Discrete Mathematics I

Practice

There are 2+1 tests:
- 1st test (Logic, Sets, Relations and Complex Numbers), probably on the week 7-9.
- 2nd test (Combinatorics and Number Theory) at the end of the semester (probably on the last week).
- Retake test of the first and second test is (usually) in the last week of the term-time (week 15) or the first week of the exam season (week 16).
The tests consist of problem solving, usually material practised in class.
To have a passing mark (from practice) you need at least two successful tests (grades >1 pass).
- If you fail one of the first two tests, you have one more chance to the retake it.
- If you fail both tests, usually you fail the course...

Lecture

The exam season starts on the week 16.
You can take the (final) exam two times.
On the final exam, you have to know the material from the lectures, which is mostly theory (see below)

Final Exam

The 10 questions from the first part will ask for theorems, definitions and simple problems directly followed from them. Every question of the first part is worth 2 points.
The second part contains two theorems. Both of them are worth 10 points. Students must formulate the appropriate assertions and prove them.
Minimal requirements: 8 points from both parts.
Scoring: 1: 0 – 19 points, 2: 20 – 24, 3: 25 – 29, 4:30 – 34, 5: 35 – 40.

Logic.
Sets.
Relations: definitions, properties equivalence, ordering, composition and functions.
Complex numbers: rectangular (algebraic) and polar (trigonometric) form, roots of unity.
Combinatorics: permutations, variations, combinations, binomial theorem, pigeon hole principle, logical sieve (inclusion-exclusion principle).
Number theory l: divisibility, primes, irreducible elements, Euclidean division and algorithm, elementary number theory.
Number theory ll: congruences, residue classes, Euler-totient function, Euler and Fermat theorem, Diophantine equations and Chinese remainder theorem.

Theoretical summaries

Problems and Solutions