| Instructor: | Jonathan Rogness | |
| Office: | Vincent Hall 431 | |
| Phone: | (Ask me after I switch offices.) | |
| Email: | rogness@math.umn.edu | |
| Web Page: | http://www.math.umn.edu/~rogness/ | |
| Course Page: | http://www.math.umn.edu/~rogness/math5345/ |
The fastest, most reliable way to reach me is via email. I have two different offices on campus, so I may not always be in Vincent 431, but I check my email (very) frequently. Occasionally I get a deluge of email, but anything with "Math 5345" in the subject line will get tagged as a high priority message.
| Course Description: |
This course is an introduction to various topics in topology. Roughly speaking, topology is the study of continuous functions. At the most basic level, we begin with a set of points and determine what additional information is needed to be able to define concepts like open, closed and continuous function. (This is analogous to abstract algebra, where we begin with a set of points and determine what we need to perform operations such as addition and multiplication.)
In the past the course was often taught as a precursor to Analysis, and yet it was never a prerequisite for any of our analysis courses. With this in mind, the department is slightly shifting the focus of the course this year. A rough outline of topics is as follows:
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| Prerequisites: |
Either [ Math 2263, 2374 or 2573 ] or [ concurrent enrollment in Math 2283, 2574 or 3283 ]
The ability to read, write, and understand proofs is important for success in this course. If you haven't previously taken such a course, pay careful attention to comments on your homework, and make use of office hours to ask me questions. The sections on Euclidean space and metric spaces will require you to work with ε's and δ's. |
| Textbook: |
Required: Topology Now!, Messer & Straffin, MAA, 2006.
Strongly Recommended: Topology, Kahn, Dover, 1995. As discussed in the course description, we are shifting the focus of the course slightly this semester. Kahn's book is a standard one for this course, and I will still draw heavily from it for topics which are covered in less depth (or left out entirely) in the required textbook. As a Dover book it's inexpensive and I'd highly recommend buying it. Roughly speaking we will cover Chapters 1, 3, 4, and 7 from Messer & Straffin, and Chapters 1-4 and 7 from Kahn. (There is a lot of overlap between the various chapters in the two books, so this does not mean that we are covering nine full chapters.) We will cover selections from Chapters 5 and 6 in Kahn, but less than in previous years. There are many other books which you may find useful as other references, including nearly any of the inexpensive Dover books on topology. A standard reference (and common textbook choice for this course in the past) is Topology by Munkres. If you have trouble with the sections on surfaces and/or three dimensional manifolds, The Shape of Space by Jeff weeks is a fantastic book. |
| Homework and Exams: |
Homework will be due roughly every 1-2 weeks, depending on our pace, selection of material, scheduled exams, etc. Assignments will be announced in class and placed online. Homework will not be accepted after an announced due date unless you've made previous arrangements with me. Collaboration is highly encouraged -- please work with other students! However, your solutions need to be written in your own words, and your homework should include a note saying whom you worked with. Occasionally I might give a special problem in class which is not required, but might be worth some extra credit.
We'll have in-class two midterms, tentatively scheduled for Wednesday 10/17 and Monday 11/15. Our final exam is scheduled for 8:00-10:00am on Wednesday, 12/19, unless at least 90% of the students in the class vote to have a take-home final instead. Make-up exams will only be permitted in extraordinary situations. (Think "emergency surgery," not "oversleeping.") |
| Grading Scheme: |
30% Homework 40% Midterms (20% each) 30% Final Exam Overall course grades will be at least this generous; I reserve the right to lower gradelines if a test or homework assignment turns out to be harder than intended.
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| Other Policies: | We will follow all University and IT policies regarding academic honesty and other matters. The most common situation involves asking for a grade of incomplete. Incompletes are given only in extremely unusual circumstances, and only if you arrange it with me in advance. Incompletes are given only if you have completed most of the course material at a satisfactory level -- at least two midterms at a C level -- but some terrible, unexpected event prevents you from finishing the course. In particular, we cannot give you an incomplete if you simply fall behind in your work. |