MA640: Introduction to Differential Geometry

Wed. 6:00 to 8:30 JAB 777

Books

• "Differential Geometry of Curves and Surfaces" by Manfredo DoCarmo: required textbook.
• "Topology from the Differential Viewpoint" by John Milnor: recommended supplementary text.

Syllabus

• Lectures 1 and 2: Chapter 1.
• Lectures 3 and 4: Chapter 2.
• Lectures 5, 6, and 7: Chapter 3.
• Lecture 8: Midterm Exam.
• Lectures 9, 10, and 11: Chapter 4.
• Lectures 12 and 13: topics.

The grade distribution will be 30% homework, 30% midterm, and 40% a final project or paper. An outstanding final project/paper may be worth more, but I advise you to play it safe and secure your grade early.

Homework. Homework will consist of five sets of five problems taken from the textbook and handed in biweekly. The homework must be TeXed and presentation, spelling, grammar, and other basic literary skills will be part of the grade. Scroll down for the homework assignment.

Midterm.The ``midterm'' will be the week after lecture 7 and will cover the intersection of the lectures and the first three chapters of the textbook.

Final project. The final project can be a paper, an interactive web document, or a (well-documented!) computer program. The topics will be suggested during the course, or chosen by the student after consulting with me. Students not interested in pursuing independent work, may submit an individualized take-home exam.

Homework 1.

Section 1.3. Exercises 4 and 10.
Section 1.5. Exercises 9, 11 and 12.

Homework 2.

Section 2.2. Exercises 16 and 17.
Section 2.4. Exercise 15.
Section 2.5 Exercises 1 and 3.

Homework 3.

Section 3.2 Exercises 5 and 8.
Section 3.5. Exercises 5, 6 and 22.