Title: Introduction to Topology
Instructor: Professor Joel M. Cohen

Office: MTH 2313,
Telephone: (301)405-5109, Home phone: (202)546-1823.
Class Time: T-Th, 9:30-10:45 Section 0101
Location:Math B0425
E-mail address: jcohen@umd.edu
Grader:

Prerequisite: MATH 410 or equivalent.

Office Hours: T-Th 1:00-2:00. Occasionally, it may be necessary to change this time, so let me know if you are planning to see me.  You can also send me email.  I will answer queries as quickly as possible during office hours, and as time permits otherwise.

Topics

Metric spaces, topological spaces, connectedness, compactness (including Heine-Borel and Bolzano-Weierstrass theorems), Cantor sets, continuous maps and homeomorphisms, fundamental group (homotopy, covering spaces, the fundamental theorem of algebra, Brouwer fixed point theorem), surfaces (e.g., Euler characteristic, the index of a vector field, hairy sphere theorem), elements of combinatorial topology (graphs and trees, planarity, coloring problems).  We will cover Munkres: Chapters 2-4, 9, and either 10, 12 or 13.  Supplementary material is in Armstrong: Chapters 1-5, and perhaps 7.

Makeup exams will not be given.  If you have an excused absence for an exam, the grade will be replaced by 1/2 of the final.  If you have taken both, the lowest grade will count for half.  Excused absences will be given only for valid medical reasons, University business, or appearances in court.  Excused homework or quizzes will not be used in computing the final grade.   Make-up quizzes will not be given.  Any unexcused absences on quizzes or exams or unexcused late homework will be counted as 0, including the final exam.  Any student with a valid reason to be excused from an exam must contact me prior to the exam, either by email or by phone, and present documentation at the next class session attended.   If you need to be excused for a religious observance, you should let me know as soon as possible, but in any case no later than the end of the first week.

Sample tests:  Sample tests are available by clicking here.

Homework:  Homework will be due each class day.  Each day's homework will be based on what is covered in the previous class.  If the assignment is not clear, make sure to ask before leaving the classroom!  Homework problems are listed below.  The answers to many problems can be found at the back of the text.  Exam questions will occasionally be taken directly from the homework, and more often will be only slight variations of the homework.  Homework problems will be discussed in class on request.

Grading: A total of 450 points is available in the course, allocated as follows:

   1.  Two 80-minute in-class exams, each worth 100 points.  The lowest grade will be counted for half. 
   2.  A final exam worth 200 points.
   3.  Daily homework assignments, for a total of 100 points.

First Exam: October 9

Second Exam: November 13

Final Exam: Tuesday, Dec 16, 8:00 am - 10:00 pm

Quality: The quality of presentation of solutions will be taken seriously in this course in the grading of tests and homework.

§ Homework assignments from the same section but due different weeks are separated by //.   Changes may be made during the course of the semester.  The Math 432 website www.joelmcohen.org/ will be kept up-to-date as changes are made.