WEEK |
DATES |
LECTURES |
SECTIONS |
TUTORIALS |
1 |
Sep. 9-13 |
Pigeonhole and addition principle. Counting sets of pairs. Euler's function. | 2.4; 3.1 - 3.3 |
No tutorial. |
2 |
Sep. 16-20 |
Functions, words and selections. Ordered selections without repetitions. Permutations. |
3.4 - 3.6 |
Review of Chapters 1 and 2. |
3 |
Sep. 23-27 |
Binomial numbers. Unordered selections with repetitions. Binomial thm. Sieve principle. |
4.1 - 4.4 |
Review of Chapter 3. |
4 |
Sep. 30 - Oct. 4 |
Partitions of sets and positive numbers. Multinomial numbers. |
5.1 - 5.4 |
Review of Chapters 4 and 5; |
5 |
Oct. 7-11 |
Power series and algebraic properties. Partial fractions. |
18.1 - 18.2 |
Test #1 (Chapter 3, 4 and 5) |
6 |
Oct. 14-18 |
No lecture on October 14. Binom thm w/negative exponents. |
18.3 |
Review of Test #1 and Chapter 18. |
7 |
Oct. 21-25 |
Generating functions. Linear recurrences. |
18.4 - 18.6 |
Review of Chapter 18; |
8 |
Oct. 28 - Nov. 1 |
Partitions and diagrams. Conjugate partitions. Partitions and generating funcs. Restricted partitions. |
19.1 - 19.4 |
Test #2 (Chapters 3, 4, 5 and 18) |
9 |
Nov. 4-8 |
Graphs. Representations. Isomorphisms. Valency. Paths and cycles. Trees. Vertex colouring. |
8.1 - 8.6 |
Review of Test #2 and Chapter 19; |
10 |
Nov. 11-15 |
Planar graphs. Euler's theorem. |
class notes |
Review of Chapter 8. |
11 |
Nov. 18-22 |
Words, codes and errors. Linear codes and their construction. |
17.1 - 17.3 |
Test #3 (Chapters 18, 19 and 8) |
12 |
Nov. 25-29 |
Designs, t-designs and latin squares. Designs, finite fields and finite geometry. |
4.6-4.7; 6.5; 16.5-16.6 |
Review of Test #3, planar graphs, and Chapter 17; [A2 handed in] |
~ |
Dec. 2 |
Course revision. |
~ |
No tutorial. |
All sections are from the textbook (Discrete Mathematics by Norman L. Biggs). Class notes are required for planar graphs.