Packing and Covering 2013


   János Pach 


   Andres J. Ruiz-Vargas


We will be using Combinatorial Geometry by János Pach and Pankaj K. Agarwal.

For the assignments, the last exercise (the one marked with an asterisk) will be the one that you should turn in. 

Office hours:14 to 17 hours on 7th of June. 

Course Syllabus

The following is a list of the main results seen in class. When a theorem was presented, it is assumed that you are also acquainted with the Lemmas and observations used for proving it. 


 Chapter one with the exception of Theorem 1.13

 Theorem 1.7 and Theorem 1.12 are the highlights
Chapter 2 with the exception of last section. That is, section: Approximation of a convex body by polytopes, was not seen in class.
Theorem 2.1 and Theorem 2.6 are the highlights. 
Chapter 3: Last section has not been presented (between packing and coverings) 
Theorem 3.2 and Theorem 3.8 and Theorem 3.7 are the highlights.
Chapter 4: Theorem 4.1 was presented.
Section Double-Lattice Packing was skipped
Chapter 5: Theorem 5.5 was presented.
Chapter 6:
Theorem 6.1
Lemma 6.2
Corollary 6.4
Theorem 6.6
Theorem 6.8
Section Sections of a ball packing was skipped
Chapter 7:
In this chapter, all of the results proved were without using Riemann’s zeta function, where it is written, it was replaced by a one. 
Lemma 7.3 was discussed and was proved in the exercise sessions for d=2. 
Lemma 7.5
Theorem 7.6
Theorem 7.7 (i)
Corollary 7.10
Theorem 7.11
Section Lattice packing and codes was skipped. 
Weak version of Theorem 7.17 
Chapter 8: Weak version of Theorem 8.3