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 |