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The term "Monte Carlo" refers to a broad class of numerical algorithms which rely on repeated random sampling. Since its beginnings in the late 1940s at the Los Alamos National Laboratory, Monte Carlo has continued to gain in importance in scientific use. The continued growth of computing power coupled with a drastic decrease in price in the last decade, means that Monte Carlo methods are now more practical than ever.

In this course, we will discuss what Monte Carlo methods are, and we will look at their varied applications. The three main topics we will cover are (a) random number generation, (b) "basic" Monte Carlo integration, including variance reduction techniques etc. and (c) the bootstrap. If time permits, we will also consider (d) Markov chain Monte Carlo (MCMC). Applications will be taken from various sciences, including statistics, operations research, and actuarial science.

This course is atypical in that a significant portion of the course will be spent in the computer lab, using the statistical software R to perform Monte Carlo simulations. Previous experience with computing will be an asset, but is not required. Attendance is not optional.

DISCLAIMER: The prerequisites for this course are unfortunately minimal. However, this is a fourth year mathematics course, and will be taught as such. Mathematical maturity will be expected.

** Instructor: ** Hanna Jankowski
** E-mail: ** hkj[at]yorku.ca

Please include "[4931]" in the subject of your e-mail. Plain text messages only, no html, no "texting".

** Office: ** N621B Ross

** Office hours: ** 9:30-10 T/R, or by appointment. No
drop-ins, please.

** Textbooks/Resources: **

- Introducing Monte Carlo Methods with R by Robert and Casella [REQUIRED]
- All of Nonparametric Statistics by Wasserman [REQUIRED]
- R [REQUIRED]
- Resources to help you learn R [REQUIRED]
- Mathematical Statistics and Data Analysis by Rice
- Bootstrap Methods and their Application by Davison and Hinkley