Prof. Ilya Kofman	Office:   1S-209   phone: (718) 982-3615 Email:   ikofmanmath.csi.cuny.edu Website:   http://www.math.csi.cuny.edu/~ikofman/

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