University of Wisconsin-Madison Mathematics Department

Math 551 Elementary Topology A first course in Topology Lecturer: Andrei Caldararu

Spring 2012

About the course: This is an introduction to the basic ideas and methods of point set topology. It is a good background for analysis courses and graduate topology courses. Normally it is advisable to have at least one previous proof-based course such as Math 341, Math 421, Math 521 or Math 541 before taking Math 551. Along with Math 521 and Math 541 this course is a necessity for students considering going on to graduate school in mathematics.

Special goal: One of the goals of this course is to reinforce what you have learned in earlier classes about how to construct and write proofs.

Lectures: There will be three 50 minute lectures per week:

Text: The textbook for the course is

Office hours: Mondays 1:30-2:30 in Van Vleck 605 and by appointment.

Grading: The term grade will be based on homework and the exams as follows: Homework: 30% Midterm: 30% Final Exam: 40%. Final grades are computed by totalling the points from the homework, the midterms and the final. Grade letters will be assigned with the following curve as a guideline: 20% A's, 30% B's, 30% C's, 20% D's and F's.

Homework: Homework will be due a week after it is assigned, during lecture. All claims that you make in your homework MUST BE PROVED in order to receive credit.

Homework assignments:

Homework assignment 1, due February 3: §1: 1, 4, 5, 7; §2: 2, 4, 5; §3: 3, 4

Homework assignment 2, due February 17: §3: 7, 11, 12, 13; §5: 1, 5; §6: 3; §7: 1, 5

Homework assignment 3, due March 5: §10: 2, 6, 7; §13: 1, 3, 5; §16: 1, 2, 4, 6

Homework assignment 4, due March 16: §17: 3, 5, 13, 14, 17; §18: 2, 5, 6, 13

Homework assignment 5, due March 28: §19: 5, 6, 7; §20: 1, 2, 5, 9; §22: 4, 5

Homework assignment 6, due April 23: §23: 2, 5, 9, 11; §24: 2, 3, 8; §26: 2, 3, 5, 6, 9, 11

Homework assignment 7, due Friday May 11: §51: 1,3; §52: 1, 3, 4; §53: 2, 4; §54: 5

Exams: There will be one 50 minute in-class midterm on Monday, March 12. There will be a 2 hour final exam on Monday, May 14, 7:25pm-9:25pm, in a room TBA. The exams will be a random selection of problems similar to homework problems from the homework assignments. The final exam will be cumulative.

Syllabus: The syllabus will be announced here shortly after the start of term.