Course Material for Introduction to Topology, 110.413, Spring 2017.

Professor: W. Stephen Wilson, Krieger 421,

Textbook: Introduction to Topological Manifolds, Second Edition, John M. Lee. ISBN: 978-1-4419-7939-1

There is a cheap paperback version.

Corrections to the book.

Class meets Tuesday and Thursday, 10:30 to 11:45 in Krieger 309.

Your TA is Cuiqing Li. His help room hours (Krieger 213) are 3-5pm Wednesdays and his office hours are 9-11am Fridays.

Office hours are Tuesday 11:45-12:45. However, the way they work is I'll be there for the first 15 minutes, and if no one comes, I'll feel free to leave unless someone has emailed me and told me they are coming but won't be there in the first 15 minutes.

You MUST own a physical copy of the textbook. I will give lots of open book exams, but the "book" cannot be on your computer. Sorry.

Many more students than usual are signed up for this course. It is NOT an "introduction to proofs" course. Students are assumed to have had a proof based course before this course, however, it isn't absolutely necessary. A good student might make the transition using the tried and true "sink or swim" technique. At the end of the semester, I will go back and do grades deleting the first 3 weeks of the semester just in case someone started with "sink" but learned how to "swim."

This being an advanced course, I have had some issues trying to deal with students appropriately. In particular, there are some students who are not interested in coming to class and being tested on whether they read the material or not. In some cases, they just want to sleep all morning. Other students need structure to the course. The one structure that isn't there is LECTURE. This is not a straightforward lecture course. The text is good, so, in general, we'll find better things to do in class. See below.

The point of that is to let you know that I will make up grades in two entirely different ways. One way does not penalize students who don't want to come to class. They still have to hand in weekly homework and take a serious test every 3 weeks, but asside from that, they are free to learn. The regular way of grading involves multiple inputs, see below.

For students who don't come to class

Here's how the course works for those who don't come to class. You hand in homework (somehow, we'll figure out how) every week, on time (i.e. Tuesday). You show up for the big EXAMS every 3 weeks.

For students who do come to class

Here's how the course works for those who come to class.


Ignoring the first Tuesday where nothing much gets done, Tuesdays are the day you hand in your homework. You also get to take a test at the start of class. It will probably consist of 2 problems, one that was on the homework, and one that is from the book, but not assigned as homework. The rest of Tuesday you will be assigned to groups to work on problems from the book. These problems might well show up on the big EXAMS that happen every 3 weeks.


On Thursday, we start with a quiz to see if you have read the required material. Then I'll probably give a sort of overview lecture on the material, except that every 3 weeks, there will be a major EXAM for the rest of the day.


The reading assignments are posted below. You will be quizzed on the reading on Thursday. Thursday, I will post the homework, due on that reading the next Tuesday. The test that Tuesday will be on that material, as will the in-class group work.


Grades will be figured in 3 ways.

First. 50% homework and 50% big exams given every 3 weeks.

Second. 20% homework, 20% big exams, 20% Thursday quizzes, 20% Tuesday tests, 20% Tuesday in-class group work. (You cannot do worse with this option than with the First option.)

Third. At the end of the semester I will run grades again after deleting the first 3 weeks.


You can work with others on the homework, but you should do your own writeup. Only 3 problems will be graded, but you don't know which 3.

Big EXAM days

Feb 16, Mar 9, Apr 6, Apr 27.

Reading Assignments

Quiz 1. Feb 2. Appendices A and B.

Problem Set Number 1. Due Feb 7.

Quiz 2. Feb 9. Appendix C and Chapter 2, Sections 1 and 2.

Problem Set Number 2. Due Feb 14.

Quiz 3. Feb 16. Chapter 2, Sections 3, 4, and 5.

Problem Set Number 3. Due Feb 21.

Quiz 4. Feb 23. Chapter 3, Sections 1, 2, and 3.

Problem Set Number 4. Due Feb 28.

Quiz 5. Mar 2. Chapter 3, Sections 4, 5, 6.

Problem Set Number 5. Due Mar 7.

Quiz 6. Mar 9. Chapter 4, Sections 1 and 2.

Problem Set Number 6. Due Mar 14.

Quiz 7. Mar 16. Chapter 4, Sections 3 and 5. Chapter 5, Section 1.

Problem Set Number 7. Due Mar 28.

Quiz 8. Mar 30. Chapter 5, Sections 2, 3, and 4.

Problem Set Number 8. Due Apr 4.

Quiz 9. Apr 6. Chapter 7, Sections 1, 2, and 3.

Problem Set Number 9. Due Apr 11.

Quiz 10. Apr 13. Chapter 7, Sections 4 and 5.

Problem Set Number 10. Due Apr 18.

Quiz 11. Apr 20. Chapter 7, Section 6. Chapter 8, Sections 1, 2, and 3.

Problem Set Number 11. Due Apr 25.

Quiz 12. Apr 27. Chapter 11, Sections 1, 2, and 3.

Alas, however unfair, our last problem set.

Problem Set Number 12. Due May 2.

Quiz 13. May 4. Chapter 11, Sections 4 and 5. Chapter 12, Sections 1, 2, and 3.