Course: Math 441/541
Instructor: Prof. Joe Borzellino
Time: MTRF 2:10–3:00pm, Mathematics & Science 38-218
Office Hours:
TR 9:30am-11:00am F 10:10am-11:00am, (or by appt/email) in FOE 25-302
Phone: 756–5192
E–Mail: jborzell
Web Page:
Text: Milnor, Topology from a Differentiable Viewpoint
Chapters Covered: As much as we can!

Other References:

  1. Gauld, Differential Topology: an introduction
  2. Guillemin & Pollack, Differential Topology
  3. Bröcker & Jänich, Introduction to Differential Topology
  4. Wallace, Differential Topology: first steps

Your grade for the course will be determined by a cumulative point total weighted as follows:

Homework 33% Midterm 33% Final Exam 34%


The dates for the exams are as follows:

Midterm: Friday, May 11
Final Exam:
Friday, June 15, 1:10pm–4:00pm

NOTE: All exams are CLOSED book. Notes and books will not be allowed. There are NO makeup exams. If an emergency situation arises which will cause you to miss an exam, you must contact me BEFORE the exam is given. Academic dishonesty will not be tolerated. Possible penalties include a failing grade for the course.

Homework: I will be assigning homework on a regular basis. Unlike last quarter, solutions to problems are not outlined in the back of the text. As a result, the number of problems assigned will be less than last quarter. What I will be looking for is well-written, understandable and correct solutions to the homework problems. If you make a claim in the solution to a problem, you should be able to justify it – this includes clearly explaining your reasoning to classmates in front of the board. You can collaborate on solutions to homework, but the work you turn in should be your own.

Note for Graduate Students: You will be responsible for the supplementary exercises in addition to the regular exercises from the book. I will expect you to present your solutions to the supplementary exercises to the class. We will work out the who/what/when as the quarter progresses.

Differential topology is in many ways a unifying mathematical subject. It will incorporate aspects of single and multivariable analysis, linear algebra, group theory and, of course, topology. I hope you enjoy it.

Math 441/541