Goals

The general goals of this course are to learn some geometry and have some fun while we're at it. More specifically, I'd like to talk about possible mathematical shapes for space and the geometries associated to each of these shapes. We will talk about sets and transformations, symmetries and groups (it will help if you have had group theory before, but it is not strictly necessary), manifolds and orbifolds, and current theories about the shape of the universe we live in.

Grading Scale

The grading scale below will determine your final grade.

Course Summary          ......................................................   5%
Classwork / Particip.   ......................................................  10%
Research Project        ......................................................  15%
Homework                ......................................................  20%
Exam 1, Mar 18          ......................................................  25%
Exam 2, May 15          ......................................................  25%

Course Summary

At the end of the course, you will each turn in an individual written summary of the course. This summary can include proofs, pictures, examples, and anything else you think is relevant. It should be something more than just handing me your notes for the course -- I'd like to see that you've given some thought to how all the topics we cover fit together; what the big picture is. I'll talk more about the course summary in a few weeks, but for now you might want to keep the question of the "big picture" in mind while you're in class.

Classwork / Participation

My goal is to make this an active class. During many class periods, I'll be giving you a problem or project to work on in class with one or two of your classmates. You'll be expected to attend class and to participate in these events. You're also expected to be reasonably awake during class. If you follow these guidelines, you'll easily get full credit for this portion of your grade.

Research Project

Near the middle of the term, I'll be handing out ideas for geometry research projects, for you to work on with one other classmate. If you become particularly interested in some topic we discuss in class and can come up with your own interesting, mathematically substantial, and instructor approved project topic, then that will be worth extra credit on your project score. These projects will be due some time during the last week of class, and will include a written report AND some sort of presentation. We will have a "geometry showcase" during the last week of classes in which you will be able to show off (explain) your project to other classmates, faculty, and maybe even some geometry high school students. I'll give you more details about this later in the course.

Homework

Homework will assigned in almost every class period, and will be due the following Friday. You are allowed 2 late homework assignments, to be turned in the following Monday. After that, late homework will not be accepted under any circumstances. I encourage you to work with other students in the class when solving the homework problems; however, your final write-up of the problems should be done on your own.

Exams

There will be 2 exams in the course, on March 18 and May 15 7:30-9:30 (am!) during finals week. These exams are closed book, closed notes, closed friends, open brain, and under the honor system.

Cheating

Any student caught cheating will be sterilized so that their genes cannot be passed on to future generations.

Extra Help

You can get extra help for this class from any one of the following sources:

• My office hours
• Send me email after class hours
• Our weekly homework sessions, to be scheduled during the first week of class.
• Your fellow classmates

Accomodations

Any student with a documented disability needing academic adjustments or accomodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential.