Math 455: Applicable Geometry

Course Home Page
Instructor:
Edward Swartz
Office: 592 Malott Hall
Phone : 255-1443
Email: ebs@math.cornell.edu
Office Hours: Monday - 1:10-2:10. Wed. - Sometimes 2:40-3:40, other times 4-5. 4/29: 2:40 - 3:40   Also, by appointment.


Teaching Assistant:
Juan Alonso
Office hours: Monday and Wednesday 10:30-11:30
Room: Malott 218
Optional Text:
Lectures on Polytopes: G. Ziegler
        Approximately two-thirds of the course will be based on this text.
Course description:
         An introduction to the theory of n-dimensional convex polytopes and polyhedra.  We will discuss both combinatorial properties (such as face counts) as well as metric properties.  We will apply these ideas to a variety of situations.    

Grading: Class participation 10%, HW 50%, two take home prelims 20% each. The two lowest HW grades will be dropped.


Prelims:
The first prelim will be handed out on March 26 and will be due April 2. HERE   is the first prelim. (CORRECTED 3/28) There will be extra office hours Tues. 4:15 - ? and Wed. 4 - ?  
The second will be handed out the last day of class and will be due May 13. HERE  is the second prelim.

Lecture topics;
 1/20 - What are we going to study?
1/22 - Introduction to affine geometry and convexity
1/29 - Faces of convex sets
2/5   - Compact convex sets
2/12 - H-polytopes = V-polytopes. Intro. to simplicial complexes.
2/19 - Geometric simplicial complexes. Face counting and shellability.
2/26 - Line shellings, Dehn-Sommerville equations and Euler's formula.
3/5   - g-thm, Intro. to duality.
3/12 - Duality continued. Intro. to Möbius functions.
3/26 - Möbius inversion.
4/2   - Hyperplane arrangements and graphs
4/9   - Euler's formula. Zonotopes.
4/16 - Graphs of polytopes - Balinski's Theorem. Graphs of simple polytopes
4/23 - Graphs of polytopes cont. - Steinitz theorem.
4/30 - Four dimensional polytopes and Schlegel diagrams.

Homework:
  Every Tuesday students will present in class the solutions to problems assigned the previous Thursday. At the end of class on Tuesdays (or shortly thereafter) a short problem set will be assigned whose written solution is due two days later at the next class (Thursday).  

Problems for Tuesday

1/27    Hints     Problem 6
2/3
2/10     Hints
2/17    Hints
2/24    Hints    Stanley's trick
 3/3    Hints
 3/10   Hints
 3/24   Hints
 4/14   Hints
 4/21   Hints
 4/28   

HW

HW1    
HW2     Solution to #4
HW3    
HW4    
HW5    
HW6    
HW7    
HW8    
HW9    
HW10    
HW11    
HW12