WEEK |
DATES |
LECTURES |
SECTIONS |
TUTORIALS |
1 |
Jan. 6-10 |
Pigeonhole and addition principle. Counting sets of pairs. Euler's function. | 6.2, 6.4; 10.1 - 10.3 |
No tutorial. |
2 |
Jan. 13-17 |
Functions, words and selections. Ordered selections without repetitions. Permutations. |
10.4 - 10.6 |
Euler's function. |
3 |
Jan. 20-24 |
Unordered selections with repetitions. Binomial thm. Sieve principle. |
11.1 - 11.4 |
Binomial numbers. |
4 |
Jan. 27-31 |
Partitions of positive numbers. Multinomial numbers. Power series and algebraic properties. |
12.1 - 12.4; 25.1 |
Partitions of sets. |
5 |
Feb. 3-7 |
Partial fractions. Binom thm w/negative exponents. |
25.2 - 25.3 |
Test #1 (Chapters 6, 10, 11 and 12). |
6 |
Feb. 10-14 |
Generating functions. Linear recurrences. Nonhomogeneous linear recurrences. |
25.4 - 25.6 |
Solutions of test #1. Binomial theorem with negative exponents. |
7 |
Feb. 17-21 |
Reading Week |
~ |
~ |
8 |
Feb. 24-28 |
Partitions and generating funcs. Restricted partitions. |
26.1 - 26.4 |
Partitions and diagrams. Conjugate partitions. |
9 |
Mar. 3-7 |
Graphs and their representation. Isomorphisms. Valency. |
15.1 - 15.3 |
Test #2 (Chapters 25 and 26). |
10 |
Mar. 10-14 |
Trees. Vertex colouring. Planar graphs. Euler's theorem. |
15.4 - 15.6; class notes |
Solutions of test #2. Paths and cycles. |
11 |
Mar. 17-21 |
Words, codes and errors. Linear codes. Construction of linear codes. |
24.1 - 24.3; class notes |
Degree of a region. Necessary conditions for planarity. Kuratowski theorem. |
12 |
Mar. 24-28 |
Designs, t-designs. Latin squares. |
11.6 - 11.7; 13.5 |
Test #3 (Chapters 15 and 24, and planar graphs). |
13 |
Mar 31 - Apr 4 |
Finite geometry and designs. Course revision. |
23.6 |
Solutions of test #3. Latin squares (cont.). |
All sections are from the textbook (Discrete Mathematics, 2nd edition by Norman L. Biggs). Class notes are required for planar graphs.