General Information

Subject Matter: A rigorous treatment of metric and general topology, linear and multi-linear algebra, differential and integral calculus in several variables. Mathematics 55a is an intense course for students with a strong interest in mathematics.

Prerequisites: A love of mathematics, a very solid background in one-variable calculus, and instructor's permission.

Should you take Math 25a instead?: The two courses cover similar topics. Math 55a puts even greater emphasis on abstraction and rigor. In practice, it may not be immediately obvious which of the two courses better fits your needs. Math 25a and 55a are closely coordinated during the first three weeks. If you feel comfortable in 55a during those three weeks, that is likely to continue. On the other hand, if  you are straining to keep up with 55a in the beginning, then the course is most likely not appropriate for you. A quiz on October 5 will also help you decide. During the first three weeks, you can easily switch to 25a, without penalty. If you do make the switch, you need to inform the registrar's office that there is a special arrangement for moving between 55a and 25a until October 8.

Instructor: Wilfried Schmid, Science Center 519, 495-7840; email: schmid@math, office hours TuTh 2:30-3:30pm.

Course Assistant: Tseno Tselkov, email tselkov@fas. Section meetings: Mondays, 8:00 - 9:00 pm, Science Center 507.

Textbooks: The course does not follow any particular textbook. For the first part of the course, Topology and Modern Analysis by George F. Simmons is a good reference. Towards the end of 55a and in all of 55b, we shall use Calculus on Manifolds by Michael Spivak.

Homework: Homework is a very important part of this course, and you should expect to spend a substantial amount of time doing it. Problems are posted on this website each Tuesday, and will be due in class on the following Tuesday". You are encouraged to discuss the homework with your fellow students, but you must write up the solutions by yourself. Late homework will not be accepted. Your two lowest homework scores are disregarded when your average homework grade is computed.

Exams: In-class quiz on October 5, midterm on November 8, and a take-home final exam.

Grading: Your final grade will be based on your performance on the homework (40%), the midterm (25%), and the final (35%).

A Word of Caution: This course is demanding and time-consuming. It would be unwise to take a second similarly time-consuming course concurrently.