# MAN 240 : Diskret Matematik

New information relevant to this year is as follows :

I have decided to reorder the topics somewhat and insert some extra "elementary" stuff at the beginning. A rough plan is to divide the course into three parts as follows :

Part I : Enumerative combinatorics

Covers sections 2.4, 3.1-3.5, 4.1-4.4, 12.1-12.2, 18.3-18.6 (new edition : 6.1-6.4, 10.1-10.2, 10.4-10.5, 11.1-11.5, 19.1-19.2, 25.3-25.6)

Part II : Graph theory

Covers chapters 8-11 (new edition : chapters 15-18).

Part III : To be decided later.

OBS! The most important change is in how the course will be examined. Namely, I intend to give more homeworks this time (probably four) and assign 1/3 of the final grade to these. It is allowed to work in groups on the homework problems, but each person must write up their own solutions. Evidence of copying will be severely punished !!

LECTURES AND LEKTIONER :

I will write up short summaries of my lectures. I expect that much of the time during the 9 lektioner will be used to answer your questions about the homework problems. The first homework will be ready by Friday. However, I will also write up a list of suggested exercises for the övningsledare to do in advance of each lektion, in case there is time over.

Here follows the day-by-day plan, which will be updated regularly.

DAY 1 : Wednesday, March 26

Lecture : Sections 3.4, 4.1, 4.3 (new edition : 10.4, 10.5, 11.1, 11.3).

Lektion : suggested exercises 2.4.3, 3.1.4, 3.2.1, 3.4.1, 3.5.4, 3.7.4, 4.1.7, 4.2.2, 4.3.2(iv)

(new edition : 6.4.2, 10.1.4, 10.2.1, 10.4.1, 10.5.4, 10.7.4, 11.1.7, 11.2.2, 11.3.2(iv))

DAY 2 : Friday, March 28

Lecture : Sections 4.2, 4.4, 4.5 (Theorem 4.5.1) (new edition : 11.2, 11.4, 11.5)

DAY 3 : Wednesday, April 2

Lecture : 4.2, 4.4 (ctd.), 12.1 (new edition : 11.2, 11.4 (ctd.), 19.1)

Lektion : suggested exercises 4.4.1, 12.2.3 (new edition : 11.4.1, 19.2.3)

DAY 4 : Friday, April 4

Lecture : 12.2, 18.3 (new edition : 19.2, 25.3)

DAY 5 : Wednesday, April 9

Lecture : 18.3 - 18.6 (new edition : 25.3 - 25.6). Extra : Catalan numbers. ps pdf dvi tex

Lektion : 18.3.4, 18.4.1, 18.6.1 (new edition : 25.3.4, 25.4.1, 25.6.1)

DAY 6 : Friday, April 11.

Lecture : We finished Chapter 18.

DAY 7 : Wednesday, April 23.

Lecture : 8.1-8.4. Extra : Dirac's theorem on Hamilton cycles. ps pdf dvi tex

Lektion : 8.1.2, 8.2.1, 8.3.1, 8.4.3 (new edition : 15.1.2, 15.2.1, 15.3.1, 15.4.3)

DAY 8 : Friday, April 25.

Lecture : 8.6, 8.7. Extra : Some remarks on planar graphs. ps pdf dvi tex

DAY 9 : Wednesday, April 30.

Lecture : Extra : Mantel/Turan theorem, Euler's theorem for planar graphs. ps pdf dvi tex

Lektion : 8.6.2, 8.7.1, 8.7.2 (new edition : 15.6.2, 15.7.1, 15.7.2).

DAY 10 : Wednesday, May 7.

Lecture : 8.5. Some extra stuff on counting trees. ps pdf dvi tex

Lektion : 8.5.1, 9.1.4, 9.1.6 (new edition : 15.5.1, 16.1.4, 16.1.6)

DAY 11 : Friday, May 9.

Lecture : 9.3, 9.4, 9.5, 9.6, 11.1 (started)

DAY 12 : Wednesday, May 14.

Lecture : 11.1-11.5, 10.4 (started) (new edition : 18.1-18.5, 17.4)

Lektion : 9.3.3, 9.4.3, 9.6.1, 11.1.2, 11.5.2, 10.4.1, 10.4.2 (new edition : 16.3.3, 16.4.3, 16.6.1, 17.1.2, 17.5.2, 16.4.1, 16.4.2)

DAY 13 : Friday, May 16.

Lecture : 10.4, 10.5. Extra : König's theorem and connection to MFMC theorem ps pdf dvi tex

DAY 14 : Wednesday, May 21.

Lecture : 10.2 (started).

Lektion : 10.5.3, 10.7.2, 10.7.13, 10.7.17, 10.2.1, 10.2.3, 10.2.5 (new edition : 17.5.3, 17.7.2, 17.7.13, 17.7.17, 17.2.1, 17.2.3, 17.2.5)

DAY 15 : Friday, May 23.

Lecture : 10.2 (finished). Extra : Posets ps pdf dvi tex

DAY 16 : Wednesday, May 28.

Lecture : repitition (see övningstentan below).

Lektion : repitition.

For some further exercises on enumerative combinatorics, check out Hemuppgift 1 at the following link

Homework 1 (deadline 15:00 on Friday April 11) ps pdf and solutions ps pdf

Homework 2 (deadline 17:00 on Monday, May 5) ps pdf and solutions ps pdf

Homework 3 (deadline 17:00 on Monday, May 26) ps pdf and solutions ps pdf

List of required theorems ps pdf dvi tex

Övningstenta ps pdf dvi tex

Tentamen 040603 ps pdf dvi tex och lösningar ps pdf dvi tex

Tentamen 230803 ps pdf dvi tex och lösningar ps pdf dvi tex

A useful website

Some cool 3-D graphs : dodecahedron icosahedron football