**Instructor:**Richard Laugesen**e-mail:**laugesen@illinois.edu**Homepage:**`www.math.uiuc.edu/~laugesen`

**Office:**376 Altgeld Hall**Phone:**333-1329**Class meets:**MWF 3-4pm, in 347 Altgeld Hall**Final exam:**1:30-4:30pm Wednesday 10 May**Office Hours:**Mon 4-5 (from Feb 6), Tue 4:30-5:30, Fri 2-3, and by appointment at other times

- the basic limit theorems (the law of large numbers, large deviations and the central limit theorem);
- martingales and their applications;
- random walks;
- Markov chains;
- and if time permits, Brownian motion, and the construction of Wiener measure.

**Text:** *Probability: Theory and Examples*, 3rd Edition (2004), by
Richard Durrett. We cover most of Chapters 1-5.

Two other other useful texts are on reserve at the Mathematics Library:

S. Ross, *A First Course in Probability*, 6th
edition, covering undergraduate probability with no measure theory

P. Billingsley, *Probability and Measure*, 3rd edition

**Prerequisites:** Math 540 (measure theory) or consent of the instructor.

Homework | Due every week or two, to my office | 40% |

Test Information and Solutions | Friday 10 March, in class | 20% |

Exam Information | Wednesday 10 May, 1:30-4:30pm | 40% |

I encourage students to work together on the homework. But you must write up your own solutions in your own words, so that you really learn the material before the tests. Please write on the first page of your homework the names of all people with whom you discussed it (this is an ethical matter: "give credit where credit is due").

The test and exam are closed book (you may not use any written or printed materials, or any electronic devices).

Make up tests or exams will be given **only**
if you present written evidence, as soon as possible, that you did (or will
have to) miss an exam for a legitimate reason, e.g. illness or family
emergency. Travel and leisure plans are never a
legitimate reason. Late homework accepted only if you get an extension
from me.

There is no formula fixed in advance for turning your numerical score into a letter grade. But after the test, I will indicate approximate grade ranges so that you have some idea of how you are doing.

**IPROM Software.**
We might spend a day having fun with the free probabilistic simulation
software package Iprom, which
runs under Matlab.
Mathemtics students can run Matlab on the Mathematics department unix system,
and engineering students can install Iprom on their EWS account at
`www.math.uiuc.edu/iprom/ewsstart.html`

. (The download page also
gives a link for buying Matlab at the student price, if desired.)

**How to Succeed:**
Always re-work your lecture notes before the next class, checking every
step and filling in missing details.
Read the text as you re-work your notes - we cover only the most essential
points in class. Before each class, ask me about the
points you didn't follow in the last class!

Go over your HW solutions the day you get them back.

- Undergraduate handouts on the standard discrete probability densities and standard continuous probability densities, using notation from the text by S. Ross.