Fall 2004

MTHS 635
Elements Of Probability


09/13/2004 - 12/18/2004
Monday 07:00 PM - 09:30 PM

Science Tower 139

In this introduction to the basic ideas of probability theory, our objective is to learn how to convert informal descriptions about probabilities into mathematical statements. We then learn to use these statements as a basis for calculation and deduction. The major themes are the passage from the discrete to the continuous, and the passage from randomness to order. These themes are exemplified by the theorems that describe the average or typical behavior of repeated random events. The main example is the fact that repeated independent events organize themselves (under suitable conditions) according to the normal and Poisson distributions.

We begin with a study of the basic formalism of probability theory: outcome spaces and distributions on them, conditional probabilities, and independence. We move on to the binomial distribution and talk about its relation to the normal and Poisson distributions. We discuss random variables and the associated concepts such as expected value and standard deviation, first in the case of discrete distributions, and then for continuous distributions.

Problem solving is an essential part of this course. There will be regular homework assignments that include both computational exercises and more conceptual problems.

Students are expected to be comfortable with mathematics at the level of typical high school curricula. In particular, the natural logarithm and exponential functions will play a central role. Some ideas from calculus will appear, but no prior experience with them will be required.

A syllabus for this course is available at:

Adam Fieldsteel (A.B. Brown University; Ph.D. University of California, Berkeley) is professor of mathematics. His research focuses on ergodic theory and topological dynamics, and his recent publications include: (with A. Blokh), "Sets that force recurrence," Proceedings of the American Mathematical Society (2002); (with K. Dajani), "Equipartition of interval partitions and an application to number theory," Proceedings of the American Mathematical Society (2001); (with R. Hasfura), "Dyadic equivalence to completely positive entropy," Transactions of the American Mathematical Society (1998). Click here for more information about Adam Fieldsteel.


Consent of Instructor Required: No

Format: Seminar

Level: GLSP Credits: 3 Enrollment Limit: 18

Texts to purchase for this course:
Jim Pitman, PROBABILITY, 1999, (Springer-Verlag Telos), Hardcover


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