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Title: Introduction to Probability Theory
Course: MAT 570
Section: 75528
Credits: 4
Semester: Spring/Summer, 1996
Room: 116 State
Hall
Computer Lab: 31 State Hall
Time: MW 5:30-7:35 PM
Professor: Robert Berman
Office: 1105 Faculty Administration Building
e-mail: rberman@math.wayne.edu
URL http://www.math.wayne.edu/~rberman
Phone: 313-577-2494
Fax: 313-577-7596
Office Hours: Monday, Wednesday 4:25-5:25 PM, or by appointment
made in class, by phone, or by e-mail.
Graduate Assistant: Dan Mayernik
Office: 1110 Faculty Administration Building
e-mail: mayernik@math.wayne.edu
URL http://www.math.wayne.edu/~mayernik
Phone: 313-577-2609
Office Hours: Monday, Wednesday 3:30-5:25 PM in 31 State, or
by appointment made in class, by phone, or by e-mail.
Required:
[P] Jim Pitman. Probability,
Springer Verlag, 1993, ISBN 0-387-97974-3.
[S]David Schneider. An Introduction
to Programming Using Visual Basic®, Prentice Hall, 1995, ISBN 0-13-191263-1.
Optional:
[BM] J. Bradley and A. Millspaugh,
Programming in Visual Basic, Version 4.0Irwin, 1996, ISBN 0-697-20273-9.
[S2] David Schneider. Microsoft
QBasic® with an Introduction to Microsoft Visual Basic® 3rd
Ed., Dellen MacMillan 1994, ISBN 0-02-407734-8.
This course is intended to give an elementary introduction to the mathematical theory of probability. It is designed to lay the groundwork for applications to a wide range of areas in the sciences and engineering as well as the more advanced study of probability and statistics. Some algorithms relating to the theory will be implemented in the BASIC programming language Microsoft Visual Basic®. Students will be expected to understand these and to create similar programs as part of the homework.
The course is a 1-semester course in probability aimed at mathematics and science majors who have completed 3 semesters of calculus. It will cover as much of the material in Chapters 1-6 of the main text [P] as time permits. Topics include probability spaces, conditional probability, independence, discrete and continuous random variables; expectations, the normal, Poisson, and binomial distributions; joint, marginal and conditional distribution functions; the law of large numbers, and central limit theorems. Computer material will come from handouts as well as the texts [S] and [BM], and will deal with calculations and simulations related to the theory.
Final grades will be assigned according to the traditional scale:
A valid excuse (according to University rules) is necessary if an exam must be missed. Only in such cases can make-up exams be given. Both the midterm and final will be given in the usual room and time, and will consist of approximately 10 problems. Tentatively, the exam schedule is:
Midterms will be returned on the following Monday, June 24. The final exams will be graded and final grades assigned by Friday, August 2. The university sends out grades within a month. If you give me a stamped, self-addressed envelope I will be happy to send you your grade as soon as I determine them.
The goal in the computing portion of the course is to use Microsoft Visual Basic to
The following software is available in the lab and is supported by the "Microsoft Instructional Lab Grant":
The lab will also be available during hours that will be announced. The necessary software is installed on these computers. Programming examples and problems will be posted on the World Wide Web (WWW) and can be accessed through the Computer Examples and Problems Index.
Function
Approximation: Assignment 0
The
Birthday Problem: Assignment 0.5
Using
'RND' to simulate simple probability experiments: Assignment
1
Applications
of Bayes' Formula: Assignment 1.5
Bernoulli
Trials: Assignment 2
The
Normal Approximation and Confidence Intervals: Assignment 2.5
Graphing
and the Law of Large Numbers (under construction)
Naming Conventions