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Aut2003: MAP6472 5026 PROB.&.POTEN.THEO.1 MWF2 LIT217

Probability Theory

This branch of mathematics is the only one, I believe, in which good writers frequently get results entirely erroneous. ... It may be doubted if there is a single extensive treatise on probabilities in existence which does not contain solutions absolutely indefensible.
in Popular Science Monthly (1878).

Welcome. Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the ChecklistThe checklist (pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students). We have a Syllabus (pdf).

For the first semester we used Probability.

Author: Leo Breiman ISBN: 0-89871-296-3
Year: 1992 Publisher: SIAM
Photo of text cover
For the second semester we decided to switch to Billingsley's text (see below).
Those enrolling in the 2nd semester only need the Billingsley.

[Image: Coffee cup] Homework and reading, so far.

I'll assign HW in class, and also via the mailing list. Sarva has kindly agreed to type up the class problems (ps), statements of HW that is NOT from our textbook. Sarva is also maintaining the Mind Benders (ps) which have no fixed due-date, and which often have a prize attached. A solution to the second Mind Bender (Wanna quit now?) wins a prize of $1. The prize for the third mind-bender (Can a broken stick form a triangle?) is a Linear Algebra text, Transform Linear Algebra.
    The Soldier Problem (pdf), is stated here.
    Sarva's home page [as of 2015] (Saravanan Vijayakumaran) has other useful information.

Some Solutions

Here are some solutions by Sarva (ps). Alas, I no longer have the solns by Dan Warren.
    I'd like to see other students solutions here too. You can either email me a link to a webpage that you maintain, OR if you have an account at UFMath, then you can email me the full pathname of the postscript file and make sure that the file is world-readable.
    A third possibility is for you to contact Dan or Sarva and ask if one of them could post your solution(s).

An expanded version of my Skorokhod notes (pdf) is now available.

A preliminary version of Conditional probability & conditional measures (pdf) is available. It now has a proof of Doob's optional sampling theorem for Martingales, and Doob's proof of the MCT. It also also some solutions from the below exam; in particular, it has the Doob Decomposition thm for subMGs.

I have augmented the Markov chain notes (pdf).

The Checklist (pdf) gives pointers on what I consider to be good mathematical writing; which will be useful for this enjoyable exam on martingales (pdf). The exam was due no later than 4PM on Friday, 12Dec2003 .

Spr2004: MAP6473 4810 PROB.&.POTEN.THEO.2..MWF7 FLO100

Probability Theory II

The second semester will be in the Statistics building Griffin-Floyd Hall in room 100; hooray, it has four blackboards.

Our textbook is Probability and Measure (3rd edition).

Author: Patrick Billingsley ISBN: 0471007102
Year: 1995 Publisher: Wiley, John & Sons
Photo of text cover

Here are the h1a (pdf). and h1b (pdf) homework assignments.

Problem-set h2 (pdf) is due Monday, 26Jan2004.

Homework h6 (pdf) is due Friday, 20Feb2004.

Here is the enjoyable exam mostly on characteristic fncs (pdf) for your thinking pleasure.

Please send me corrections to this claimed solution sheet to exam B (pdf)

Possible topics:

  1. Continuing Martingale (Gambling systems) theory. Markov theory.
  2. An introduction to Brownian motion.
  3. Entropy, and the uses of entropy in Probability theory.
  4. Dynamical-systems ideas in Probability theory.
  5. Probabilistic number theory (Erdos style).
  6. Probabilistic methods in combinatorics. (The Uneducated Soldiers Problem is an example.)

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____End: Probability Theory