WEEK |
DATES |
LECTURES |
SECTIONS |
TUTORIALS |
1 |
Jan. 5-9 |
Pigeonhole and addition principle. Counting sets of pairs. Euler's function. | 6.2, 6.4; 10.1 - 10.3 |
No tutorial. |
2 |
Jan. 12-16 |
Functions, words and selections. Ordered selections without repetitions. Permutations. |
10.4 - 10.6 |
Review of Chapters 6 and 10. |
3 |
Jan. 19-23 |
Binomial numbers. Unordered selections with repetitions. Binomial thm. Sieve principle. |
11.1 - 11.4 |
Review of Chapter 10. |
4 |
Jan. 26-30 |
Partitions of sets and positive numbers. Multinomial numbers. |
12.1 - 12.4 |
Review of Chapter 11. |
5 |
Feb. 2-6 |
Power series and algebraic properties. Partial fractions. |
25.1 - 25.2 |
Review of Chapter 12. |
6 |
Feb. 9-13 |
Binom thm w/negative exponents. Generating functions. |
25.3 - 25.4 |
Review of Chapter 25. |
7 |
Feb. 16-20 |
Reading Week |
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8 |
Feb. 23-27 |
Linear recurrences. Nonhomogeneous linear recurrences. Partitions and diagrams. Conjugate partitions. |
25.5 - 25.6; 26.1 - 26.2 |
Review of Chapter 25. |
9 |
Mar. 1-5 |
Partitions and generating funcs. Test (Chapters 6, 10, 11, 12 and 25). |
26.3 |
Review of Test. |
10 |
Mar. 8-12 |
Restricted partitions. Graphs and their representation. |
26.4; 15.1 |
Review of Chapter 26. |
11 |
Mar. 15-19 |
Isomorphisms. Valency. Paths and cycles. Trees. Vertex colouring. Planar graphs. |
15.2 - 15.6 |
Review of Chapter 15. |
12 |
Mar. 22-26 |
Euler's theorem. Words, codes and errors. Linear codes. |
class notes; 24.1 - 24.2 |
Review of Chapter 15 and planar graphs. |
13 |
Mar. 29 - Apr 2 |
Construction of linear codes. Designs, t-designs. Course revision. |
24.3; 11.6 - 11.7 |
Review of Chapter 24 and designs. |
All sections are from the textbook (Discrete Mathematics, 2nd edition by Norman L. Biggs). Class notes are required for planar graphs.