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This is a course in experimental mathematics. In small groups, students investigate questions from different parts of mathematics, using computers whenever appropriate. They write reports and give oral presentations.
Staff:
Giorgia Fortuna, 2-229, x3-1589, giorgia AT mit DOT edu
Julee Kim, 2-281, x3-7576, julee AT math DOT mit DOT edu
Susan Ruff, 38-583, x4-1983 or (617)-455-8248, ruff AT mit DOT edu
Paul Seidel, 2-270, x3-3773, seidel AT math DOT mit DOT edu
How the class works:
Registration: This class has limited enrolment. The math department Undergraduate Office conducts a lottery based on pre-registration.
Class time: The scheduled times are Monday and Friday 1-2:30, in 2-105. The first meeting on Friday will be organizational: it is essential that everyone attend it. After that, we will have presentations (initially by staff, then by students) scheduled on Mondays. Attendance to these is obligatory: absence without prior permission or explanation may affect your grade. The Friday timeslot is primarily for practice presentations. You'll have to be free during that time when your turn comes to practice your presentation, since we usually won't be able to find other time to schedule this. Otherwise, you can use the Friday time as a common time for the whole team to meet, either by yourselves of with your assigned staff member.
Choosing and carrying out projects:
Students will be divided into teams (of three, usually). Each team has a primary staff member assigned to them, who will meet with them weekly. Each team will carry out three projects during the semester, usually taken from our project list
(you're welcome to propose your own project as well). We will choose the initial round of projects during the organizational meeting. After that, you can choose a new project as soon as the deadline for the draft submission for the previous one has passed (please give us two possible choices, in case your first preference turns out to be taken already). We encourage you to choose projects from different parts of mathematics, including ones that you've not yet had much exposure to.
Many projects are experimental, which means that it is sensible to start by gathering as much data and intuition as possible, including computer experiments. A short list of available computer packages is here. After that, you should try to make your answers as precise as possible, and see how far you can get in the direction of rigorous proofs. More questions may emerge as you progress. Many projects are open-ended, and do not have a unique answer or solution.
It is ok to consult books for background, especially if there are mathematical concepts that you're unfamiliar with. However, you will get credit only for your own creative thinking, not for insights gathered from the literature (hence, trailing the web for related material is not a good strategy). In order to make the distinction clear, it is important to cite your sources (from books to webpages; see this guideline). A few things are explicitly forbidden: you may not discuss the project with class members from previous semesters, or read their reports; and the same holds for notes coming from similar courses at other schools.
Writing project reports:
Each team member should contribute a part of each report. Please mark clearly which parts were written by whom. In spite of such divisions, the report should be readable as a whole (ideally, the whole team will revise it together). A sample report is here, but this should not be taken as an ideal model; instead, we will have a special in-class session dedicated to discussing writing. There is a 12-page limit, excluding data (code, tables, graphics).
LaTeX is well suited for mathematical texts, see here for some tutorials. Drafts should be submitted to the Stellar course page. We encourage submission as a single pdf file, if possible (and only one submission per team, please). You will receive extensive feedback, and use that to prepare a final version, which will then again be uploaded via Stellar.
Project presentations:
Each team will present one of their projects in class. This presentation is preceded by a practice talk (given the Friday before to part of the staff). You will get extensive feedback on the practice talk. Each team member is expected to speak for about 20 minutes (at least 15, not more than 25), so the total length of the presentation is about an hour, with extra time for questions and discussion. We will collect audience feedback, take that into account when grading your presentation, and also forward it to you. Here is a useful summary of an old in-class discussion about presentations, and here is a whole article (by Susan Ruff) on how to prepare for a presentation. We will also have an in-class discussion of the goals and strategies of giving a presentation.
The classroom is equipped for various styles of presentation (blackboard, written slides, and computer projection).
Grading policy:
Grades will be based on the project results (1/2), the quality of the writing (1/4), and the oral presentation (1/4). In borderline cases, we reserve the right to tweak the arithmetic slightly by taking into account attendance at presentations, as well as the quality of the teamwork. In order to get a passing grade, you have to be actively involved in all of your team's projects and the presentation.
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