This subject offers an introduction to Discrete Mathematics
oriented toward Computer Science and Engineering. See also the
introductory video on the website
There are three main topics:
The prerequisite is 18.01 (first term calculus), in particular, some familiarity is expected with sequences and series, limits, and differentiation/integration of single variable functions.
The goals of the class are summarized in a statement of Class Objectives and Educational Outcomes.
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.
Team Problem SolvingThis 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 team problem solving and studying with teams of 6 to 8 students sitting around a table and sharing a nearby whiteboard. 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 extraneous stuff like email or facebook is a no-no).
Each team will have a TA/LA coach who serves as a facilitator and provides feedback on 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. An instructor and a supervising TA circulate among the teams and oversee 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 1.25 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 '18, Math Department faculty are expected to teach the class in standard lecture/recitation style.)
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.
Some students already have a firm understanding of sound proofs and familiarity with a significant fraction of the covered topics from Math Team, competition, or similar experience. They 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.
The class has a comprehensive Stellar website where notes, problem sets, solutions, etc., will be posted. Announcements 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.
Complete class materials including solutions from Spring '15 are available for reference on the MIT Open Courseware site. Spring '18 will use the same text (except for minor updates) and largely the same in-class materials as Spring '15. Exams and psets will differ of course.
Grades for this course will be based on your scores in the following categories.
Each section will be graded out of 5 points. A weighted average of 4.5 or better will get an A; 3.5 - 4.5 will get a B; 2.5 - 3.5 will get a C; and any score below 2.5 will be discussed. We may lower these cutoffs, but we will not raise them.
Midterms and Final Exam
The material will be divided into 5 sections. There will be midterms on the first 4 sections during the semester, and a final exam that will cover all 5 sections. Dates for the midterms can be found in the class schedule and will take place from 7:30－9PM in a location TBA.
Your score for the first four sections will be the maximum of your grade on the midterm and the corresponding material on the final. Your score for the fifth section will be your score for that portion of the final. This means you are required to attend the final to receive a score for the fifth section (but you are welcome to skip the remaining 4 sections). This also means you can skip the midterms and take just the final, but we do not necessarily recommend this. The sections are weighted 12% each. Note that each numerical quiz score will be translated into an integer from 1-5 with the following meanings:
These will not be based on class averages but rather decided on an exam-by-exam basis. You may want to read Professor Winston's article on grades for more information.
Exam questions will typically be variations of prior problems from class and psets. The best way to prepare is to review the published solutions of these problems. Each exam focuses on material not covered by prior exams; midterms will not cover material introduced the day before the exam. A single double-sided crib sheet is allowed for each midterm. Two double-sided crib sheets are allowed for the final exam.
Your team coach will assign you a grade for each class session. See the description of team protocols and grading for more information on how class session scores are assigned. The lowest three (3) class session scores will not count in grade calculation. No makeup is required for these dropped scores. This effectively gives you three class sessions you can miss without penalty. The three absences are treated as personal days which may be used for sick leave, professional conflicts like job interviews, or sleeping in. However, we strongly recommend saving these absences for valid excused reasons (e.g. medical emergencies, religious holidays, personal emergencies). Provided your previous absences are excused, we can definitely help you make up any additional absences beyond the three. Please email email@example.com for more information or clarification on these policies.
Note that missing credit for three or fewer class sessions guarantees you a grade of a 5. Any additional absences (that have not been excused) will penalize your grade significantly.
There will be eight PSets during the semester. Psets are 15% of the final grade. Devoting up to 3.5 hours each week working on a PSet is, for most students, crucial for mastering the covered material. A good portion of each midterm exam and the final will be based on PSet problems. There are separate web pages with PSet submission instructions. You may make up one PSet during the semester and that score will be dropped when calculating the average. We suggest making up your numerically lowest score. The Makeup Policy page has more details on making up a PSet.
Online Feedback Problems
Online problems to be completed before most class meetings are posted on the 6.042r/MITx website. These consist of straightforward questions that provide useful feedback on comprehension of the covered material. (Some students prefer as an advance guide to try the online problems before reading the text or watching videos; that's fine.) Watching designated videos on the 6.042r/MITx website is helpful for many students but is optional. It's always a good idea to review the four-per-page slide handouts and have them handy in class.
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, but you must write up your own solutions alone without your collaborators.
Questions, Suggestions, and Complaints to the Staff
Messages for the staff can be posted (publicly or privately) on the
or by email to
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