WEEK |
DATES |
LECTURES |
SECTIONS |
TUTORIALS |
1 |
Jan. 3-7 |
Pigeonhole and addition principle. Counting sets of pairs. Euler's function. | 6.2, 6.4; 10.1 - 10.3 |
No tutorial. |
2 |
Jan. 10-14 |
Functions, words and selections. Ordered selections without repetitions. Permutations. |
10.4 - 10.6 |
No tutorial. |
3 |
Jan. 17-21 |
Binomial numbers. Unordered selections with repetitions. Binomial thm. Sieve principle. |
11.1 - 11.4 |
No tutorial. |
4 |
Jan. 24-28 |
Partitions of sets and positive numbers. Multinomial numbers. |
12.1 - 12.4 |
No tutorial. |
5 |
Jan. 31 - Feb. 4 |
Power series and algebraic properties. Partial fractions. |
25.1 - 25.2 |
Review for Test #1. |
6 |
Feb. 7-11 |
Binom thm w/negative exponents. Generating functions. |
25.3 - 25.4 |
Test #1 (Chapters 6, 10, 11 and 12). |
7 |
Feb. 14-18 |
Linear recurrences. Nonhomogeneous linear recurrences. Partitions and diagrams. Conjugate partitions. |
25.5 - 25.6; 26.1 - 26.2 |
Solutions of Test #1. |
8 |
Feb. 21-25 |
Reading Week |
~ |
~ |
9 |
Feb. 28 - Mar. 4 |
Partitions and generating funcs. Restricted partitions. |
26.3 |
No tutorial. |
10 |
Mar. 7-11 |
Graphs and their representation. Isomorphisms. Valency. Paths and cycles. |
26.4; 15.1 |
Review for Test #2. |
11 |
Mar. 14-18 |
Trees. Vertex colouring. Planar graphs. Euler's theorem. |
15.2 - 15.6 |
Test #2 (Chapters 25, 26 and 15). |
12 |
Mar. 21-25 |
Words, codes and errors. Linear codes. Construction of linear codes. |
class notes; 24.1 - 24.2 |
Solutions of Test #2. |
13 |
Mar. 28 - Apr 1 |
Designs, t-designs. Course revision. |
24.3; 11.6 - 11.7 |
No tutorial. |
All sections are from the textbook (Discrete Mathematics, 2nd edition by Norman L. Biggs). Class notes are required for planar graphs.