About This Class
|#||Week of...||Links (edit)|
|1||Sep 12||About, Tue, Thu, Std2Disc|
|2||Sep 19||Tue, Thu, HW1, 14 Sets|
|3||Sep 26||Tue, Thu, Photo|
|4||Oct 3||Tue, Thu|
|5||Oct 10||HW2, Tue, Thu|
|6||Oct 17||Tue, Thu, HW3|
|7||Oct 24||Mon, Tue, Thu|
|8||Oct 31||Tue, Thu, HW4|
|9||Nov 7||TE1, Tue, Thu|
|10||Nov 14||Tue, Thu, HW5|
|11||Nov 21||Tue, Thu|
|12||Nov 28||Tue, Thu, HW6|
|13||Dec 5||Tue, Thu|
|14||Jan 9||Tue, IT83, Thu, HW7|
|15||Jan 16||Tue, Thu|
|16||Jan 23||Tue, HW8, Thu|
|17||Jan 30||Tue, Thu|
|18||Feb 6||TE3, Tue, Thu|
|19||Feb 13||Tue, Thu|
|20||Feb 27||Tue, Thu, HW9|
|21||Mar 6||Tue, Thu, HW10|
|22||Mar 13||Tue, Thu|
|23||Mar 20||Tue, Thu, HW11|
|24||Mar 27||Tue, Thu|
|25||Apr 3||Tue, Thu, HW12|
|26||Apr 10||Tue, Thu|
|Study||Apr 17||Office Hours|
|Exams||Apr 24||Final, PM|
|Table of contents|
Agenda: Learn about the surprising relation between the easily deformed (topology) and the most rigid (algebra).
Instructor: Dror Bar-Natan (http://www.math.toronto.edu/~drorbn/), email@example.com, Bahen 6178, 416-946-5438. Office hours: Thursdays 11:30-12:30.
Teaching Assistant: Andy Hammerlindl, firstname.lastname@example.org, Sidney Smith 6027A (temporary). TA Office Hours.
Classes: Tuesdays 10-12 and Thursdays 10-11 at Bahen 6183.
Optimistic Plan for the First Semester:
- Point set topology: Topological spaces and continuous functions, connectedness and compactness, Tychonoff's theorem and the Stone-Cech compactification, metric spaces, countability and separation axioms.
- Homotopy: Fundamental groups, Van Kampen theorem, Brouwer's theorem for the 2-disk. Homotopy of spaces and maps, higher homotopy groups.
- The language of category theory.
- A word about the classification of surfaces.
Optimistic Plan for the Second Semester:
- More on category theory, the fundamental theorem of covering spaces.
- Homology: Simplicial and singular homology, homotopy invariance, exact sequences, excision, Brouwer's theorem for the n-disk, Mayer-Vietoris, degrees of maps, CW-complexes, the topology of Euclidean spaces, Borsuk-Ulam.
- Cohomology: Cohomology groups, cup products, cohomology with coefficients.
- Topological manifolds: Orientation, fundamental class, Poincare duality.
We will mainly use James Munkres' Topology (http://vig.pearsoned.ca/catalog/academic/product/0,4096,0131816292,00.html) and Allen Hatcher's Algebraic Topology (http://www.math.cornell.edu/~hatcher/AT/ATpage.html) (Free!). Additional texts by Bredon, Bott-Tu, Dugundji, Fulton, Greenberg-Harper, Massey, Munkres and others are also excellent.
Students will be able to earn up to 40 "good deeds" points (30 if taking this as 427S) throughout the year for doing services to the class as a whole. There is no pre-set system for awarding these points, but the following will definitely count:
- Drawing a beautiful picture to illustrate a point discussed in class and posting it on this site.
- Taking classnotes in nice handwriting, scanning them and posting them here.
- Formatting somebody else's classnotes, correcting them or expanding them in any way.
- Writing an essay on expanding on anything mentioned in class and posting it here; correcting or expanding somebody else's article.
- Doing anything on our To do list.
- Any other service to the class as a whole.
Good deed points will count towards your final grade! If you got n of those, they are solidly your and the formula for the final grade below will only be applied to the remaining 100 − n points. So if you got 40 good deed points (say) and your final grade is 80, I will report your grade as 40 + 80(100 − 40) / 100 = 88. Yet you can get an overall 100 even without doing a single good deed.
Important. For your good deeds to count, you must do them under your own name. So you must set up an account for yourself on this wiki and you must use it whenever you edit something. I will periodically check Recent changes to assign good deeds credits.
The Final Grade
For students taking this course all year the final grade will be determined by applying an increasing continuous function (to be determined later) to 0.2HW + O.1TE1 + 0.2TE2 + 0.1TE3 + 0.4F, where HW, TE1, TE2, TE3 and F are the Home Work, Term Exam 1, Term Exam 2, Term Exam 3 and Final exam grades respectively. For students taking only the second half of the course the final grade will be determined by applying an increasing continuous function (possibly a different one) to 0.2HW + 0.15TE3 + 0.65F.
There will be about 12 problem sets. I encourage you to discuss the homeworks with other students or even browse the web, so long as you do at least some of the thinking on your own and you write up your own solutions. The assignments will be assigned on Thursdays and each will be due (unless otherwise noted) on the date of the following assignment, in class at 11AM. There will be 10 points penalty for late assignments (20 points if late by more than a week and another 10 points for every week beyond that). Your 10 best assignments will count towards your homework grade. If you are only taking the second half of the course, you'll only see 7 of the assignments and only your best 6 will count towards your homework grade.
The Term Exams
Term exam 1 and Term Exam 3 will take place in the afternoons or evenings outside of class time, on or around the weeks of November 7 and February 6, respectively. Term Exam 2 will take place sometime in the fall semester examination period. All term exams will be 2 hours long.
To help me learn your names, I will take a class photo on Thursday of the third week of classes. I will post the picture on the class' web site and you will be required to send me an email and identify yourself in the picture or to identify yourself on the Class Photo page of this wiki.
--Drorbn 18:44, 12 Sep 2005 (EDT)