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Aut2003: MAP6472 5026 PROB.&.POTEN.THEO.1 MWF2 LIT217
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.
C. S. PEIRCE,
in Popular Science Monthly (1878).
Our Teaching Page
has useful information for students in all of my classes.
It has my schedule,
and Usually Useful Pamphlets.
One of them is the
which gives pointers on what I consider to be good mathematical
Further information is at our
(I email this private URL directly to students).
We have a
For the first semester we used
|Author: ||Leo Breiman
For the second semester we decided to switch to
Those enrolling in the 2nd
semester only need the
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
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
Soldier Problem (pdf)
is stated here.
page [as of 2015]
(Saravanan Vijayakumaran) has other useful information.
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)
It now has a proof of Doob's optional sampling theorem for Martingales,
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).
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
Friday, 12Dec2003 .
Spr2004: MAP6473 4810 PROB.&.POTEN.THEO.2..MWF7 FLO100
The second semester will be in the Statistics building
in room 100; hooray, it has four blackboards.
Our textbook is Probability and
Measure (3rd edition).
|Author: ||Patrick Billingsley
||Publisher: ||Wiley, John & Sons
Here are the
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)
- Continuing Martingale
(Gambling systems) theory. Markov theory.
- An introduction to Brownian motion.
- Entropy, and the uses of entropy in Probability theory.
- Dynamical-systems ideas in Probability theory.
- Probabilistic number theory (Erdos style).
- Probabilistic methods in combinatorics.
Uneducated Soldiers Problem is an example.)
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