This page will be updated gradually.
The readings are from James Oxley, Matroid Theory, second edition, Oxford University Press, 2011.
Readings: Read these lightly first, then carefully.
Do the recommended problems and your choice of other problems.
Hand in the specified problems.
Extra problems and some definitions are on a separate page.
There are some errors in the book. Check the corrections page often.
| No. | Week of: | Reading: | Recommended problems: | Hand in: | Notes: |
|---|---|---|---|---|---|
| I | Jan. 28: | 1.1-5 | 1.1 # 1, 3-5, 6(two of the larger examples)
1.2 # 1-4; 1.3 # 1-4, 7 |
I. Feb. 4: 1.1 # 2, 14;
1.2 # 9; 1.3 # 6 | |
| II | Feb. 4: | 1.1-8 |
1.4 # 1-2, 5-7;
1.5 # 2, 5, 9, 11, 15(M1), 16(A1,2,4); 1.6 # 1, 6; 1.7 # 2, 5; 1.8 # 1 |
II. Feb. 12:
1.1 # 7, 11;
1.2 # 5;
1.3 # 6; 1.4 # 11; 1.5 # 8, 15(M2), 16(A3) | Makeup class Thurs. |
| III | Feb. 11: | 2.1-3
Chain-group matroids |
1.7 # 9(M1);
2.1 # 1, 3-5, 10, 19;
2.2 # 2, 7, 8, |
III. Feb. 20:
1.7 # 2.1 # 9, 11; 2.2 # 5-6 | |
| IV | Feb. 18: | 2.4,
Extra page on duality |
2.1 # 13, 15;
2.2 # 11;
2.4 # 1, 3, 4;
Duality # I(2), II(3), III(1); 3.1 # 2, 7-9; 3.2 # 1, 6-7 |
IV. Feb. 25:
2.2 # 4, 10;
2.3 # 5;
2.4 # 7; Duality # III(2); Rep'n # 1 | No class Fri. |
| V | Feb. 25: | 3.1-3, 4.1-2 |
3.1 # 1, 2, 8, 12;
3.2 # 6, 10;
3.3 # 2, 6, 8;
4.1 # 1, 6, 7; 4.2 # 1, 2, 4-6; Minors # 1, 2 |
V. Mar. 4:
2.2 # 12;
3.1 # 3, 15; 3.2 # 8, 11b; Minors # 4 | Makeup class Thurs. |
| VI | Mar. 11: | 4.3 | 4.3 # 2, 4, 5, 7 | VI. Mar. 14:
4.1 # 4;
4.2 # 1; 4.3 # 8, 9 | |
| VII | Mar. 18: | 5.1-4 |
5.1 # 2-4;
5.2 # 1, 3;
5.3 # 2;
5.4 # 1, 2, 8
In 5.4: Note Thm. 5.4.10 and Lemma 5.4.11. Learn series and parallel operations for graphs and matroids, especially parallel and series extensions. |
VII. Mar. 22:
5.1 # 3; 5.2 # 5; 5.3 # 3 [corrected from | Bull session Thurs. |
| — | Apr. 1: | No classes this week. | |||
| VIII | Apr. 8: | 6.1-4;
Notes on projective geometry |
Projective geometry # 1, 2;
6.1 # 1, 2(read), 3, 4, 6; 6.2 # 1-3; 6.3 # 1-3, 5(i), 6; 6.4 # 1, 4, 6 |
VIII. Apr. 12:
Projective geometry # 3, 4; 6.2 # 4; 6.3 # 4; 6.4 # 7 |
Makeup class Thurs. |
| IX | Apr. 15: | 6.4-6;
Skim Sects. 6.7-8 for the main ideas. |
6.2 # 9;
6.4 # 8(a);
6.5 # 1, and prove Prop. 6.5.6 and Conj. 6.5.11; 6.6 # 3(i), 6; 6.9 # 2, 8 |
IX. Apr 19:
6.4 # 8(b); 6.5 # 2, 5; 6.6 # 4; 6.9 # 10 |
Makeup class Thurs. |
| Apr. 22: | Special lecture | Alex Fink: Matroids over Rings | |||
| X | Apr. 24: | 6.6, 6.9, 6.10 | 6.6 # 5;
6.9 # 4, 5, and study the extra problem on modularity; |
X. Apr. 29: 6.9 # 2 | Makeup class Thurs. |
| XI | Apr. 29: | 6.10, Biased graphs |
Problems on biased graphs # 6 | Makeup class Thurs. | |
| XII | May 6: | 6.10, Biased graphs |
XII. May 10: Biased graphs # 5, 6 | Makeup class Thurs. | |