Department of Mathematical Sciences
Binghamton University

Math 580A, Convex Polytopes
Assignments

Fall 2012

Readings

• Chapter 0. Introduction and Examples. (Sept. 4 – 24.)
  Read it for early September (see syllabus).


• Chapter 1. Polytopes, Polyhedra, and Cones. (Sept. 28 – Oct. 22.)
  Read Sects. 1.1–3 for the end of September and the beginning of October.
  Read Sect. 1.4 for Oct. 10.
  Read Sects. 1.5–6 for Oct. 15.


• Chapter 2. Faces of Polytopes. (Oct. 24 – Nov. 14.)
  Read Sects. 2.1– 2.3 for the end of October.
  Finish the chapter for Nov. 14.


• Chapter 6. Duality, Gale Diagrams, and Applications. (Nov. 12 – Dec. 10.)
  Read Sects. 6.1–2 for Nov. 14–16. Note (if you're in the matroid seminar) that this is matroid theory!
  Read Sect. 6.3 for Nov. 19.
  Read Sects. 6.4, 6.5(intro)&(a) for Dec. 7.


• Chapter 7. Fans, Arrangements, Zonotopes, and Tilings (Dec. 12 – 17)
  Recommended readings: TBA.
  

Homework Exercises

After the initial submission, improved rewrites are expected. If you miss the deadline entirely, I still expect "improved rewrites", i.e., late submissions; there will normally be a slight deduction due to lateness. However, there are final deadlines, as I don't want piles of papers submitted at the last minute, and you shouldn't, either (that's today's moral).

I've marked certain problems as obligatory^† (the dagger marks them). Those are a minimum list. I expect to see more than the minimum list. An A requires significantly more than the minimum list.

1. First submissions due Sept. 19: Additional Exercise I.


2. First submissions due Mon., Oct. 1: Additional Exercise II^†.


3. First submissions due Mon., Oct. 1: Exercises 0.0^†, 0.1, 0.3, 0.5, 0.6.


4. First submissions due Mon., Oct. 15: Exercises 1.0, 1.1(a,b), 1.2.
   And catch up on previous work!


5. First submissions due Fri., Oct. 19: Exercises 0.7^†, 0.8^†, and Additional Exercises III, IV^†, V.


6. First submissions due Wed., Nov. 28: Exercises 1.4^†, 2.0, 2.2^†, and Additional Exercise VII, VII(c)^†, VIII^†.


7. First submissions due Fri., Dec. 7: Exercises 1.5^†, 2.7^†.


8. First submissions due Mon., Dec. 10: Exercises 2.3, 2.12^†, 2.14^†, 6.3^†.


9. First submissions due Fri., Dec. 14: Exercises 6.1, 6.2, 6.4, 6.5(a,b,c)^†, 6.8^†, 6.13, 6.14.


10. First submissions due January: Exercise 7.10.

Deadlines:

• Sets 1–3 preliminary final rewrites are due Fri., Nov. 16. Final rewrites must reach me Mon., Nov. 26.


• Set 4 preliminary final rewrites are due Mon., Nov. 26. Final rewrites due Fri., Nov. 30.


• Sets 5–6 final rewrites are due Wed., Dec. 12.


• Later sets: Final deadline will be Friday, January 11 Wednesday, January 16 (at midnight) – changed due to my tardiness returning papers.

Additional Exercises

• See the separate page in PDF format.