MATHEMATICS 3825/3855, CLASS OUTLINE FOR WINTER 2011 (TENTATIVE)

WEEK 

DATES 

LECTURES 

SECTIONS 

TUTORIALS 

1

Jan. 3-7

Pigeonhole and addition principle. Counting sets of pairs. Euler's function.

6.2, 6.4; 10.1 - 10.3

No tutorial.

2

Jan. 10-14

Functions, words and selections. Ordered selections without repetitions. Permutations.

10.4 - 10.6

No tutorial.

3

Jan. 17-21

Binomial numbers. Unordered selections with repetitions. Binomial thm. Sieve principle.

11.1 - 11.4

No tutorial.

4

Jan. 24-28

Partitions of sets and positive numbers. Multinomial numbers.

12.1 - 12.4

No tutorial.

5

Jan. 31 - Feb. 4

Power series and algebraic properties. Partial fractions.

25.1 - 25.2

Review for Test #1.

6

Feb. 7-11

Binom thm w/negative exponents. Generating functions.

25.3 - 25.4

Test #1 (Chapters 6, 10, 11 and 12).

7

Feb. 14-18

Linear recurrences. Nonhomogeneous linear recurrences. Partitions and diagrams. Conjugate partitions.

25.5 - 25.6; 26.1 - 26.2

Solutions of Test #1.

8

Feb. 21-25

Reading Week

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9

Feb. 28 - Mar. 4

Partitions and generating funcs. Restricted partitions.

26.3

No tutorial.

10

Mar. 7-11

Graphs and their representation. Isomorphisms. Valency. Paths and cycles.

26.4; 15.1

Review for Test #2.

11

Mar. 14-18

Trees. Vertex colouring. Planar graphs. Euler's theorem.

15.2 - 15.6

Test #2 (Chapters 25, 26 and 15).

12

Mar. 21-25

Words, codes and errors. Linear codes. Construction of linear codes.

class notes; 24.1 - 24.2

Solutions of Test #2.

13

Mar. 28 - Apr 1

Designs, t-designs. Course revision.

24.3; 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.