Course Overview



This subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. This Fall there are three class sessions MWF, two of them in parallel:

  • L01: 1-2:30PM in 32-044 (EECS Tutorial Lounge)
  • L02: 2:30PM-4:00PM in 32-044 (EECS Tutorial Lounge)
  • L03: 2:30PM-4:00PM in 32-052 (Stata TEAL)
There are no separate recitations. In-class problem-solving teams will be assigned by the second week of class. You will need to work with the same team in the same session at each class meeting. (Contact the staff about needed assignment changes.)

The subject coverage divides into three parts:

  1. Fundamental concepts of Mathematics: definitions, proofs, sets, functions.
  2. Discrete structures: elementary number theory, graphs, counting.
  3. Discrete probability theory.

The prerequisite is 18.01 (first term calculus), in particular, some familiarity with sequences and series, limits, and differentiation and integration of functions of one variable.

The goals of the course are summarized in a statement of Course Objectives and Educational Outcomes. A detailed schedule of topic coverage appears in the Course Calendar.

Considerations for Taking the Subject This Term

There are two main considerations for students in deciding to take 6.042J/18.062J this term ––or at all.
  1. Team Problem Solving

    This is a "flipped" class: students prepare by doing assigned reading and looking at recorded video presentations before class. Class meeting time is then devoted almost entirely to problem solving in teams of 6 to 8 students sitting around a table with a nearby whiteboard where a team can write their solutions. The sessions are open book, and laptops, tablets, etc., for viewing class related material are encouraged (but if you're caught viewing other things like email or facebook, your participation grade will suffer).

    Each team will have a TA and/or an LA acting as coach and providing feedback on students' solutions. The Lecturer acts likewise, circulating among all the tables. The coach will initially resist answering questions about the material, always trying first to find a team member who can explain the answer to the rest of the team. Of course the coach will provide hints and explanations when the whole team is stuck. See the description of team protocols and grading for more information about team activities.

    The Good News is that the immediate, active engagement in problem solving sessions is an effective and enjoyable way for most students to master the material. Team sessions also provide a supervised setting to acquire and practice technical communication skills. Student grades for problem solving sessions depend on degree of active, prepared participation, rather than problem solving success. Sessions are not aimed to test how well a student can solve the problems in class; the goal is to have them understand how to solve them by the end of the session. Participation in team sessions counts for 25% of the final grade.

    The Bad News is that a team problem solving approach to teaching requires students to arrive prepared at the sessions: they need to have read (though not carefully studied) the assigned reading, done the online problems, and watched designated videos before class. The team problem solving aims to help solidify students' understanding of material they have already seen.

    There is no way to make up for not working with the team, so it is necessary to keep up and be there ––no focusing on some other activity for a month, aiming to catch up afterward. If you cannot commit to keeping up, you may prefer to take the subject some other term. (In Fall '14, Prof. Tom Leighton will teach the class in standard lecture/recitation style.)

  2. Department Requirement

    This subject is required of all Computer Science (6-3) majors and is in a required category for Math majors taking the Computer Science option (18C). It covers many mathematical topics that are essential in Computer Science and are not covered in the standard calculus or algebra curriculum. In addition, the subject teaches students about careful mathematics: precisely stating assertions about well-defined mathematical objects and verifying these assertions using mathematically sound proofs. While some students have had earlier exposure to some of these topics, in most cases they learn a lot more in 6.042J/18.062J.

    However, students who have a firm understanding of sound proofs and who are familiar with a significant fraction of the covered topics should discuss with their advisor and the instructor the possibility of substituting a more advanced Math subject for 6.042. It is also possible for qualified students to get credit for the class by serving as a Lab Assistant.

Weekly Schedule

  • Class Text & Slide Shows

    Weekly reading will be assigned from our own class textbook. Video slide shows with voiceover will be also be posted for advance viewing before most classes.
  • Online Feedback Problems

    These are due before each class that they cover.
  • Problem Sets

    Problem sets are due on most Fridays. They are assigned a week or more in advance. The exact schedule is posted on the Course Calendar.
  • Preparation checks, Miniquizzes & Midterms

    Five minute preparation checks are given at the beginning of every class without another exam. Fifteen minute miniquizzes are given on most Mondays. One hour midterm exams will be given in class on Wednesday, Oct. 9 and Wednesday, Nov. 6.

