Math 10 has two complementary purposes. The first is for you to learn how to communicate mathematics to a live audience. The second is for you to meet some of the math faculty and learn about their research. Typically, a class will consist of a talk by a faculty member and several shorter talks by students.
You will give two talks in the course of the quarter. Mathematicians typically use one of two modes in a talk or lecture to provide the visuals. The first is with chalk and a chalkboard. The other is transparencies ("slides") on an overhead projector, and is often used for shorter talks or for presentations at conferences. You will give one talk with each method. As the slide method is in many ways easier for the beginner, we'll start with that. The slide presentation will be 20 minutes long. The chalkboard talk will be 30 minutes long.
Content: Your talk should be about some aspect of mathematics, or an application of mathematics to another subject. You should aim for something that is not known to the majority of the folks in the class, but, at the same time, is comprehensible to most of them. In terms of background, here's what the class knows:
Your talk should not be something that you learned in a math class here at Caltech, though it could be a different point of view on something you learned here. If you need ideas for topics, talk to me after class, or during my office hours.
First talk: For your first talk, I need to approve your topic ahead of time. Email me your proposed title and a brief 2-4 sentence description of your proposed topic anytime prior to 2pm Monday of the week of your talk. I will let you know shortly thereafter whether your proposed topic is acceptable. To help make your first talk go as smoothly as possible, I will look at a draft of your transparencies before your talk. Prior to 11am on the Wednesday before your talk, turn in your draft slides to the envelope on my door. I will look them over, make some comments, and put them back the envelope for you to pick up after 4pm on that same day. I have an office hour on Thursday if you have any further questions before your talk. (In instead you are talking on a Wednesday, your abstract is due Friday and your slides on Monday.)
Second talk: Your second talk will be a 20 minute chalk talk (or a bit longer for some of you, consult the schedule for details). For your second talk, you do not need to clear your topic with me beforehand. However, if you are having difficulties thinking of a topic, I would be happy to give you some suggestions. I can also comment on the notes you prepare for your talk ahead of time, if you like.
Special Classes: As there are so many enrolled, in order to make the your talks a reasonable length we will have two "special weeks". During the special weeks, there will be two meetings of Ma 10, the usual one of Friday and an extra one on Wednesday from 2-4. However, each of you will only attend one of them. There will be no faculty speakers on special weeks, and so each each class will consist entirely of student talks. The special weeks will be Oct 18-22 and Nov 15-19.
Because many of you have little experience in giving talks, and because you only have two opportunities to speak, you will not graded on the actual quality of your talk per se. As one of the course's points is to meet some of the math faculty, as well as listen to your fellow students, class attendance, and in particular timely attendance, also counts. First, you must give both your talks to get a quality grade (A-C). If you give only one, you'll get a D; neither, an F. Beyond this, I will use the following mechanical system to determine your letter grade. You start with 25 points which you can lose by: