MATHEMATICS 3805, CLASS OUTLINE FOR WINTER 2004

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

~

~

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.