MA 611 A, Fall 2004 (Stevens Institute of Technology)

MA 611, PROBABILITY, Fall 2004

Communications to the class

The final course grades are in. You can email me or see me (no later than Dec. 22) to learn your final exam grade.

Course information

Brief description: This will be a course on the mathematical formulation of elementary probability theory. While the purpose of the class is to give the students a set of notions and concepts that find application in the real world (and we will see many concrete, if simple, examples), the methods will be those of rigorous mathematics.

Time & Place: Monday 6:15--8:45, Burchard 118.

Lecturer: Marco Lenci. (Office: Kidde 219B. Tel.: x-5453. E-mail: mlenci@math.stevens.edu)

Office hours: The official office hours are posted here, but students are welcome to meet me at other times as well (by appointment).

(Tentative) syllabus:

Foundational questions
Discrete probability spaces
Conditional probability and independence
Random variables
General probability spaces
Expectation, moments, and their properties
Determining distributions of random variables
Rudiments of measure theory
Sequences of independent trials
Law(s) of large numbers and applications
The Moivre-Laplace Theorem
The normal distribution
Other notable distributions
Convergence of distributions
The characteristic function
The Central Limit Theorem
Large deviations
Finite Markov Chains
Random walks in the lattice

Textbooks:

In general, for a graduate course, I don't like to single out a book as the textbook. Graduate students are expected to use a good deal of independence in their study and be able to approach more than one book (keeping the notes from class as a reference). Plus, the course will be rather introductory and you are sure to find, in the library or elsewhere, many books that cover most of the material.

However, since it is the University policy to have an official textbook, that will be

Ya. G. Sinai, Probability: An Introductory Course, Springer-Verlag, 1992,

which comes closest to my approach to this course. To mention a few other texts,

K. L. Chung, A course in probability theory, Harcourt, Brace & World, 1968

is very easy but perhaps too elementary;

A. F. Karr, Probability, Springer-Verlag, 1993.

seems rather good, but I don't it know it very well. As for heftier and more complete references,

   P. Billingsley, Probability and Measure, Wiley, 1986.
   W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, Wiley, 1968
   A. N. Shiryayev (sometimes spelled Shiriaev), Probability, Springer-Verlag, 1984.

Homework, exams and grading policy:

There will be two types of homework in this class: occasional homework given while lecturing, and officially assigned homework. The first type can be worked out by the student at his/her discretion and possibly given to me for comments. The second type will consist of two homework sheets, each containing a short list of problems, given at two different times during the semester. These will have a due date and will be graded, the grade counting in (small) part towards the class grade.

Also, there will a midterm exam and a final exam, whose dates we will agree on during the semester.

Both the official homework and the exams will receive letter grades, to emphasize that the final grade for the class will depend more on the progress shown by the student than on his or her average (not that this should give anybody license to flunk an exam!).

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