WEEK |
DATES |
LECTURES |
SECTIONS |
TUTORIALS |
1 |
Sep. 10-14 |
Pigeonhole and addition principle. Counting sets of pairs. Euler's function. | 2.4; |
No tutorial. |
2 |
Sep. 17-21 |
Functions, words and selections. Ordered selections without repetitions. Permutations. |
3.4 - 3.6 |
Chapters 1 and 2. |
3 |
Sep. 24-28 |
Binomial numbers. Unordered selections with repetitions. Binomial thm. Sieve principle. |
4.1 - 4.4 |
Chapter 3. |
4 |
Oct. 1-5 |
Arithmetical applications. Partitions of sets and positive numbers. Multinomial numbers. |
4.5; |
Test 1 |
5 |
Oct. 8-12 |
No lecture on October 8. Recursive technique examples. |
notes |
No tutorial. |
6 |
Oct. 15-19 |
Power series and algebraic properties. Partial fractions. Binom thm w/negative exponents. |
18.1 - 18.3 |
Chapters 4, 5. |
7 |
Oct. 22-26 |
Generating functions. Linear recurrences. Partitions and diagrams. |
18.4 - 18.6; |
Test 2 |
8 |
Oct. 29 - Nov. 2 |
Conjugate partitions. Partitions and generating funcs. Restricted partitions. Calculation of p(n). |
19.2 - 19.6 |
Chapter 18. |
9 |
Nov. 5-9 |
Graphs. Representations. Isomorphisms. Valency. Paths and cycles. |
8.1 - 8.4 |
Chapter 19. |
10 |
Nov. 12-16 |
Trees. Vertex colouring. Planar graphs. |
8.5 - 8.6; |
Test 3 |
11 |
Nov. 19-23 |
Planar graphs (cont). Words, codes and errors. |
notes; |
Chapter 8. |
12 |
Nov. 26-30 |
Linear codes and their construction. Correcting errors in linear codes. |
17.2 - 17.4 |
Planar graphs; |
~ |
Dec. 3 |
Error-correcting codes. Course revision. |
17.4 |
Chapter 17. |
All sections are from the textbook (Discrete Mathematics by
Norman L. Biggs).
Notes will be provided for recursive technique examples
and for planar graphs.