Write out your thinking about each question and place it in the box on the door of my office (Malott 403). Kristin Camenga will be my assistant and will help me read your papers. Everything turned in will be looked at by me and most of them will also be looked at by Kristin. Usually only one of us will go over any particular response in full detail. We will both (usually) write comments. I will always use green ink and Kristin will use other colors. Your papers with comments will be returned during class. We expect that any paper turned in by 10 am on Monday will be returned to you in class on Tuesday and any paper turned in by class time on Tuesday will be returned to you in class on Thursday. There will be assignments due every Monday.
Respond to our comments - use them as invitations to explore, or to clarify your understanding, or as an opportunity to clarify our understanding. (We learn by reading what you write.) Keep responding (in writing and/or in office hours) to our comments until you understand. Turn in whatever your thinking is on a question even if only to say: "I don't understand such and so" or "I'm stuck here". (Be as specific as possible.) Also, ask questions in class, after class, on your papers, or in our offices. In this way we can share with each other, and I will be better able to tell where the class is at, and you will benefit more from class sessions. Do not fall behind -- you should turn in homework every week.
Allow yourself to be open-minded and flexible when exploring the questions. Let your thinking wander. Some questions will have short, fairly definitive answers; and others will lead into deep areas of meaning which can be probed almost indefinitely. Don't accept anything just because you remember it from high school or because some authority (including me) says it's good. Insist on understanding (or seeing) why it is true or what it means for you. Make models, draw pictures, use rubber bands on a ball or orange, use scissors and paper - Play.
Sharing your ideas with another person and then listening to that person's ideas is an effective way of learning. It will also tend to break down the isolation and competitiveness that we often feel in academia. If two (or more) of you work out an answer together - that is good. But make sure that you understand it your way and that you communicate that understanding in your own words and please write your collaborator's name on your paper.
You may use ideas you see in class, even if you turn in a response to a question after it has been discussed in class. But again make sure that you understand it your way and that you communicate that understanding in your own words and that you acknowledge the class' contribution.
I will ask and encourage people to share their thinking in class. It is important for all of us to listen carefully to each person who speaks in class and to respond in constructive, thoughtful ways. Many ideas will come up that will feel very strange to you and to me. You will learn, if you listen well to the person and ask questions. If something seems wrong to you start out by finding which parts you agree with and then proceed from that base.
The first assignment will be assigned at the end of class on Thursday and is due on my door by 10 am on Monday. If there are too many students wanting to be in the class then I will give preference to those who turn in thoughtful (not necessarily correct or complete) homework on Monday.
Text: Experiencing Geometry in Euclidean, Spherical , and Hyperbolic Spaces by Henderson (with Taimina). Look for the list of errata at
http://www.math.cornell.edu/~henderson/books/eg00/errata.html
Please report to me any errata you find (no matter how trivial).
We cover in class most of Chapters 1-8 and then several other chapters chosen by the class. At the end of the course, each of you (as a final project) will cover on your own a chapter of your choosing that we have not covered in class.
David