Matroid Theory Assignments:
Readings and Problems

This list will be updated gradually.


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Readings

Study for the week of

Aug. 30: Sections 1.1-1.5. This is a lot. First you should skim it to get some ideas. Then go back and start studying thoroughly.
Sept. 6: Sections 1.4-8.
Sept. 13: Section 2.1.
Sept. 20: Sections 2.2-4.
Sept. 27: Same.
Oct. 4: Sections 3.1-3.
Sections 4.1-2.
Oct. 11: Sections 4.1-3.
Sections 5.1-2.
Oct. 25: Sections 6.1, 6.3.
Nov. 1: Section 6.4.
Nov. 15: Sections 6.2, 6.6.
Nov. 22: Section 6.9.
Nov. 29: Recommended: Skim Sections 6.7-8 to get the basic ideas. If you are interested in algebraic matroids (matroids of algebraic dependence), the first two pages of Section 6.7 are a nice review of the basics. The rest of the section discusses various basic properties and open problems.
Nov. 29
(more):
Sections 5.3-4. Read them to learn the main theorem of each section and, in Section 5.4, the definitions of series and parallel operations for graphs and matroids. The most important operations are the parallel and series extensions; parallel and series minors are less important.
Dec. 6: Sections 7.1-3.
Dec. 13
(special
finals-week
classes):
Sections 8.1-4.
Learn the main results in Sections 8.2 and 8.4; skip the proofs unless you're interested.
Arrangements of hyperplanes and their matroids, from lecture.
Matroids of biased graphs, from Zaslavsky, ``Biased graphs. I, II''.

Problems

Basic problem assignment for the week of

Aug. 30: Problems in Sections 1.1-1.5.
Sept. 6: Problems in Sections 1.4-8. (In Sections 1.6 and 1.8, one or two will be enough.)
Sept. 13: Problems in Section 1.7-8, and start 2.1.
Sept. 20: Problems in Sections 2.1-2.
Sept. 27: Problems in Sections 2.2-4. (In Section 2.4, one problem will be enough.) Also see the extra problems on duality, below.
Oct. 4: Problems in Sections 3.1-3.
Oct. 11: Problems in Sections 4.1-3.
Problems in Sections 5.1-2.
Later: A few problems in Sections 5.3, 5.4.
Problems in Section 6.1, including the extra problems below. (I especially recommend, to begin with, ## 3, 5. Then both extra problems and other problems in the book.)
Problems 1-2 in Section 6.2.
Problems in Sections 6.3-6, 6.9.
Problems in Sections 7.1-3; also see the extra problems on coextensions and lifts.
Problems in Sections 8.1 (and see extra problems on connectivity below) and 8.3.
The problems on hyperplane arrangements.

Hand-In Assignments

Your choices must be approved in advance by me. This is to make sure they aren't too easy or too hard. (N.B. I trust you to pick reasonable problems in the later assignments.)

I'll accept a second version if you're not satisfied with the first version. Final versions must be in by Monday, February 21, 2005 (all students) (changed to Wednesday, Feb. 23).

Due Mon., 9/27: Two problems from each of Sections 1.4 and 1.7.
Due Thurs., 10/7: Two problems from each of Sections 2.1 and 2.2 in the book or the duality problem list.
Approved:
  • 2.1: 9 - 14, 16, 21, Duality page (1.1), (1.2); not 2 - 4, 6, 15, 20.
  • 2.2: 4, 6 (contained in Duality (1.1)), 8, 11; not 1, 2, 5, 7, 10 (proved in class), Duality (2.1).
Due Mon., 10/18: Two from each of Section 3.3 and 4.1.
Due whenever: One problem from Section 4.3.
One problem each from Sections 5.3 (not #1 or 5) and 5.4.
One problem each from Sections 6.1, 6.2, and 6.3.
Two problems from Section 6.4.
One problem from Section 6.5.
Two problems each from Section 6.6 and 6.9.
One problem from Section 7.1.
Two problems each from Sections 7.2 and 7.3.
Two problems from Section 8.1.
One problem from Section 8.3.

Extra Problems


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main course page.