Topology - Math 441:  Spring 2013 Syllabus

Department of Mathematics, College of Staten Island (CUNY)

Prof. Ilya Kofman

Office:   1S-209   phone: (718) 982-3615

Course Time and Place:  Mondays and Wednesdays   2:30pm - 4:25pm   in 1S-218

Textbook:  Introduction to Topology: Pure and Applied by Colin Adams and Robert Franzosa  Available at the University Bookstore or online.  ISBN: 0131-84869-0   ISBN 13: 978-0131-84869-6

Goals:  The primary goal of this course is to introduce you to topology, which is a major branch of modern mathematics.  Another goal is to learn how to do research in mathematics, including how to write concise but complete proofs, and how to present to others what you have learned.

Homework:  Assignments will be announced in class. Incomplete work with good progress will be rewarded. I highly recommend working jointly on homework problems with fellow students, but in the end you must hand in your own work.

Grading:  The course grade will be determined as follows:  homework and quizzes 20%,  two midterm exams 50%,   final in-class presentation and written report 30%.

Help:  My office hours are on Mondays and Wednesdays 11am - 12:15pm in my office, 1S-209.

How to Study:  (1.) Come to class.  (2.) Read the relevant sections after class.  (3.) Do the homework. Leave time to think--do not put homework off until it is due!  (4.) Compare your solutions with other students.  (5.) Come to office hours with any questions.

Topic Reading
Introduction: Euler's theorem for polyhedra Handout, notes
Sets and functions Chapter 0
Topological spaces Chapter 1
Interior, closure, boundary Chapter 2
Subspace, product and quotient topology Chapter 3
Continuous functions, homeomorphisms Chapter 4
Exam 1  
Metric spaces Chapter 5
Connected and path-connected spaces Chapter 6, and Hatcher's notes, p.21 on cut points, and pp.26-28 on the Cantor set.
Compactness Chapter 7
Quotient spaces and maps Handout, notes
Homotopy and degree theory Chapter 9
Euler characteristic, classification of surfaces Chapter 14, ZIP proof, online notes
Exam 2  
Student presentations  

  • How to doodle if you are bored in class.