# CME 308: Stochastic Methods in Engineering (MATH 228, MS&E 324)

## Spring Quarter, 2018

All course materials are distributed through Canvas.

Remark: Students wishing to take the course who find that the enrollment cap for CME 308 has been exceeded should consider registering in either Math 228 or MS&E 324 (which have uncapped enrollments).

## Course Information

Intructor |
Professor Peter W. Glynn |
---|---|

Office |
Huang Engineering Center, Room 359A |

E-mail |
glynn at stanford dot edu |

Lectures |
Tue, Thu 10:30 AM - 11:50 AM at 380-380Y |

Office Hours |
TBD |

Course Assistant |
Alex Infanger | Zeyu Zheng |
---|---|---|

E-mail |
alexinf at stanford dot edu | zyzheng at stanford dot edu |

Office Hours |
TBD | TBD |

Location |
TBD | TBD |

## Course Description

This graduate level course is intended to give students a broad sense of the different mathematical and computational tools and models available to analyze systems in which uncertainty is present. The key ideas underlying stochastic analysis will be presented and illustrated using various applications chosen from engineering, the physical sciences, and economics. This course is intended both to introduce students to the subject matter at an advanced level and to offer an entry point into the many other high-level stochastics courses that Stanford offers.

## Prerequisites

Students should have a reasonable background in real variables (e.g. limits, epsilon-delta arguments, etc) and linear algebra (e.g. vector spaces, matrices, eigenvalues, eigenvectors, diagonalization). In addition, I will be assuming that students enter the class with some basic preparation in probability (Knowledge of sample space, events, probability, conditional probability, independence, random variables, jointly distributed rvs, probability mass functions, probability density functions, expectations, the law of large numbers, central limit theorem).

## CME 308 vs CME 298

The main target group of CME 308 is ICME PhD students and the ICME MS students in MCF and DS. Compared to CME 298, it moves at a faster pace, covers a wider span of topics, and provides more depth. This naturally means that 308 has a bigger emphasis on proofs than 298, as it is also meant to prepare students for more theoretical classes (e.g. Stats 300 A, B, C, Stats 310 A, B, C) or to do research in areas related to statistics and probability. Historically, people without an adequate math background have found parts of this class hard and time consuming in the past.

CME 298 is more engineering/applications oriented, with fewer math details and simpler homework problems. Because of the applications focus, this class will contain some material not covered in CME 308. However, the knowledge gained from 308 would be sufficient to understand this material. For people who are only interested in directly applying statistics and probability, 298 is usually the better choice.

## Suggested References

Probability and Random Processes by Geoffrey R. Grimmett & David Stirzaker (Oxford)

A Course in Large Sample Theory by T.S. Ferguson (Springer 1996)

Statistical Inference by George Casella and Roger L. Berger (Duxbury)

Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues by Pierre Bremaud (Springer)

See also Math 136 Lecture Notes by Amir Dembo (for a treatment on probability theory)

## Text Book

There is no required textbook for this class.

## Assignments

There will be assignments due roughly every two weeks. Collaboration among students is encouraged. You should feel free to discuss problems with your fellow students (please document on each assignment with whom you worked). However, you must write your own solutions, and copying homework from another student (past or present) is forbidden. The Stanford Honor Code will apply to all assignments, both in and out of class.

## Exams

Midterm exam: in-class, date to be announced

Final exam: Monday, June 11th, 12:15-3:15pm, (Please make sure you can
physically attend the final exam.)

## Grading

The course grade will be 25% homework, 25% midterm and 50% final.

## Materials

All course materials will be distributed via Canvas.

Last modified Tuesday, 03-Apr-2018 10:09:43 PDT