Introduction to Topology, Spring 2019

Introduction to Topology, 110.413, Spring 2019
W. Stephen Wilson

W. Stephen Wilson: wwilson3@jhu.edu or wsw@math.jhu.edu

Textbook: Topology, Second Edition by James R. Munkres. ISBN: 0-13-181629-2

Class meets Tuesday and Thursday, 10:30 to 11:45 in the Smokler Center Library.

Office hours are Thursday, 11:45-12:45. (Krieger 421.) This is right after class, so if you want to come to office hours, you arrange that in class, or I won't be there. You can always email me with questions or to set up a meeting if the office hours don't work for you or aren't enough.

In addition, you should all know about the math department help room that is open nearly all day and most evenings during the week. It is in Krieger 213. Your grader will be there in the help room on Wednewsdays, 3-5pm, but most in the help room can help you with topology.

Students in this course are assumed to be (the equivalent of) serious math majors and will be treated as such. This is not an introduction to proofs course but assumes all students have had such a course already. Each week there will be a reading assignment and homework. Each class there will be a test and graded group work.

All students must attend every class and maintain a high level of consciousness during the entire class. You will have something serious to do during the entire class, every class (except the first one on Jan 29).

The reading assignments are already set for the entire course and are at the bottom of this website.

The pattern for the course is:

Tuesday: Your homework is due at the start of class on Tuesday. A test will be given immediately. The test will cover the material that you read for the homework just handed in. There will probably be two problems, one from the homework just handed in, and one from the sections the homework was based on. I reserve the right to ask whatever I want though.

More Tuesday: I will give a very short lecture on the material you are about to read for Thursday so you'll know the high points to look out for.

Tuesday Continued: After the test, I will assign small groups to work on a sequence of problems. These problems will be from the material you read for the homework you just handed in, so you should be really good at it. The group will write them up to be handed in at the end of the class for the whole group. The whole group will get the same grade on this. The groups will vary day to day.

Thursday: I give you a quiz when you walk into class. The primary purpose is to see if you have done the reading. It will cover really basic things like definitions and statements of theorems. No understanding is required to do well on this, but I want people prepared to work, not read, when they come to class on Thursday. You can teach a 10 year old to do this perfectly, so to make it college level, I'll add a serious topology content problem to the quiz.

Thursday continued: You will be assigned to small groups to work on problems. These problems will be for the reading you were just quizzed on. As above: The group will do as many of them as they can and write them up to be handed in at the end of the class for the whole group. The whole group will get the same grade on this. The groups will vary day to day.

More Thursday: I will post the homework on the next reading assignment sometime before the end of the day on Thursday.

Terminology: We call the Thursday exam on reading (plus some content) a "quiz" and the Tuesday exam on content a "test."

Grades, homework, and stuff: You have homework. Two or three problems of my choice, unknown to you, will be graded by the TA. Also, on Tuesday and Thursday you will be working problems in groups most of the class. Some of these problems will be graded. There are the two exams each week. All in all, there are lots of things that get graded that will go into your grade. How they will all be weighted will get worked out during the semester. For example, you will probably get graded on more problems worked in groups than individually, but your individual work will probably dominate the grade.

Group work: You are welcome to, even encouraged to, work together on homework, but you must write up your own homework. If you write up your own, it will not be the same as that written up by students you worked with.

The syllabus, subject to, but not likely to, change.

The first week is a bit awkward. You won't know anything on the first day of class, Jan 29, so you really can't be expected to do anything. The first chapter of the book (all 74 pages of it) are stuff I usually skip at the start of the course as it is mostly about basic terminology, notation, and elementary background. In general, I feel I should be able to assume this. However, this year I've decided to give the class a week to read this stuff.

So, what I'm going to do is give a long long quiz on sections 1.1 to 1.4 on Thursday, the second class, Jan 31, to see if you have read the material. Similarly, I'll give a long long quiz on sections 1.5 to 1.11 on Tuesday, Feb 5. This will give all of you a large number of points at the beginning of the course. It will also seriously penalize anyone who decided they didn't need to read the chapter I have so generously and unnecessarily given you a week to read. The first chapter amounts to reading assignment # 0. If I find any content in those chapters worth asking you about, I might slip content questions on those quizzes.

Problem set # 0.

Reading assignment # 1: Sections 12, 13, 14, and 15. Quiz to see if you read it, Feb 7.

Problem set # 1.

Homework # 1 due Feb 12. Test to see if you understood it same day.

Reading assignment # 2: Sections 16 and 17. Quiz to see if you read it, Feb 14.

Problem set # 2.

Homework # 2 due Feb 19. Test to see if you understood it same day.

Reading assignment # 3: Sections 18 and 19. Quiz to see if you read it, Feb 21.

Problem set # 3.

Homework # 3 due Feb 26. Test to see if you understood it same day.

Reading assignment # 4: Sections 20 and 21. Quiz to see if you read it, Feb 28.

Problem set # 4.