This section contains detailed information about the course components. A list of topics covered in the course is available in the calendar section.

Course Meeting Times

Lectures: 2 sessions / week, 1 hour / session

Recitations: 2 sessions / week, 1 hour / session

Tutorials: 1 session / week, 1 hour / session


The prerequisite for 6.041 and 6.431 is 18.02, or a year of college level calculus for those with undergraduate degrees from other universities. Students who have not completed the prerequisite with a grade of A, B, C or P may not enroll.

6.041 and 6.431

Students intending to take the undergraduate version of the course need to sign up for 6.041, while those intending to take the graduate version should sign up for 6.431, which includes full participation in 6.041, together with some additional homework problems, additional topics, and possibly different quiz and exam questions.

6.041/6.431 has three types of class sessions: lectures, recitations, and tutorials. The lectures and recitations each meet twice a week. In addition, there will be a tutorial once a week, which is not mandatory, but is highly recommended.


Lectures serve to introduce new concepts. They have an overview character, but also include some derivations and motivating applications. You are expected to attend. Lectures are at 12-1 p.m. on Mondays and Wednesdays.

Study Habits

In order to get the most out of the course, try to stay ahead. By the weekend, make sure you have reviewed 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.

Make it a point to go to staff office hours if you have any questions or just want to chat about the course; we count on seeing you during the term! Also, it is a good idea to retain a copy of your homework solutions before you turn them in. This lets you compare them with our solutions right away, rather then waiting a week until the graded homework comes back to you.


Recitations meet on Tuesdays and Thursdays, and attendance is mandatory. In recitation, your instructor elaborates on the theory, works through new examples with your participation, and answers your questions about them. The recitation assignments will be based on the recitation and tutorial schedule forms you complete and turn in immediately at the end of the first lecture. The recitation assignments will be available in Rec #1 by 8 a.m., so that you can attend recitations. The recitation assignments will be available in the recitations section, and for the entire semester. Requests for a change of recitation must include a revised and complete listing of your schedule, with MIT course numbers accompanying any conflicts. Submit your revised schedule by email to the Head TA.


Tutorials for 6.041 and 6.431 meet on Thursday afternoons and Fridays, and will be assigned in response to the recitation and tutorial schedule form, within a few days. 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 not mandatory, but are highly recommended. Past students have found them to be very helpful. The TA who leads the tutorial you are assigned to, will be your first point of contact for questions on the problem sets. Tutorial assignments will be available in the assignments section. Requests for a change of tutorial must include a revised listing of your schedule, and should be submitted promptly by email to the Head TA.

Administrative Matters

Recitation and tutorial assignments will be handled by the Head TA. Scheduling of makeup exams are also handled by the Head TA. Copies of material distributed in lecture and tutorials can be found in the lecture notes and recitations sections, respectively. Other administrative matters, such as reasons for missing recitations and tutorials can be handled by discussion with your recitation instructor and assigned TA. Graded homework problems will be returned to you in your assigned tutorial.


The text for this course is Introduction to Probability, by Bertsekas and Tsitsiklis. Solutions to end-of-chapter problems are also available (PDF). We recommend that you print out these solutions. A few of these problems will be covered in recitation and tutorial. The remaining ones can be used for self-study (for best results, always try to solve a problem on your own, before reading the solution).

Bertsekas, Dimitri P., and John N. Tsitsiklis. Introduction to Probability. Belmont, MA: Athena Scientific Press, June 2002. ISBN: 188652940X.

Additionally, the following books are useful. 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:

Buy at Amazon Drake, A. Fundamentals of Applied Probability Theory. New York, NY: McGraw-Hill, 1988. ISBN: 0070178151.

Buy at Amazon Ross, S. A First Course in Probability. Upper Saddle River, NJ: Prentice Hall, 2005. ISBN: 0131856626.

Homework Problems

Homework problems will be handed out on Wednesdays and will be due at the beginning of lecture the following Wednesday (unless otherwise stated). Solutions are available in the assignments section. There will be a total of 11 homework's collected, with problem set 12 not handed in.

Since problem set solutions are available immediately after they are due, we cannot accept any late problem sets. In light of this strict policy we do allow everyone to miss one problem set for any reason. Thus your final problem set grade will be the average of your best 10 problem set grades (i.e. best 10 out of 11). Students who submit a note from the MIT Medical Department or other appropriate offices, will also be excused from additional problem sets. In such cases, all additional excused problem set grades will simply be dropped from the final average. Contact the EECS Administrator or the EECS undergrad office to find out more details on obtaining medical and/or personal notes. Also note that the first missed problem set is used as the one time free drop, regardless of the reason. Please see the head TA if you have further questions regarding this policy.

We grade homework, but often only a small, randomly chosen subset of the problems. 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 or TA help you whenever such issues occur. If the intent of a question on a problem set is unclear, you may e-mail your TA.

Quizzes and Exams

There will be two quizzes, the first on Wednesday, two days after Lec #10, 7:30-9:30 p.m., the second on Wednesday, seven days after Lec #15, 7:30-9:30 p.m. Both quizzes locations will be announced a week before the quiz. There will also be a comprehensive final examination during finals week, time and place to be announced.

Conflict Exams

Arrangements for conflict quizzes and final exams, and for special exams for special needs students will be made by the Head TA. The deadline to register for a conflict quiz or final exam is three weeks in advance of the quiz or exam date. If you miss a quiz or exam without prior authorization, you will need to provide the Head TA a written excuse from the MIT Medical Department or other appropriate office. We will not offer conflict quizzes or final exams to students who are absent without prior authorization or a written excuse from the Medical Department or the MIT administration.


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 and TA will have a pretty good idea of your understanding of the material. Final grades are assigned in a meeting by the entire staff. Your TA is not allowed to discuss likely final grades with you.

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

First Quiz 25%
Second Quiz 25%
Final Exam 35%
Homework (Based on your best 10 out of 11 homeworks) 10%
Interest, Effort and Mastery 5%

Interest, effort and mastery: 5% (Your recitation instructor's and tutorial TA's combined assessment, based primarily on their personal contact with you during recitations, tutorials and office hours.)

6.041/6.431 Statement on Collaboration, Academic Honesty, and Plagiarism

We encourage working together whenever possible – homework, working problems in tutorials, and discussing and interpreting reading assignments. Talking about the course material 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.

We discourage, but do not forbid, use of materials from prior terms that students may have access to. Furthermore, at the time that you are actually writing up your solutions, these materials must be set aside; copy-editing from a bible is not acceptable.

At the top of each homework you turn in, we expect you to briefly list all sources of information you used, other than the text, books on reserve for this course, or discussions with 6.041/6.431 staff. A brief note such as "Did homework with John Thompson and Jane Appleby in study group" or "Looked at old bible for Problem 4" would be sufficient. To use such sources without reference is plagiarism and is not acceptable.

After a quiz 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. We will reconsider the grade based on the explanation in your note, but TAs are not allowed to discuss the grading with you personally. 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.

In general, 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.

Additional Help from Staff Members

Your tutorial TA and your recitation instructor will both have office hours every week. 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 Personal Situations

Unforeseen events happen to many of us during the semester. If any are likely to affect your performance, please keep your TA, recitation instructor and/or the Head TA and lecturer aware of your situation. If you have quizzes immediately before or after our quizzes, we are usually able to find an arrangement that eliminates the need for you to race from one exam to another.