Freshmen seminar, Spring 2009 - N. Reshetikhin
office: 917 Evans Hall
email: reshetik@math.berkeley.edu
Seminars: Tuesday 1-3pm, 740 Evans Hall
Office Hours: Monday 4-5:30 pm,
email: reshetik@math.berkeley.edu
Seminars: Tuesday 1-3pm, 740 Evans Hall
Office Hours: Monday 4-5:30 pm,
Description
The goal of this course is an introduction to
probability and its applications. Flipping a coin
and estimating how many times it will land on one side
and how many times it will land on the other side
is a good illustration to how determinism enters into
randomness. We will start with this example (after a short
recollection of basic principles of probability).
We will compute the probability of a coin landing n times
on one side after N flipping for large n and N.
Then we will discuss random processes and an important class
them known as Markov processes. We will also discuss the
question known in probability theory as large deviations
and will see that some times there is an element of determinism
in randomness. We will consider some simple combinatorial examples
such as pile of squares to illustrate this phenomenon.
The seminar will start with a series of introductory lectures,
and then, towards the end of the seminar, students will give presentations.
Knowledge of elements of probability theory is desirable but
not required.
It is expected that during the seminar every participating student will give a short presentation on the subject of the seminar
(in a broad sense).
Suggested references may look rather advanced. Their goal
is to demonstrate where the seminar could go if we all would have
an appropriate prerequisites. We will use them as much as
reasonable.
Suggested References
1. Sheldon Ross, "A First Course in Probability",
Prentice Hall, 1998
2. Barry D. Hughes, " Random Walks and Random Environments", volume 1,Oxford Science Publications, 1995
2. Barry D. Hughes, " Random Walks and Random Environments", volume 1,Oxford Science Publications, 1995
Tentative syllabus
The syllabus will evolve as the seminar will go on. Below is a tentative (perhaps too ambitious) schedule and the list of topics. Corrections will be posted. It is very likely that the seminar will go much slower then outlined.Seminar 1
This is an introductory meeting. Grading policy.
Main subjects: random walks, random surfaces, ....
Will start the detailed discussion of flipping coins:
how the outcome is distributed for large n and N, where
n is the number of heads and N i the number of flips.
Seminar 2
We will finish the coins and will start
discussing random walks.
Seminar 3
More random walks
Seminar 4
Random surfaces.
Seminar 5
to be posted
Seminar 6
to be posted