Course Website

The class has a comprehensive web site (you're looking at it now):

Notes, problem sets, solutions, etc., will be posted on the course main page. Other course information such as staff contact information and announcements are also available on this website. It is always worth checking the website for corrections and announcements before starting problem sets.

Problem Sets

Problem Sets are normally due by electronic submission at 1PM on Friday. See the detailed problem set submission instructions.

Making a reasonable effort on the problem sets is, for most students, crucial for mastering the course material. Late submissions will not be accepted once the solutions are posted. Note that solutions are generally posted promptly after the time they are due.

The guidelines for a good solution are similar to those for class problems: a capable, prepared student who didn't see right away how to solve the problem should be able to read your answer and promptly see how to go about solving the problem themselves. If you cannot solve a problem in a reasonable time, don't lose sleep over it: you can get useful credit by including an explanation of where and how you got stuck.

Graders' time is limited, and they have been instructed to deny credit without struggling unduly to understand answers. For this reason, entirely correct but nonstandard answers are occasionally denied credit. We encourage you to seek the credit you deserve by asking either your TA, LA, or the Grades master to review your solution outside of class. If you are not satisfied with their response, you may appeal to the instructor-in-charge.

Problem sets count for 20% of the final grade.

Online Feedback Problems

Online problems to be completed before most class meetings are posted on the 6.042r website. These consist of straightforward questions that provide useful feedback about the assigned material. (Some students prefer to try the online problems before reading the text or watching videos as an advance guide to going over the material; that's fine.)

Like team problem-solving in class, online problems are graded solely on participation: students receive full credit as long as they try the problem, even if their answer is wrong. Online feedback problems count for 5% of the final grade.


You are encouraged to collaborate on problem sets as you do on teams in class. However, you must cite all your collaborators and any sources beyond this term's course materials that you consulted while working on a problem––for example, an "expert" consultant other than 6.042 staff, or another text––must be given a proper scholarly citation, which you should include with the collaboration statement accompanying your submission.

Other Sources

Most class materials other than problem solutions are available for Spring '13, and Fall '12. Materials are also available on OCW for Fall '10, Spring '10.

A problem from prior terms may occasionally be assigned again without change. If you find a published solution, you should cite it, and may not simply copy the published solution. Instead, a critique of the published solution or an improved version should be submitted instead.

We discourage, but do not forbid, use of materials from prior terms. We repeat, however, that use of material from a previous term requires a proper scholarly citation. As long as you provide an accurate citation and collaboration statement, a questionable submission will rarely be sanctioned––instead, we'll explain why we judge the submission unsatisfactory (and maybe deny credit for a specific, clearly copied solution). But omission of such a citation will be taken as a priori evidence of cheating, with unpleasant consequences for everyone.

Preparation checks

A preparation check consists of one or two questions which will be easy to answer in 3––5 minutes if you have prepared for class (looked at the assigned reading and slides/videos)-but not so easy if you haven't prepared. Prep checks are given at the beginning of nearly every class unless there is another exam. Your response is ranked P for prepared or U for unprepared. Your team coach takes the preparation check into account when assigning you a participation grade for the day's class.

To write your preparation check solutions, you are expected to bring a piece of paper (8.5 x 11in) and a pen to class. Preparation checks are closed book; no cribsheets. You may fill out your name, session (1PM, 2:30TEAL, 2:30Lounge) and Team label (1––13 or A––L), and heading "Prep Check [month day], 2013" in advance.

If you get a U or miss a prep-check, you may email an appeal for upgrade to your coach within one week of the prep-check. The email should include

  • an honest indication of whether you actually made an effort to prepare for class-admitting you were not prepared will not disqualify you from an upgrade,
  • an indication that you have found the proper answer to the prep-check (prep-check solns are usually not posted)
  • a new prep-check question that would be suitable for this prep-check in a future term.
Upgrades are not guaranteed but remain at the discretion of your coach. (We do guarantee that you will not be downgraded because of an appeal.) The bar for upgrades will be set high enough to ensure that counting on appeals to make up for being unprepared will not be a good strategy.

