Prof. Ilya Kofman |
Office: 607 Mathematics, phone: 854-3210
Email: ikofman@math.columbia.edu Web site: http://www.math.columbia.edu/~ikofman/ |
Course Time and Place: 1:10pm - 2:25pm Monday and Wednesday, 405 Mathematics Building (Note room change)
Text: Differental Topology by Guillemin and Pollack
Supplementary Texts: Topology from the Differentiable Viewpoint by Milnor and Calculus on Manifolds by Spivak
Requirements: We will assume familiarity with linear algebra and vector calculus (Calculus IIIS/IVA). Basic Topology is not required, though it provides another useful perspective for much of what we will discuss.
Material Covered: Manifolds and smooth maps, tangent spaces and derivatives, transversality, intersection theory, vector fields, differential forms and Stokes Theorem, and some interesting consequences.
Homework: The homework assignments will be posted on this website, and any changes will be announced in class. Starred problems are extra credit. Incomplete work with good progress will be rewarded. I highly recommend working jointly on homework problems with fellow students, but in the end you must hand in your own work.
Grading: The course grade is apportioned as follows: homework 40%, take-home midterm exam 30%, final in-class presentation and written report 30%.
Help: My office hours are right after class in my office 607 Mathematics. The help room, 406 Mathematics, is open with people to answer questions all day long on weekdays, but some topics we cover require specialized knowledge.
Optimal Method of Study: (1.) Read appropriate sections
before coming to class. (2.) Come to class. (3.) Read the sections
again after class. (4.) Do the homework. Leave time to think--do
not put homework off until it is due! (5.) Come to office hours or
the help room with any remaining questions.
Week | Reading | Homework | Due |
January 22 | Sec. 1.1 | 1.1: 5,6,7,8,10,15 | Jan. 29 |
January 27 | Sec. 1.2, 1.3 | 1.2: 1,4,5,10,11, 1.3: 4,7,8 | Feb. 5 |
February 3 | Sec. 1.4, 1.5 | 1.4: 1,5,7,8,10 | Feb. 12 |
February 10-17 | Sec. 1.5, 1.6 | 1.5: 2,4,5,6,9, 1.6: 8,9,10 | Feb. 24 |
February 17-24 | Sec. 1.7, 1.8 | 1.7: 3,6,7,11,14, 1.8: 6,7,8,10 | March 5 |
March 3 | Sec. 2.1, 2.2, 2.3 | 2.1: 2,8, 2.2: 3, 2.3: | March 12 |
March 3 | Sec. 2.4, 2.5 | 2.4: 2.5: | Mar. 12 |
March 10 | Sec. 2.6, Review | Take-home Midterm Exam | Mar. 24 |
March 24 | Sec. 3.1, 3.2 | 3.1: 3.2: | April 2 |
March 31 | Sec. 3.3, 3.4 | 3.3: 3.4: | April 9 |
April 7 | Sec. 3.5, 3.6 | 3.5: 3.6: | April 16 |
April 14 | Sec. 3.7, Chapter 4 | 3.7: Chapter 4: | April 23 |
April 21 | Chapter 4 | Chapter 4: | April 30 |
April 28 | Presentations | In-class presentation and written report | |
May 5 | Presentations | In-class presentation and written report |