Mathematics 5010 - 1
Introduction to Probability
Fall 2004, The University of Utah
Dr. David A. Levin
Probability is a branch of mathematics, having
intrinsic interest of its own, but also having
powerful applications in computer science, finance,
genetics, electrical engineering, operations research
and industrial engineering, physics, economics, and
statistics, to name a few fields. It also has
applications within mathematics to fields such as combinatorics, analysis, and geometry.
In this class, you will learn how to calculate and estimate probabilities. Click here for more information.
Examples of questions we will learn how to answer:
(Under construction).
- Many applied problems can be modelled as simple random walks.
This is a random process which moves either up or down at each unit
of time according to a (possibly biased) coin flip.
What is the chance that such a walk reaches height b
before sinking to 0, when starting at a?
- Some algorithms are much slower in the worst case
than in the average case (quicksort, for
example). Can we use randomization to guard against
the worst case?
- Suppose you have available a noisy channel over which you
wish to communicate. What is the maximum data rate at which
you can reliably send data?
- Ordinarily, in the game of blackjack, the player is
payed 1.5 times her bet if she receives a blackjack,
an ace with a 10-valued card. Many single-deck games
on the Las Vegas strip now pay (6/5) times your bet
for a blackjack. How much worse is this version of the game?