Course goals: The main goal of this course is to apply the ideas of calculus in order to understand the geometry of curves and surfaces in 3-space. Writing and understanding rigorous proofs forms a centerpiece of this course. Although students will need some background in writing proofs, one of the principal goals of the course is to improve proof-writing skills.

Textbook: Elementary Differential Geometry (2nd edition), by Andrew Pressley.

Prerequisites: A thorough understanding of Calculus III (Math 2043) and Linear Algebra (Math 2101 or 2103 or 3051). We will draw many ideas from both courses. From calculus, we will need the notions of speed and acceleration for parametric curves, as well as partial derivatives and vector fields. From linear algebra, we will need the concepts of linear transformation, determinant, eigenvalues and eigenvectors, etc.

• You should try to do all of the problems on your own before getting together with others. It does not benefit you (on exams and in the real world when you need to use math) to simply get solutions from your classmates! In fact, there is research suggesting that group work is much more productive when everyone has thought about the problems before getting together.
• Everyone must turn in their own solutions. In other words, you should write up your final solutions in the privacy of your own room (or your own library, cafe, bar, roof, etc.).

Here are a few guidelines for how to write up the proofs:

• Write up the problems in order, using only one side of the page and leaving lots of space for me to write comments. Please staple your sheets together.
  
• Begin each problem with a statement of that problem.
  
• Proofs should be written in complete sentences, with appropriate use made of mathematical notation (your textbook will serve as a guide to how to do this). Proofread what you've done to be sure that it's complete and makes sense. Remember that proof-writing is above all an act of communication, and that the ultimage goal is clarity.
  
• If you leave a small gap in a proof that you're not able to fill in, note this down. I'll try to indicate how to fill it in my comments.
  
• Start early! This way, if you are stuck, you can still discuss the problem with other students or with me.

• The first day of classes is Tuesday, January 19.
• The last day to drop/add (tuition refund available) is Monday, February 1.
• Spring break is the week of Monday, March 8.
• The last day to withdraw (no refund) is Monday, March 29.
• The last day of classes is Thursday, April 29.
• The final exam is Thursday, May 6.