Course Overview

Contents

• Introduction
• Considerations for Taking the Subject This Term
• Team Problem Solving
• Weekly Schedule
• Course Website
• Problem Sets
• Online Tutor Problems
• Weekly Email Comments
• Biweekly Miniquizzes
• Collaboration
• Grades
• Email Forum
• Latex Macros

Introduction

This subject offers an introduction to Discrete Mathematics oriented toward Computer Science and Engineering. It meets MWF in 32-082 11:30－1:00PM and alternatively 3:00－4:30. There are no separate recitations. The subject coverage divides roughly into thirds:

1. Fundamental concepts of Mathematics: definitions, proofs, sets, functions, relations.
2. Discrete structures: graphs, state machines, modular arithmetic, 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. More than half the class meeting time will generally be devoted to problem solving in teams of 7 or 8 sitting around a table with a nearby whiteboard where a team can write their solutions. Each TA covers 3 tables, 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.

   Problem solving sessions will generally be preceded by half hour presentations by the lecturer, usually reviewing just the topics needed to understand the problems. These overviews are not intended as first-time introductions to the material nor as complete coverage of the assigned reading.

   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.

   In-class team problem solving works to solidify students' understanding of material they have already seen. The Bad News is that this requires students to arrive prepared at the sessions: they need to have read (though not carefully studied) the assigned reading and done the Online Tutor problems before 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 something else 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.

2. This subject covers many of mathematical topics that are essential in Computer Science but 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). But students with a firm understanding of sound proofs, and who are familiar with many of the covered topics, should discuss substituting a more advanced Math subject for 6.042 with the Lecturer or their advisor.

Weekly Schedule

• Class Text

  Our own textbook will be available for download at the beginning of the term.

• Online Tutor Problems & Email Reading Comments

  These are generally due Monday mornings. See the Online Tutor and email comments information below.

• Problem Sets

  Problem sets will usually be due at the beginning of class Friday. They are assigned a week or more in advance. The exact schedule is posted the Course Calendar. See Problem Sets below for further information.

• Miniquizzes

  Miniquizzes are given every other week, usually on Wednesdays. See Biweekly Miniquizzes below for further information.

Course Website

The class has a comprehensive web site:

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

Notes, problem sets, solutions, etc., will be posted in the course calendar. 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 nannouncements before starting problem sets.

Problem Sets

Problem Sets are normally due at the beginning of lecture on Fridays, but a few may be due at alternate times because of holidays. Doing 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.

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 teaching ––as opposed to testing ––purpose, students can make up half the credit for a pset on the subsequent miniquiz and on the final. But aiming only for half credit on problem sets with intention of making up the missing half credit on subsequent exams is a risky strategy, especially since grades on the final tend to be lower than on problem sets.

For example, if a student missed 4 points on a 10 point pset, then 2 of those missed points get added to the weight of the next miniquiz and 2 to the final exam. If a student missed more than half the points on a 10 point pset, then 5 points can be made up ––2.5 of the missed points get added to the weight of the next miniquiz and 2.5 to the final exam.

Students are encouraged to collaborate on problem sets as on teams in class. 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.

TA's don't have enough time to grade pset problems in detail, and when in doubt about an unclear student solution, they are instructed initially to deny credit. If a student is concerned about how a pset has been graded, they should take it up with their TA in office hours. If they're not satisfied with the TA's response, the Lecturer 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.

Weekly Reading Comments

A comment citing some paragraph in the reading is due weekly, generally by Monday 10AM. This allows the lecturer to adjust class coverage in response to the comments. More extended comments are very welcome, but not required.

Any paragraph that specially catches your attention may be cited. You should explain in a few sentences why this paragraph stood out, for example, because you found it especially

• difficult/confusing, or
• surprising, or
• mistaken (pointing out typos & suggesting corrections is appreciated), or
• funny, or
• boring, or
• lacking Computer Science motivation, or
• poorly written,
• something you'd like reviewed in class, ....

Note that comments such as "I understood everything in the reading, found it all interesting, and have no questions" are not considered responsive. Even if you understood everything, there must, in the 15 to 30 pages assigned each week, have been something that stood out for you as suggested above. Comments may be submitted using the NB annotation system or by email to 6042-probs at csail.mit.edu  . The staff is able to respond individually to a majority of the reading comments.

Reading comments count for 5% of the final grade.

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 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.

The Fall '05 course materials are available on OCW, as well as Spring '05 and Fall '02. The material this term will be similar to that of the Fall '05 term, and a problem from these prior terms may occasionally be assigned again without change. If a student looks at the published solution, they 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 specific, clearly copied solutions). But omission of such a citation will be taken as a priori evidence of cheating, with unpleasant consequences for everyone.

Biweekly Miniquizzes

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

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 final and selected quizzes as explained in the Problem Sets section above.

Email Forum

The forum is intended for general course-related communication by class members. We encourage students to use it to arrange study sessions, discuss homework, and send comments to the entire class. The staff also emails announcements and corrections to this list.

General information about the mailing list, including subscribe/unsubscribe instructions, is at:

Questions, Suggestions, and Complaints

Latex macros

	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 .