Please note:  Non-NYU students who wish to register for summer session graduate mathematics courses will apply as summer non-degree students through the Graduate School of Arts and Science (GSAS) at http://gsas.nyu.edu/object/grad.app.summer Applicants must pay close attention to the prerequisite(s) for the course(s) of their choice and make a decision about their eligibility to apply for summer graduate mathematics courses.  When in doubt, please contact the course instructor .

Please also note that meeting the prerequisites does not, in itself, guarantee that an offer of admission will be made by the Department.


Course Descriptions: Summer Session 2016

Course Schedule

Undergraduate

Graduate


MATH-GA 2901  BASIC PROBABILITY

May 23 - July 5
Tuesday, Thursday 6:00–8:20 p.m.
Credits: 3 points
Instructor: Robert Thompson

Prerequisites: Single variable and multivariable calculus, including sequences and series, partial derivatives and multiple integrals.

The text for this course is Probability and Random Processes, 3rd edition, by Geoffrey Grimmett and David Stirzaker, Oxford University Press. We will cover the first five chapters and portions of the sixth and thirteenth chapter of the text. Topics will include probability spaces, random variables, probability distributions, generating functions, law of large numbers and the central limit theorem, random walks, discrete and continous Markov processes. Homework will be due once a week (and will be put up on the board in class and posted on the instructor's website). We will have a one hour midterm exam, announced a week in advance. There will be NO MAKEUPS. The final exam will be cumulative, but skewed toward the last half of the term.

For more information about the Basic Probability course, please visit the website: http://math.hunter.cuny.edu/thompson/NYUprobability

Text: Grimmett, G.R., & Stirzaker, D.R. (2001). Probability and Random Processes (3rd ed.). New York, NY: Oxford University Press.


MATH-GA 2902 STOCHASTIC CALCULUS

May 23 - August 16
Tuesday, 6:00-8:20 p.m.
Credits: 3 points
Instructor: Alexey Kuptsov

Prerequisite: MATH-GA 2901 Basic Probability or equivalent.

Review of basic probability and useful tools. Bernoulli trials and random walk. Law of large numbers and central limit theorem. Conditional expectation and martingales. Brownian motion and its simplest properties. Diffusion in general: forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus. Feynman-Kac and Cameron-Martin Formulas. Applications as time permits.

Recommended Text: Durrett, R. (1996). Probability and Stochastics Series [Series, Bk. 6]. Stochastic Calculus: A Practical Introduction. New York, NY: CRC Press.


Revised January 2016