Mathematics for Computer Science

6.042 Spring '15 Class Overview



This subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. This Spring there are two class sessions MWF in 32-044 (EECS Tutorial Lounge):

  • L01: 1-2:30PM
  • L02: 2:30PM-4:00PM
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 class are summarized in a statement of Class Objectives and Educational Outcomes. A detailed schedule of topic coverage appears in the Class 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 answering online questions 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. Participation in team sessions counts for 25% of the final grade.

    The sessions are open book, and laptops, tablets, etc., are encouraged for viewing class related material (viewing email, facebook and the like during class will be penalized).

    Each team will have a TA/LA coach providing feedback on students' solutions. 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. Instructors circulate among the teams overseeing class activity. 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 students understand how to solve them by the end of the session.

    The Bad News is that a team problem solving approach to teaching requires students to arrive prepared at the sessions: they need to do (though not carefully study) the assigned reading and do the online problems before class. The team problem solving aims to help solidify students' understanding of material they have already seen. Watching designated videos, or at least looking at the lecture-slide handouts, is generally helpful but optional. We expect that class preparation, including assigned reading and online material, will take 1.5 hours per class.

    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 '16, Math Department faculty are expected to 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 the instructor and their advisor the possibility of substituting another 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 Website

The class has a comprehensive Stellar web site where notes, problem sets, solutions, etc., will be posted. Announcement and staff contact information 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 count for 15% of the final grade. Making a reasonable effort on the problem sets is, for most students, crucial for mastering the course material. Problem sets are designed to be completed in at most 3 hours; the time is monitored through student reports.

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.) Watching designated videos, or at least looking at the lecture-slide handouts, is generally helpful but optional.

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 class 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. Class materials (excluding solutions) from Spring '14 are available on the Spring '14 Stellar web site. Materials including some solutions are available on MIT 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 you may not simply copy it. Instead, submit a critique of the published solution, an improved solution, or a suggestion for an improved or variant version––basically any commentary that shows engagement with the material comparable to that required to solve the problem on its own.

We discourage, but do not forbid, use of materials from terms prior to Spring '14. 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 undesirable consequences for everyone.

Midterm Exams

Three 80 minute midterm exams will be given in class on on Wednesday, February 25, March 18, and April 15. The midterm exams each count for a total of 10% of the final grade.

Midterm questions will typically be variations of prior problems from class and psets, and the best way to prepare is to review on the published solutions to these problems. The first exam covers all previous weeks' material; subsequent exams focus on the material after the previous exam. The material on the Monday before midterms 2 & 3 will not be covered, but because of lost days to snow, induction will be covered by midterm 1. A single two-sided crib sheet is allowed for each midterm.

Final Exam

There will be a three hour final exam during exam period on Thursday, May 21, 9AM in 34-101. This exam is worth 25% of the final class grade.

The final exam will cover the entire subject with somewhat greater emphasis on material from after Midterm 3. Most exam questions will be variants of problems assigned during the term (pset, class, midterm, and online). It may include a few questions which combine topics that were originally covered separately. A pair of two-sided crib sheets (total: 4 sides) are allowed for the final.


Grades for the class are based on the following weighting:

Class participation25%
Online Feedback Problems: 05%
Problem Sets: 15%
Midterm exams: 30%
Final: 25%

The lowest problem set score and lowest three (3) class session scores will not count in grade calculation. This effectively gives you a problem set 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 missed psets or absences will be considered only after the one pset or three allowed absence waivers are used up.

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, it is expected that 6.042J/18.062J will be "(A-/B+)-centered" with more than 10% unsatisfactory grades (D or F) unlikely.

Questions, Suggestions, and Complaints to the Staff

Messages for the staff can be posted (publicly or privately) on the class Piazza forum or by email to

Email addresses for individual staff members are available on the Stellar site.

Creative Commons License
MIT 6.042 class material by Albert R Meyer is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License .
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This document last modified Saturday, 17-Feb-2018 20:51:03 EST