Discrete Mathematics for Computer Science

Spring term (24032)

Harry R. Lewis, PhD, Gordon McKay Professor of Computer Science, Harvard University
Deborah Abel

Web Conference Course, offered online only. Tuesdays 9-11pm, Thursdays 9-10pm beginning Jan.28. If you cannot repliably attend class at these particular hours, you will not be able to take the course.

This course covers widely applicable mathematical tools for computer science, including topics from logic, set theory, combinatorics, number theory, probability theory, and graph theory. It includes practice in reasoning formally and proving theorems. The recorded lectures are from the Harvard School of Engineering and Applied Sciences course Computer Science 20. Prerequisite: MATH E-15, or the equivalent. (4 credits)

This course parallels the Harvard College course CS 20. The pedagogy will be novel, and enrollment will be limited to 20.

Pedagogy. The course will be taught in two sessions per week, one lasting two hours and one lasting one hour. Each class will be a combination of instructor presentation and active learning. In an active learning session, students will meet, virtually, in small groups (probably 4 students each) using Web conferencing software to solve problems collaboratively. A member of the course staff will visit each group (virtually) to provide assistance and coaching.

The presentation segment of each class will be videorecorded so students can view it at their convenience. However, because of the importance of the collaborative, active learning component of the course, students must be available at the fixed times listed in the previous paragraph.

Text. We are not assigning a textbook -- there are several satisfactory ones, but they are mostly heavy and expensive. Instead, the text will be Professor Albert Meyer's course notes from MIT, which can be downloaded for free. (Thank you, Professor Meyer!) Students will be expected to read a short section of these notes before each class and to use a Web tool to answer a few questions based on the reading. It is essential that students be able to do a little bit of work several days per week -- this is not a course where the work can be saved up and done all at once on weekends, for example. (For those who wish to have a physical book in hand, one of the editions of Rosen's Discrete Mathematics and its Applications is a possibility.)

Hardware. CSCI E-20 students may wish to buy a tablet such as the Wacom Intuos so they can interact with their learning group via graphical input (may be available cheaper elsewhere). Some students find they can do graphical input well enough with a mouse. Students should also have an ordinary telephone-style headset to plug into their computer so they can talk at the same time as they are typing or scribbling during the class essions.

The class will use the Blackboard Collaborate software for web conferencing. Please read the Extenstion School's explanation of Web Conferncing courses, and in particular make sure that you will reliably have access during class times to a personal computer capable of running a Blackboard Collaborate session (if your machine has an old operating system, you may have to upgrade the OS). Note that while there is a mobile app version of this software it is not fully-featured enough to use for this course -- at class time you should be in front of your personal computer, and you should already have checked out its compatibility with the software against the Extension School's description of the requirements.

Are you prepared to take CSCI E-20? Math E-15 (calculus) is listed as the prerequisite, not so much because we will use a lot of calculus as because we will expect students to have a certain level of ability to read and write mathematics. One exercise you could use to test your readiness to take the course is simply to try to read the first chapter or two of the notes. If you can't understand them, you may need a refresher on high school math.

Do you know too much to need to take CSCI E-20? This course is designed to teach you the math you need to take the more advanced theoretical CS courses, specifically CSCI E-124 and CSCI E-121. A "placement test" has been posted here -- if you are familiar with the terminology and can do most of the problems you probably don't need CSCI E-20, but if you can do only half of it you probably need the course.

Evaluation. Though class participation is not intended to be competitive, students will be evaluated on their participation and will lose credit for absences. In addition, there will be weekly problem sets, a proctored midterm examination on February 21, 2014, and a proctored final examination. As is standard for Harvard Extension School web conferencing courses, you will have to arrange for exam proctoring if you are not near enough to Cambridge to come to Harvard to take the exams.

The material parallels that of CS 20.