WEEK |
DATES |
LECTURES |
SECTIONS |
TUTORIALS |
1 |
Sep. 12-16 |
Pigeonhole and addition principles. Counting sets of pairs. Euler's function. | 6.2, 6.4; 10.1 - 10.3 |
No tutorial. |
2 |
Sep. 19-23 |
Functions, words and selections. Ordered selections without repetitions. Permutations. |
10.4 - 10.6 |
Review of Chapters 6 and 10. |
3 |
Sep. 26-30 |
Binomial numbers. Unordered selections with repetitions. Binomial thm. Sieve principle. |
11.1 - 11.4 |
Review of Chapters 10 and 11. |
4 |
Oct. 3-7 |
Partitions of sets and positive numbers. Multinomial numbers. |
12.1 - 12.4 |
Review of Chapters 11 and 12. |
5 |
Oct. 10-14 |
No lecture on Oct. 10. Power series and algebraic properties. |
25.1 |
Midterm test #1 (Chapters 6, 10, 11 and 12) |
6 |
Oct. 17-21 |
Partial fractions. Binom thm w/negative exponents. |
25.2 - 25.3 |
Review of Chapter 25. |
7 |
Oct. 24-28 |
Generating functions. Linear recurrences. Nonhomogeneous linear recurrences. |
25.4 - 25.6 |
Review of Chapter 25. |
8 |
Oct. 31-Nov. 4 |
Partitions and diagrams. Conjugate partitions. Partitions and generating funcs. |
26.1 - 26.3 |
Midterm test #2 (Chapters 6, 10, 11, 12 and 25) |
9 |
Nov. 7-11 |
Restricted partitions. Graphs and their representation. |
26.4; 15.1 |
Review of Chapter 26. |
10 |
Nov. 14-18 |
Isomorphisms. Valency. Paths and cycles. Trees. Vertex colouring. Planar graphs. |
15.2 - 15.6 |
Review of Chapter 15 and planar graphs. |
11 |
Nov. 21-25 |
Euler's theorem. Words, codes and errors. Linear codes. |
class notes; 24.1 - 24.2 |
Midterm test #3 (Chapters 25, 26 and 15) |
12 |
Nov. 28-Dec. 2 |
Construction of linear codes. Designs. |
24.3; 11.6 |
Review of Chapter 24 and designs. |
13 |
Dec. 5 |
Designs and t-designs. Course revision. |
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.