Course Overview

Contents

• Introduction
• Considerations for Taking the Subject This Term
• Team Problem Solving
• Team Protocols & Grading
• Weekly Schedule
• Course Website
• Problem Sets
  • Submission Instructions
• Online Tutor Problems
• Weekly Reading Comments
• Quizzes & Exams
• Collaboration
• Grades
• There is a Piazza forum for 6.042. Piazza is for general comments & questions for the whole class. Posting questions or comments to Piazza is optional.

Introduction

This subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. There are two class sessions this fall:

• MWF in 32-044 (EECS Lounge) 11:00AM－12:30PM.
• MWF in 32-044 (EECS Lounge) 1:00PM－2:30PM.

The subject coverage divides into three parts:

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

1. Team Problem Solving

   This term, as in many previous terms, the subject is being taught in Lecture/Team Problem Solving style. At least two thirds of class meeting time will be devoted to problem solving in teams of 5 to 7 students sitting around a table with a nearby whiteboard where a team can write their solutions. Each team will have a TA or an LA acting as coach and providing feedback on students' solutions. The Lecturer acts likewise, circulating among all the tables. The coach will 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.

   Problem solving sessions will sometimes be preceded by 20 minute presentations by the lecturer, typically reviewing just the topic needed to understand the problems. These presentations aim to refresh students' memory of their reading and to provide perspective and motivation. They do not cover every topic in the reading, and they do not introduce new material. Students who are comfortable studying from the reading are welcome to skip the lecturers' presentations －but not the team problem solving. We hope to replace many of these class presentations with recorded presentations of slides with voice-over to be viewed before class. This will allow students more time to be actively engaged in class.

   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 20% 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 Tutor problems, and watched designated slide shows before class. The point is that team problem solving helps 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 '12, Prof. Tom Leighton will teach the class in standard lecture/recitation style.)

   Team Grading & Protocols

   More about team grading and protocols can be found here.

2. Department Requirement

   This subject covers many mathematical topics that are essential in Computer Science and are not covered in the standard calculus 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.

   The 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). However, students with a firm understanding of sound proofs and who are familiar with many of the covered topics should discuss with their advisor and Prof. Meyer the possibility of substituting a more advanced Math subject for 6.042.

Weekly Schedule

• Class Text & Slide Shows

  Weekly reading will be assigned from our own class textbook, available for download in installments. Lecture slides are posted before every class, and slide shows with voiceover reviewing material for particular classes will be also be posted for viewing before class.

• Online Tutor Problems

  Online tutor problems are due before each class that they cover. See the Online Tutor information below.

• 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. See Problem Sets below for further information.

• Microquizzes, Miniquizzes & Midterm

  Miniquizzes are given on most Mondays; microquizzes are given on all other class days, starting after April 2. On Monday, March 19, there will be a one-hour midterm exam instead of a miniquiz. See Weekly Miniquizzes and Midterm Exam below for further information.

Course Website

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

http://courses.csail.mit.edu/6.042

Notes, problem sets, solutions, etc., will be posted on the course main page. Other course information such as staff contact information, mailing lists, 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 15 minutes before Friday class. Each problem must be fastened and submitted separately. 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. Solutions to the problem sets will be posted immediately after the due date. Consequently, late problem sets will not be accepted. The guidelines for a good solution are similar to those for class problems: a smart, 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 will get useful credit for explaining where and how you got stuck.

Problem sets count for 25% of the final grade. To reduce problem sets as a source of pressure, and as a reflection of their intended educational role, missed credit on a pset (up to 50%) automatically shifts to the midterm or final, whichever occurs first after the pset due date. For example,

If a student missed 4 points on a 10 point pset due before the midterm, then 40% of the weight of that pset gets added to the weight of their midterm.

If a student missed more than half the points on a pset due after the midterm, then 50% of the weight of the pset gets added to the weight of their final.

Students are encouraged to collaborate on problem sets as on teams in class, though we strongly suggest you attempt each problem on your own before talking it over with your friends, classmates, or TA. The last page of each problem set has a collaboration statement to be completed and attached as the first page of a pset submission:

"I worked alone and only with course materials"

or

"I collaborated on this assignment with <students in class>,
got help from <people other than collaborators and course staff>,
and referred to <citations to sources other than the class material from this term>".

No problem set will be given credit until it has a collaboration statement.

Graders' time is limited, and when in doubt about an unclear student solution, they are instructed to deny credit. If you are concerned that your problem set has been graded incorrectly, talk to your LA or TA after class. If you are not satisfied with their response, the lecturers will be happy to hear an appeal.

Online Tutor Problems

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

Reading Comments

Students are encouraged to use NB as their first source for questions relating to the class text, but not class problems or problems sets, though these are also available for comment in NB.

For the first half of the term, students were expected to participate in the commentary on the class materials with reasonable regularity throughout the term. NB comments were made optional on April 2, and do not affect grades after that date.

2.5% of the final grade is determined by participation in NB discussions prior to April 2, including responding to other peoples' questions, pointing out spelling and grammar errors, or suggesting on how a passage can be improved. Comments made at any time on a chapter of the text are valuable, but comments made before a chapter is covered in class are more valuable. Being among the first to report a typo or mistake in the text is considered a worthy contribution at any time.

Collaboration and Outside Sources

We encourage students to collaborate on homework as on in-class problems. Study groups can be a big help in mastering course material, besides being fun and a good way to make friends. However, students must write up solutions on their own, neither copying solutions nor providing solutions to be copied. All collaborators must be cited, and if a source beyond the course materials is used in a solution ––for example, an "expert" consultant other than 6.042 staff, or another text ––there must be a proper scholarly citation of the source.

Subject materials are available on OCW for Fall '10, Spring '10, Fall '05, and Spring '05. Problem solutions are mostly omitted from the Spring '10 and Fall '10 materials. A problem from these prior terms may occasionally be assigned again without change. If a student looks at the published solution, he or she 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 other than those available on OCW. We repeat, however, that use of material from any previous term requires a proper scholarly citation. As long as a student provides accurate citation and collaboration statements, 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.

Weekly Miniquizzes

Material to study for a miniquiz is very well defined: a miniquiz will cover only the material in problems assigned for the previous week. Miniquiz questions are often simply some parts of these online, class, and/or pset problems. Students can prepare for a miniquiz simply by reviewing the posted problem solutions for the previous week.

Midterm Exam

Microquizzes

To write your microquiz solutions, you are expected to bring a piece of paper (8.5 x 11in) and a pen to class. Microquizzes will be closed book; no cribsheets. You may fill out your name, session time (11AM or 1PM), and heading "Micro-quiz (month day), 2012" in advance.

You can try to make up for a missed or poor microquiz grade by proposing a really good new micro-quiz or mini-quiz question on the same or a subsequent topic and sending it to 6042-staff(at)csail.mit.edu. The bar for makeup credit will be set high, so don't count on this as a backup for being unprepared.

Final

Grades

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

Note that missed credit (up to a cap of 50%) on problem sets spills over as increased weight of the midterm & final, as explained in the Problem Sets section above.

Questions, Suggestions, and Complaints to the Staff

	For website issues, contact the 6042-webmaster(at)csail.mit.edu
	6.042 lectures & problems by Prof. Albert R Meyer is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.