MATHEMATICS 70.385/95.385, CLASS OUTLINE FOR FALL 2002 (TENTATIVE)

WEEK 

DATES 

LECTURES 

SECTIONS 

TUTORIALS 

1

Sep. 9-13

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

2.4; 3.1 - 3.3

No tutorial.

2

Sep. 16-20

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

3.4 - 3.6

Review of Chapters 1 and 2.

3

Sep. 23-27

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

4.1 - 4.4

Review of Chapter 3.

4

Sep. 30 - Oct. 4

Partitions of sets and positive numbers. Multinomial numbers.

5.1 - 5.4

Review of Chapters 4 and 5;
A1 handed out

Oct. 7-11

Power series and algebraic properties. Partial fractions.

18.1 - 18.2

Test #1 (Chapter 3, 4 and 5)

6

Oct. 14-18

No lecture on October 14. Binom thm w/negative exponents.

18.3

Review of Test #1 and Chapter 18.

7

Oct. 21-25

Generating functions. Linear recurrences.

18.4 - 18.6

Review of Chapter 18;
A1 handed in

8

Oct. 28 - Nov. 1 

Partitions and diagrams. Conjugate partitions. Partitions and generating funcs. Restricted partitions.

19.1 - 19.4

Test #2 (Chapters 3, 4, 5 and 18)

9

Nov. 4-8

Graphs. Representations. Isomorphisms. Valency. Paths and cycles. Trees. Vertex colouring.

8.1 - 8.6

Review of Test #2 and Chapter 19;
A2 handed out

10

Nov. 11-15

Planar graphs. Euler's theorem.

class notes

Review of Chapter 8.

11

Nov. 18-22

Words, codes and errors. Linear codes and their construction.

17.1 - 17.3

Test #3 (Chapters 18, 19 and 8)

12 

Nov. 25-29  

Designs, t-designs and latin squares. Designs, finite fields and finite geometry.

4.6-4.7; 6.5; 16.5-16.6

Review of Test #3, planar graphs, and Chapter 17; [A2 handed in]

~

Dec. 2

Course revision.

~

No tutorial.

All sections are from the textbook (Discrete Mathematics by Norman L. Biggs). Class notes are required for planar graphs.