MATHEMATICS 70.385/95.385, CLASS OUTLINE FOR FALL 2001

WEEK 

DATES 

LECTURES 

SECTIONS 

TUTORIALS 

1

Sep. 10-14

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

2.4;
3.1 - 3.3

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;
5.1 - 5.4

Test 1
(Chap. 3)

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;
19.1

Test 2
(Chaps. 4, 5)

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;
notes

Test 3
(Chaps. 18, 19)

11

Nov. 19-23

Planar graphs (cont). Words, codes and errors.

notes;
17.1

Chapter 8.

12 

Nov. 26-30  

Linear codes and their construction. Correcting errors in linear codes.

17.2 - 17.4

Planar graphs;
Chapter 17.

~

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.