Mathematics 224, Spring 2008

TuTh 11:40am--12:55pm Malott 224

W 7:30pm--9:55pm Malott 532

Professor Tara Holm
Office: Malott 589
Phone: 607-255-2392

Office Hours:

Tuesday & Thursday 1:00-1:30pm
Monday 2:40-3:40pm
By appointment

If you have any questions, please come by my office, or send me email!!

General Information

TA: Juan Alonso
TA's office hours: Monday and Friday 11am-12pm in Malott 218

Topics: Linear algebra and multivariable differential calculus.

Text: Hubbard & Hubbard, Vector Calculus, Linear Algebra, and Differential Forms, 3rd Edition. You can buy it from MatrixEditions or the Cornell bookstore.
A Student's Solutions Manual for the third edition is now available! You can pick up a copy at the Cornell bookstore, or online at MatrixEditions.

Syllabus: Available in PDF.

Questionnaire from the first lecture: Available in PDF.

Homework Assignments

The first Problem Set is due on 29 January 2008.
The second Problem Set is due on 5 February 2008.
The third Problem Set is due on 12 February 2008.
The fourth Problem Set is due on 19 February 2008.
The fifth Problem Set is due on 28 February 2008.
The sixth Problem Set is due on 6 March 2008.
The seventh Problem Set is due on 3 April 2008.
The eighth Problem Set is due on 10 April 2008.
The ninth Problem Set is due on 17 April 2008.
The tenth Problem Set is due on 24 April 2008.
The eleventh Problem Set is due on 1 May 2008.

Projects

Every student must hand in a written project. Your grade on the project will comprise 25% of your final grade. Projects should involve learning the material for a subject not covered in class, roughly a week's worth of material. You will then write up an exposition of the mathematics you have learned, including motivation, examples, at least one theorem, and at least one (detailed sketch of a) proof. You must meet with me to get your project approved.

More information is available in this PDF description. There is also some information about searching on MathSciNet in PDF.

LaTeX resources

Here are some websites that have useful information about LaTeX:

The Not-So-Short-Introduction to LaTeX2e (That's a PDF introduction to using LaTeX.)
HTML Intro (same as above, but in HTML)
LaTeX for beginners. This is an intro I found by google search
TeXShop. TeXShop is the Mac GUI for LaTeX. It's freeware.
LaTeX on Windows. This gives you an idea of how to install LaTeX on a windows machine. You will need a text editor.
WinEDT. This is a shareware text editor for Windows. I really like it. It has a lot of GUI features -- you can click on a "alpha" symbol, and it will insert \verb,\alpha, into your text. It's free for 30 days, then you have to pay (but only $30 or so). There should also be free implementations of emacs for windows machines.
A useful symbols list (PDF).
Here is a sample LaTeX file, an eps figure that it incorporates, and the PDF it should generate.

Exams

There will be one take-home prelim, to be handed out on March 6, 2008, and collected on March 13, 2008. The prelim is available in PDF!!
There will be a timed final exam on Wednesday May 14, 2008, from 2-4:30pm.

Lectures

Please take 15 or 20 minutes before each lecture to read the sections of the books that will be covered. It will help tremendously if you are familiar with the terminology and theorems that will be covered in class.

Date	Lecture Material	Notes from Lecture
Week 1
1/22/08	Overview, 4.1: defining integrals
1/24/08	4.2: probability and centers of gravity
Week 2
1/29/08	4.3: Which functions are integrable?
1/31/08	4.4, 4.5: Measure zero, Fubini's theorem
Week 3
2/5/08	4.5, 4.6: More on Fubini, Numerical methods
2/7/08	4.6, 4.7, 4.8: More numerical methods, different pavings, determinants
Week 4
2/12/08	4.8: Lots about determinants! Permutations.
2/14/08	4.8, 4.9: Permutations, Characteristic Polynomials
Week 5
2/19/08	4.9, 4.10: Characteristic polynomials, change of variables
2/21/08	4.10, 4.11: change of variables, Lebesgue integrals
Week 6
2/26/08	4.11: Lebesgue integration
2/28/08	5.1, 5.2: Volume of parallelograms, Parametrizations
Week 7
3/3/08	You must have your project approved!
3/4/08	5.2, 5.3: Volume of manifolds	Hand out prelim!
3/6/08	5.3: Volume & Integration on manifolds
Week 8
3/11/08	5.4: Integration and curvature
3/13/08	5.5: Fractals; Counting, operations on vector spaces	Prelim due!!
Spring Break!	March 15--23, 2008
Week 9
3/25/08	6.1
3/27/08	6.2,6.3	Outlines due!!
Week 10
4/1/08	6.3: Forms
4/3/08	6.4: integrating forms
Week 11
4/8/08	Video of Marston Morse
4/10/08	Simplicial complexes, discrete Morse theory
Week 12
4/15/08	6.5, 6.6: Forms in vector calculus, boundaries of paralellograms.
4/17/08	6.6, 6.7: boundary orientation; the exterior derivative	Rough drafts due!!
Week 13
4/22/08	6.9, 6.10: a bit about elctromagnetism; Stokes' Thm
4/24/08	6.11: Stokes' Thm in various guises; deRham cohomology
Week 14
4/29/08	Some more on cohomology, Gauss-Bonnet theorem
5/1/08	Comments on projects, pizza	Some final announcements
5/7/08	Projects due by 12 noon!!
5/14/08	FINAL EXAM!! 2--4:30pm