, A. (PI)
;
Yun, Z. (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 for credit

Instructors:
Bump, D. (PI)
;
Church, T. (PI)
;
Fox, J. (PI)
;
Ionel, E. (PI)
;
Mazzeo, R. (PI)
;
Vakil, R. (PI)
;
Vasy, A. (PI)

## MATH 205B: Real Analysis

Point set topology, basic functional analysis, Fourier series, and Fourier transform. Prerequisites: 171 and 205A or equivalent.

Terms: Win
| Units: 3

Instructors:
Mazzeo, R. (PI)
;
Raju, C. (TA)

## MATH 205C: Real Analysis

Continuation of 205B.

Last offered: Spring 2009

## MATH 210A: Modern Algebra I

Basic commutative ring and module theory, tensor algebra, homological constructions, linear and multilinear algebra, introduction to representation theory. Prerequisite: 122 or equivalent.

Terms: Aut
| Units: 3

Instructors:
Bump, D. (PI)
;
Klang, I. (TA)

## MATH 210B: Modern Algebra II

Continuation of 210A. Topics in Galois theory, commutative algebra, and algebraic geometry. Prerequisites: 210A, and 121 or equivalent.

Terms: Win
| Units: 3

Instructors:
Yun, Z. (PI)
;
Sauermann, L. (TA)

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