Weekly Miniquizzes

A closed book miniquiz, usually 15 minutes, will be given in class most Mondays.

Material to study for a miniquiz is well defined: a miniquiz will basically consist of excerpts or small variations of problems assigned the previous week, including class, pset, and online problems. You can prepare for a miniquiz simply by reviewing the posted problem solutions for the previous week.

NOTE: You are NOT allowed to use a crib sheet during the miniquizzes.

Miniquizzes count for a total of 5% of the final grade.

For miniquizzes, the grades are OK, NeedsWork, UnConvincing. If you get an NW or UC, you may email an appeal for upgrade to your coach. The email should include

  • a self-assessment of your miniquiz answers, indicating weaknesses you acknowledge (or deny) in comparison to the posted solution (in cases with no posted solution, you should also write a solution),
  • a new miniquiz question that would be suitable for this miniquiz in a future term.
Upgrades are not guaranteed but remain at the discretion of your coach. (We do guarantee that you will not be downgraded because of an appeal.) The bar for upgrades will be set high enough to ensure that counting on appeals to make up for being unprepared will not be a good strategy.

Midterm Exams

One hour midterm exams will be given in class on Wednesday, Oct. 9 and Wednesday, Nov. 6. The first midterm covers all previous weeks' material; the second midterm covers all previous weeks' material after the first midterm. A single two-sided crib sheet is allowed for each midterm.

The midterm exams will each count for a total of 10% of the final grade.

Final Exam

There will be a standard 3-hour final exam on December 16, 9AM--noon in du Pont. The final exam will cover the entire subject. It may include a few questions which combine topics that were originally covered separately.

You are allowed to bring a pair of two-sided crib sheets (total: 4 sides) for the final. This exam is worth 25% of the final class grade.


The lowest lowest problem set score, lowest two (2) miniquiz scores, and lowest three (3) class session scores will not count in grade calculation. This effectively gives you a problem set, two miniquizzes, and three class sessions you can miss without excuse or penalty. You should notify the staff in advance of an absence if possible, and briefly indicate the reason. Think of the three absences as "personal" days which you may use for sick leave, professional conflicts like job interviews, or sleeping in. Waivers and makeups for absences or missed miniquizzes will be considered only after the three allowed absences or two miniquiz waivers are used up. Prep-checks missed because of absences are waived with the absence.

Grades for the course will be based on the following weighting:

Class participation25%
Online Feedback Problems: 05%
Problem Sets: 20%
Miniquizzes: 05%
Midterm exams: 20%
Final: 25%

The class is not graded on a curve. In fact, MIT policy (Rules and Regulations of the Faculty, section 2.62) does not allow grading according to a fixed grade distribution. Instead, students are assessed individually. In particular, students who remain in class after Drop Date are not in jeopardy of seeing their grades change due to the change in class composition.

While there is no curve, there are historical norms. Historically, 6.042J/18.062J is a "B-centered" class. The percentage of A grades (A+, A, A-) has been between 28% and 41% nearly every past term. Similarly, the percentage of A/B grades has been between 68% and %75 for nearly every past term, with A/B/C grades between 85% and 95%.

On the other hand, in Spring '09, more than 60% of the class received an A grade and 91% of the class received an A/B grade. In this case, the instructors judged that the class had shown unusual strength--a judgment that was supported by the class's well above average overall performance on a challenging final exam.

A student who misses only a few problem sets and classes, and takes the midterm and final exams, will pass the class with at least a D, even if their performance is uniformly unsatisfactory. Grades of F are only given to students who essentially stopped participating but did not drop the class. There are not many F's, and they are no surprise when received.

Questions, Suggestions, and Complaints to the Staff

Email can be sent to the staff or to individual staff members using the addresses on the staff contact page.

Creative Commons License MIT 6.042 class material by Albert R Meyer is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
Based on a work at
For website issues, contact the

This document last modified Saturday, 14-Dec-2013 10:40:41 EST