# Syllabus

**6.041 PROBABILISTIC SYSTEMS ANALYSIS
6.431 APPLIED PROBABILITY
Fall 2002**

Included in this opening day handout:

- General Information (please digest it before next lecture).
- Statement on Collaboration, Honesty and Some Other Stuff.

Welcome to 6.041 / 6.431! This fundamental subject is concerned with the nature, formulation, and analysis of probabilistic situations. No previous experience with probability is assumed.

Undergraduates must register for 6.041. Graduate students must register for 6.431. Graduate (G) credit is given for 6.431, which includes full participation in 6.041.

We have three types of class sessions: lectures, recitations, and tutorials. For undergraduates (6.041), your recitation instructor is also your tutorial instructor.

**LECTURES** serve to introduce new concepts. They have
an overview character, but also include some derivations and motivating
applications. Lectures are twice a week and 1 hour a session.

**RECITATIONS AND TUTORIALS** will be assigned in
response to the tutorial schedule forms you complete and turn in
immediately at the end of the first lecture. In recitation, your
instructor elaborates on the theory, solves new examples, and answers
your questions about them. In tutorial, you discuss and solve new
examples with a little help from your classmates and your instructor.
Tutorials are active sessions to help you develop confidence in
thinking about probabilistic situations in real time. Tutorials are
mandatory.

**DISREGARD RECITATION ASSIGNMENTS PROVIDED BY THE REGISTRAR.**
Our actual recitation and tutorial assignments will be posted on the
course's web page. We will also have copies of these assignments on
second lecture date. Recitations and tutorials begin during the next
week after second lecture. Requests for a change of tutorial hour
must include a revised tutorial schedule form, and should be submitted
promptly to the Head TA by second lecture date.

**INDIVIDUAL MEETINGS WITH YOUR RECITATION INSTRUCTOR**
are encouraged. Be sure your instructor explains a simple way to
arrange such meetings during your first recitation and tutorial. If you
have already made a reasonable effort, your instructor will be glad to
help you with homework problems, before or after they are due. (New
problems, not homework problems, are discussed in recitations and
tutorials).

**ADMINISTRATIVE MATTERS** will generally be attended
to by our Head TA. Most matters, such as reasons for missing tutorials,
are best discussed with your own instructor. Graded homework problems
and exams will usually be returned to you by your instructor. Copies of
material distributed in lecture may be found on the course's web page.

**READINGS AND REFERENCES.** Lectures, recitations, tutorials and homework will be based primarily on the text book: D. Bertsekas and J. Tsitsiklis, *Introduction to Probability*.

Additionally, the following books will be on reserve in the Barker
Engineering Library. They cover many of the topics in this course,
although in a different style. You may wish to consult them to get a
different perspective on particular topics:

1. A.Drake, *Fundamentals of Applied Probability Theory*.

2. A. Leon Garcia, *Probability and Random Processes for Electrical Engineering*.

3. S. Ross, *A First Course in Probability*.

4. R.D. Yates and D.J. Goodman, *Probability and Stochastic Processes*.

The books by Drake and Yates & Goodman are closest to this course.
The book by Ross has a fair number of more challenging examples.

**HOMEWORK PROBLEMS AND READING ASSIGNMENTS** will
be handed out and will be due in lecture the following week. Solutions
will be handed out on the day homework problems are due.

We expect you to turn in all homework assignments on time. Late homework will not be accepted. As will be explained in class, we grade homework, but only superficially. We do distribute thorough solutions. Your TA is available to discuss your work with you, both before and after it is due.

You may encounter difficulty figuring out where your own solution of a homework problem went astray. There are many ways to approach most probability problems. Just agreeing with our problem solutions may not explain why your approach didn't work. Please let your instructor help you whenever such issues occur.

**QUIZZES AND EXAMS.** There will be two quizzes,
during regular class hours (1 hour). There will also be a comprehensive
final examination during finals week.

**GRADES** will be determined by your work in all aspects
of this subject. After all of your tutorials, homeworks, quizzes, and
final exam, your instructor has a pretty good idea of your
understanding of the material. Final grades are assigned in a meeting
by the entire staff. Your instructor is not allowed to discuss likely
final grades with you.

The "formula'' that will be used to determine your grade is:

First Quiz: 18%

Second Quiz: 24%

Final: 38%

Homework: 10% (Based on your best 9 out of 10 homeworks)

Tutorial attendance: 5% (Half a point per tutorial attended, up to a maximum of 5 points)

Tutorial performance: 5% (Your instructor's assessment)

**STUDY HABITS.** In order to get the most out of the
course, try to stay ahead. During each weekend, review the material
covered in the lectures of the preceding week. Read the assigned
material, but at a minimum, make sure to review the transparencies
handed out at lecture. This way, recitations and tutorials will be much
more informative and meaningful.

We encourage working together whenever possible - homework, working
problems in tutorials, and discussing and interpreting reading
assignments. Talking about things is a great way to learn.

Regarding homework, the following is a fruitful (and acceptable) form
of collaboration: discuss with your classmates possible approaches to
solving the problems, and then have each one fill in the details and
write her/his solution independently. An unacceptable form of dealing
with homework is to copy a solution that someone else has written.

Honesty is important, and the classroom is no exception. We expect students to adhere to basic, common sense concepts of academic honesty. Presenting another's work as if it were your own, or cheating in exams will not be tolerated. The appropriate authorities at MIT will be notified in cases of academic dishonesty.

After an exam has been returned, we give students a limited amount of time to resubmit their quizzes for regrades if they feel that there is a problem with the grading on their exam. If you submit an exam to be regraded, do not write anything at all on the exam booklet. Please write a note on a separate sheet of paper. Any attempt to modify an exam booklet is considered a serious breach of academic honesty. We photocopy a substantial fraction of the exams before they are returned and the probability of catching a change is high.

Your recitation instructor will explain how to reach her or him on reasonably short notice. Staff members will also reserve some uninterruptible, safe time for their other activities. Optional quiz reviews are presented uniformly for the entire class, not for individual sections. Similarly, any supplementary handouts will be identical for all sections.

Special things happen to many of us during the semester. If any are likely to affect your performance, please consider keeping your instructor, the Head TA, and/or the lecturer aware of your situation. If you have quizzes immediately before or after our quizzes or cannot a quiz, please contact the Head TA as soon as possible.