Professor
Tara Holm Office: Malott 589 Phone: 6072552392 


If you have any questions, please come by my office, or send me email!!
Syllabus: Available in PDF.
Questionnaire from the first lecture: Available in PDF.
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.
Here are some websites that have useful information about LaTeX:
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 1523, 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, GaussBonnet theorem 

5/1/08 
Comments on projects, pizza 
Some final announcements 
5/7/08 
Projects
due by 12 noon!! 

5/14/08 
FINAL EXAM!! 24:30pm 