6.042 Spring '15 Class Overview

Contents

• Introduction
• Considerations for Taking the Subject This Term
• Team Problem Solving
• Team Protocols & Participation Grades
• Weekly Schedule
• Class Website
• Problem Sets
  • Submission Instructions
• Online Feedback Problems
• Midterms & Exams
• Collaboration
• Grades

Introduction

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

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

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 Text

  Weekly reading will be assigned from our own class textbook.

• Videos and Online Feedback Questions

  Video mini-lectures and online questions are posted on the 6.042r website. Answers to online questions are due before each class that they cover.

• Problem Sets

  Problem sets are due at 1PM on most Fridays. They are assigned a week or more in advance. The exact schedule is posted on the Class Calendar.

Class Website

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

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.

Collaboration

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

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

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

Class participation	25%
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.

Questions, Suggestions, and Complaints to the Staff

6042-staff(at)mit.edu

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