We will discuss various aspects of knot theory, concentrating on polynomial invariants of knots. Such invariants associate a polynomial to an embedded knot which does not depend on the particular presentation of it. The Jones invariant of knots and the categorical version of it, known as the Khovanov invariant, will be the main topic of the course. Khovanov?s invariant is a very strong invariant of the knot: it is shown by Mrowka and Kronheimer that if the Khovanov invariant of a knot is 1, then the knot is the unknot.

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This course will start from stochastic calculus, including Brownian motion, stochastic integrals, the Ito formula, Black-Scholes equations, analysis of diffusion processes, Girsanov transformation, Feynmann-Kac formula. Then we'll study applications in financial math, including Kolmogorov equations and derivative securities equivalent martingale measure, risk-neutral pricing, optimal stopping, options pricing, put-call parity, etc.

Examination of the Civil Rights Movement from the Brown v. Topeka decision to the rise of Black power. All the major organizations of the period, e.g., SCLC, SNCC, CORE, NAACP, and the Urban League. The impact on white students and the anti-war movement. (Gen.Ed. HS, U)

Examination of the Civil Rights Movement from the Brown v. Topeka decision to the rise of Black power. All the major organizations of the period, e.g., SCLC, SNCC, CORE, NAACP, and the Urban League. The impact on white students and the anti-war movement. (Gen.Ed. HS, U)

Examination of the Civil Rights Movement from the Brown v. Topeka decision to the rise of Black power. All the major organizations of the period, e.g., SCLC, SNCC, CORE, NAACP, and the Urban League. The impact on white students and the anti-war movement. (Gen.Ed. HS, U)

Examination of the Civil Rights Movement from the Brown v. Topeka decision to the rise of Black power. All the major organizations of the period, e.g., SCLC, SNCC, CORE, NAACP, and the Urban League. The impact on white students and the anti-war movement. (Gen.Ed. HS, U)

Examination of the Civil Rights Movement from the Brown v. Topeka decision to the rise of Black power. All the major organizations of the period, e.g., SCLC, SNCC, CORE, NAACP, and the Urban League. The impact on white students and the anti-war movement. (Gen.Ed. HS, U)

Examination of the Civil Rights Movement from the Brown v. Topeka decision to the rise of Black power. All the major organizations of the period, e.g., SCLC, SNCC, CORE, NAACP, and the Urban League. The impact on white students and the anti-war movement. (Gen.Ed. HS, U)

Basic concepts of linear algebra. Matrices, determinants, systems of linear equations, vector spaces, linear transformations, and eigenvalues. Prerequisite or corequisite: MATH 132, or 136, or consent of instructor. (Gen.Ed. R2)

[Note: Because this course presupposes knowledge of basic math skills, it will satisfy the R1 requirement upon successful completion.]