Math 443 A - Spring 2007
Differential Geometry of Curves and Surfaces



Lectures

Monday/Wednesday/Friday
12:30 - 1:20
Communications Bldg (CMU) CMU - Room 326

Instructor

Daniel Pollack
Padelford Hall C-550
Phone: 206-543-1809
pollack@math.washington.edu

  • Office Hours

    • Topics


    The Course

     This course is an continuation of Math 442, our introduction to differential geometry through the study of curves and surfaces in Euclidean space.
    We willl begin with Chapter 4 of the text which establishes some fundamental results of a topological nature for surfaces in Euclidean 3-space.

    The Independent study component

     The last fourth of the course will consist of presentations by the students in the class on independent study topics. These topics will in general be related to the material presented in Math 441, 442 and the early portions of Math 443, however a great deal of latitude will be given to the students interests. A list of suggested topics are available here, however students are welcome to suggest their own topics as well. Each student will have periodic meetings with the instructor regarding the independent study component of the course. Initially this will be to help focus the students choice of topic and identify appropriate references. Subsequently meetings will help to understand the chosen material and its relevance to the rest of the course. This will cumulate in each student giving 25 or 50-minute lecture to the class on their chosen topic and preparing a 5-10 page written report on their topic, to be handed in by the last day of instruction: June 1, 2007.

    I expect that this will be very exciting and allow each student to pursue, in a nontrivial way, a particular area in Geometry or Topology which is of interest to them. In hearing their fellow students lecture on a diverse selection of topics, it is hoped that the entire class will be exposed to a broader range of subjects than is usually found in a lecture class.

    The Textbook

    The text for the course is again Curves and Surfaces by Sebastian Montiel and Antonio Ros.

    Homework

    Homework will be assigned on an (approximately) weekly basis, see the Weekly Assignments page for the problems due. You are responsible for all the problems assigned. The homework will be taken from the book, both from the exercises within the text as well as those at the end of each chapter. It is recommended that you do all of the Exercises from with the body of the text, not just those that are assigned. There are hints to solving many (though not all) of the exercises at the end of each chapter. You are free to use these but you will benefit from attempting to do the problems on your own first, before looking at the hints.

    It is very important to do all the homework in order to learn the material. A good way to be sure you get the most out of your homework is to work with others. I encourage you to form study groups and work collaboratively on the homework problems. The only limitation on collaboration is that, after you and your study group have worked out how to do the problems, you must each write up your own solutions in your own words. A large part of the emphasis in the homework is to practice, and improve on, your ability to write clear and rigorous proofs.

    The TA/Homework grader for the course is:

    CourseNameOfficeEmail
    442-A Robert L. Miller PDL C-406 rlmill@math.washington.edu

    Robert will hold office hours on Tuesdays from 2:00 - 4:00 PM, to enable you to ask specific questions regarding the homework.

    Exams

    There will be no midterm exam for this class.

    The final exam will take place from 8:30 - 10:20 AM on Thursday, June 7, 2007 in LOW 201 (tentative).

    Grades

    Your grade will be determined based on the following

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