Homework assignments, lecture notes and other useful things

Homework set no. 1	- solutions
Homework set no. 2	- solutions
Homework set no. 3	- solutions
Homework set no. 4	- solutions
Homework set no. 5	- solutions
Homework set no. 6	- solutions
Homework set no. 7	- solutions
Homework set no. 8	- due: 11/24/09
Lecture notes	- draft of notes for part I of the course (10/14/09)
Lecture notes 2	- draft of notes for part II (11/2/09)
Lecture notes 3	- early draft for part III (11/20/09)
Probability distributions	- summary of important distributions in probability

General Information

Instructor details:	Dan Romik
	Mathematical Sciences Building 2218
	tel: 530-752-1087
	email:
	For more information go to my home page
Lectures:	MWF 0210-0300 at Giedt 1007
Discussion section:	T 0310-0400 at Olson 205
Office hours:	MW 0310-0400 (at my office, MSB 2218), or by appointment
T.A.:	Eunghyun Lee (his office hours: T,R 0130-0230 at MSB 2141)
Textbook:	Probability: Theory and Examples, 3rd ed. by Rick Durrett (2005); see below for some other reading suggestions.

Grading Policy

The final grade will be determined based on:

Homework	50%
Final exam	50%

Homework will be given approximately every week and will be due within 7 days. Late homework submissions will not be accepted. The two lowest homework assignment grades will not be taken into account when computing the homework part of the final grade. You may discuss homework with me and with other students, but everything you turn in should be your own work.

The final exam will be a take-home exam. On this exam you must work alone and use only your notes from the class.

At my sole discretion, I may give an additional grade bonus to students who contribute to Wikipedia entries on topics related to probability theory. The contributions must be documented, i.e., it should come from a registered Wikipedia user and not from an anonymous IP address. Please consult me if you intend to do this, since most Wikipedia entries on important results of probability theory are already fairly extensive and I may have suggestions on possible entries that are missing or that could use additional work.

Syllabus

The course will be largely based on the first few chapters of the book "Probability: Theory and Examples" by Rick Durrett. Topics will include:

• Probability spaces, measure-theoretic background
• Random variables, distribution functions, examples of special distributions
• Independence
• Expected values
• Weak and strong laws of large numbers
• The Gaussian distribution and the Central Limit Theorem
• If time permits, some topics from the following: Infinite series of independent random variables; the law of the iterated logarithm; Poisson limiting law.

Course prerequisites: A solid working knowledge of advanced calculus. Measure theory will be reviewed in a self-contained manner at the beginning of the course and as the need arises, but some additional reading may be advisable if you've never seen it before. Here are the topics from measure theory: measurable spaces, Lebesgue integral, Lebesgue measure in R^d, monotone and dominant convergence theorems, Fubini's theorem. Basic combinatorics, such as permutations, combinations, selections with and without replacement.

Supplementary reading

The following books contain roughly the same material as Durrett's book, and may appeal more to some readers.

• D. Williams, Probability with Martingales (1991)
  (Roughly equal in scope to Durrett and perhaps slightly less taxing to read)
   
• L. Breiman, Probability (1968)
   
• W. Feller, An Introduction To Probability Theory and Its Applications, Vol. I (1968) and Vol. II (1971)
  (an encyclopedic work that contains much more than is required for the class, but very good for developing intuition).