# Discrete Mathematics and Graphs

## Content

This subject covers a variety of different topics

• Logic,
• Set theory,
• Number theory,
• Abstract algebra
• Combinatorics,
• Graph theory.
But most importantly, it should be taken just as an Introduction to mathematics. More detailed outline of the lectures is going to be updated below.

The script for the lecture will be available here.

### References

[DP] N. Donaldson, A. Pantano An Introduction to Abstract Mathematics Lecture notes available online

[De] M. Demlová Discrete Mathematics and Graphs Lecture notes for an earlier version of this course. 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 11, 12, 13,

[C] L. N. Childs: A Concrete Introduction to Higher Algebra

[J] R. Johnsonbaugh: Discrete Mathematics

## Requirements

### Homework

Every week, there will be two kinds of homework assigned.
• On Monday, I will assign voluntary homework A. This will be some theoretical question based on the lecture. The homework will be due to Wednesday (i.e. 2 days). Correct answers are awarded extra points to the exam. You should try to solve it on your own and be able to present the solution at the blackboard if asked.
• On Wednesday, I will assign compulsory homerwork B. You have to do this homework to get the assessment/zápočet. The homework will be due to next Wednesday (i.e. 1 week). Correctness is not evaluated, everything is allowed, this is only to check that you are making some effort.

### Assessment (Zápočet)

• Solving homeworks: There will be a compulsory homework every week. You are allowed not to hand in maximally 3 homeworks. Correctness is not evaluated.
• Passing a midterm test: see below
• Attendance is not required

### Midterm test

The midterm test will take place around the ninth week of semester (will be specified later). The time limit is 50 minutes. Maximal gain 20 points, limit to pass 10 points. Check the sample test.

### Exam (Zkouška)

You are allowed to sign in for an exam only if you already obtained your assessment (zápočet). The exam consists of a mandatory written part and optional oral part. The written part will be a test with maximal gain of 80 points, time limit 120 minutes. A bonus of (gain from the midterm) PLUS ( The gain from homework A) MINUS (10 points needed for the zápočet) is added to the gain of the written exam.

Here is a sample exam

The registration for the exam is possible via KOS.

You are allowed to take the optional oral part of the exam only if you scored at least 45 points (points from exam + midterm + bonus). You can gain at most 15 points from the oral exam. The oral part will always take place on the same day afternoon.

Finally, your grade is determined according to the following table