0708-1300/About This Class: Difference between revisions
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'''URL:''' {{SERVER}}/drorbn/index.php?title=0708-1300. |
'''URL:''' {{SERVER}}/drorbn/index.php?title=0708-1300. |
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===Optimistic Plan=== |
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* 8 weeks of local differential geometry: the differential, the inverse function theorem, smooth manifolds, the tangent space, immersions and submersions, regular points, transversality, Sard's theorem, the Whitney embedding theorem, smooth approximation, tubular neighborhoods, the Brouwer fixed point theorem. |
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* 5 weeks of differential forms: exterior algebra, forms, pullbacks, <math>d</math>, integration, Stokes' theorem, div grad curl and all, Lagrange's equation and Maxwell's equations, homotopies and Poincare's lemma, linking numbers. |
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* 5 weeks of fundamental groups: paths and homotopies, the fundamental group, coverings and the fundamental group of the circle, Van-Kampen's theorem, the general theory of covering spaces. |
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* 8 weeks of homology: simplices and boundaries, prisms and homotopies, abstract nonsense and diagram chasing, axiomatics, degrees, CW and cellular homology, subdivision and excision, the generalized Jordan curve theorem, salad bowls and Borsuk-Ulam, cohomology and de-Rham's theorem, products. |
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===Warning=== |
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The class will be hard and challenging and will include a substantial component of self-study. To take it you must feel at home with point-set topology, multivariable calculus and basic group theory. |
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===Textbooks=== |
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We will mainly use Glen E. Bredon's <em>Topology and Geometry</em> (GTM 139, ISBN 978-0-387-97926-7). Additional texts include Allen Hatcher's [http://www.math.cornell.edu/~hatcher/AT/ATpage.html Algebraic Topology] (Free!) and texts by Bott and Tu, Fulton, Massey and many others. |
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===Lecture Notes=== |
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I'll be happy to scan the lecture notes of one |
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of the students after every class and post them on the web. We need a |
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volunteer with a good handwriting! |
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===The Final Grade=== |
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The final grade will be determined by |
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applying an increasing continuous function (to be determined later) to |
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<math>0.2HW+0.15TE1+0.15TE2+0.5F</math>, where <math>HW</math>, <math>TE1</math>, |
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<math>TE2</math> and <math>F</math> are the Home Work, Term Exam 1, Term Exam 2 |
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and Final grades respectively. |
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===Homework=== |
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There will be about 12 problem sets. I encourage |
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you to discuss the homeworks with other students or even browse the |
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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 on the date of the following assignment, |
|||
in class at 1PM (see the Navigation Panel). 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. |
|||
===The Term Exams=== |
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Term exam 1 and Term Exam 2 will take place |
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in the afternoons or evenings outside of class time, on the weeks of |
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November 15 and February 28, respectively. They will be 2 hours long. |
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===Class Photo=== |
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To help me learn your names, I will take a class |
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photo on Thursday of the third week of classes. I will post the picture |
|||
on the class' web site and you will be <em>required</em> to send me an |
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email to identify yourself in the picture. |
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Revision as of 13:04, 10 September 2007
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Crucial Information
Fall Agenda. Calculus for grown-ups, in dimensions higher than one and in spaces more general than .
Spring Agenda. Learn about the surprising relation between the easily deformed (topology) and the most rigid (algebra).
Instructor. Dror Bar-Natan, drorbn@math.toronto.edu, Bahen 6178, 416-946-5438. Office hours: by appointment.
Teaching Assistant. Omar Antolin Camarena, oantolin@math.toronto.edu, Sidney Smith 622, 416-978-2967.
Classes. Tuesdays 10-12 and Thursdays 12-1 at Bahen 6183.
Grades. All grades are on CCNet. URL: https://drorbn.net/drorbn/index.php?title=0708-1300.
Optimistic Plan
- 8 weeks of local differential geometry: the differential, the inverse function theorem, smooth manifolds, the tangent space, immersions and submersions, regular points, transversality, Sard's theorem, the Whitney embedding theorem, smooth approximation, tubular neighborhoods, the Brouwer fixed point theorem.
- 5 weeks of differential forms: exterior algebra, forms, pullbacks, , integration, Stokes' theorem, div grad curl and all, Lagrange's equation and Maxwell's equations, homotopies and Poincare's lemma, linking numbers.
- 5 weeks of fundamental groups: paths and homotopies, the fundamental group, coverings and the fundamental group of the circle, Van-Kampen's theorem, the general theory of covering spaces.
- 8 weeks of homology: simplices and boundaries, prisms and homotopies, abstract nonsense and diagram chasing, axiomatics, degrees, CW and cellular homology, subdivision and excision, the generalized Jordan curve theorem, salad bowls and Borsuk-Ulam, cohomology and de-Rham's theorem, products.
Warning
The class will be hard and challenging and will include a substantial component of self-study. To take it you must feel at home with point-set topology, multivariable calculus and basic group theory.
Textbooks
We will mainly use Glen E. Bredon's Topology and Geometry (GTM 139, ISBN 978-0-387-97926-7). Additional texts include Allen Hatcher's Algebraic Topology (Free!) and texts by Bott and Tu, Fulton, Massey and many others.
Lecture Notes
I'll be happy to scan the lecture notes of one of the students after every class and post them on the web. We need a volunteer with a good handwriting!
The Final Grade
The final grade will be determined by applying an increasing continuous function (to be determined later) to , where , , and are the Home Work, Term Exam 1, Term Exam 2 and Final grades respectively.
Homework
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 on the date of the following assignment, in class at 1PM (see the Navigation Panel). 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.
The Term Exams
Term exam 1 and Term Exam 2 will take place in the afternoons or evenings outside of class time, on the weeks of November 15 and February 28, respectively. They will be 2 hours long.
Class Photo
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 to identify yourself in the picture.
