Instruction for Discrete Structures (2IT50)

Instructor: Tom Verhoeff

Q1 2017-2018

Tue 29 Aug 2017 Instructor Verhoeff is not available on Fri 22 Sep.
Please, attend an instruction of another group.
Tue 29 Aug 2017 To practice your problem solving skills for this course:

Useful Information

How to Contact Me

How to Submit Solutions for Homework

Instruction 1 (Fri 08 Sep 2017)

To prepare:

Why study relations?

Nontransitive dice

Warm-up problems on

Instruction 2 (Fri 15 Sep 2017)

To prepare:

Is the geometric relation "lies-entirely-on-top-of" transitive? See Paradoxical Triangular Braid.

How can relations appear in (Java) programming?

Note that the syntax differs considerably, but the reasoning is all similar.

Instruction 3 (Fri 22 Sep 2017)


Instruction 4 (Fri 29 Sep 2017)

To prepare:

Function notation is a bit "broken":

Alternative characterizations of injective and surjective functions:

You can (more) easily prove Lemma 3.13 using these characterizations. Similarly for exercise 3.9.9.

Euler cycles and Hamilton cycles appear in the mathematical sculptures by Koos Verhoeff.

Theorem on parity of number of nodes with odd degree.

Warm-up problems on

Instruction 5 (Fri 06 Oct 2017)

To prepare:

You can mail me your solutions (worked out as if it was an exam) for exercises 7 and 13.

In these videos, I have introduced the (convenient) notation X ⊑ y ("y is an upper bound of X") as abbreviation for
(∀ x : x ∈ X : x ⊑ y)
where X ⊆ U and y ∈ U .

This makes it possible to characterize sup(X) by (cf. Lemma 4.22):

(∀ y : y ∈ U : X ⊑ y ⇔ sup(X) ⊑ y)

Instruction 6 (Fri 13 Oct 2017)

To prepare:

Warm-up problems on about Group Theory (Ch.5):

Instruction 7 on Fri 20 Oct 2017

Warm-up problems on about Combinatorics (Ch.6):

The Twelvefold Way (Wikipedia): a systematic classification of 12 related enumerative problems concerning two finite sets.

A very nice (inexpensive and short) booklet on Combinatorics (including Graphs):

Robin Wilson.
Combinatorics: A Very Short Introduction.
Oxford University Press, 2016.
(Also available as ebook.)
For the course Discrete Structures, especially Chapters 1, 2, 3, 4, and 6 are relevant.

Instruction 8 (Fri 27 Oct 2016)

I am possibly absent!

To prepare:

Warm-up problems on about Number Theory (Ch.7):