We will formulate and prove some of the major results of
classical probability. These will include the ``laws of large
numbers" (both weak and strong), the ``central limit theorem", and
the ``law of the iterated logarithm". All of these results
originated in the mathematics of gambling, in efforts to predict
the frequency of (say) heads in repeated tosses of a coin. They
answer questions like how many heads there will be 'on average',
and how far from the 'average' values the actual frequencies are
likely to be. In answering these questions, we will develop
useful tools such as characteristic functions, and will consider
various modes of convergence for random variables. We will study
important classes of distributions, such as stable and infinitely
divisible laws. We may also study martingales.
At a more advanced level, the mathematical foundation of
probability is a subject called measure theory. This will not be
required for our course. Instead, we will merely take from measure
theory the technical results we shall need, and proceed to their
interesting probabilistic consequences. Further study of measure
theory is possible at the graduate level.
The prerequisite is an introductory course in probability. A
course in real analysis would be helpful, but is not required.
MATH4030.03 is crosslisted with MATH6600.03.
Starting in 1996-1997, MATH3030.03 will be the required probability
The text will be "Probability and Random Processes", by Grimmett
Prerequisites: AS/SC/MATH2030.03 or AS/SC/MATH3030.03
Coordinator: T. Salisbury