# MATA140 Introduction to Discrete Mathematics (4 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

Combinatorics, linear recurrence relations, graph theory

The contents correspond to Anderson: A First Course in Discrete Mathematics, chapters 1-6.

## Learning outcomes

After completing the course, the student

- can apply the basic principles of combinatorics, factorials, selections and repetitions, binomial coefficients and Pascal's triangle
- is familiar with the inclusion-exclusion principle and some of its applications
- knows how to calculate the number of partitions of a set and knows Stirling's numbers
- knows the basic properties of recurrence equations and knows some solution methods
- can model and solve combinatoric problems using linear recurrence equations
- knows graphs and the associated basic results, paths, trees, spanning trees, bipartiate graphs, and planar graphs
- knows Hamilton's graphs, the travelling salesman's problem, and Euler's graphs
- can model and solve combinatoric problems with graphs

## Description of prerequisites

Good command of the long mathematics curriculum of high school. Courses "How to prove it?" and "Introduction to mathematics" are useful.

## Study materials

Lecture notes (in Finnish)

Anderson: A First Course in Discrete Mathematics,

Springer & Biggs: Discrete Mathematics,

Matoušek & Nešetril: Invitation to Discrete Mathematics,

Hein: Discrete Mathematics

## Completion methods

### Method 1

**Evaluation criteria:**

Grading is based on the points from the course exam and the weekly exercises

Select all marked parts

### Method 2

**Evaluation criteria:**

Grading is based on the points from the final exam

Select all marked parts

**Parts of the completion methods**

x

### Teaching (4 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Evaluation criteria:**

Opintojakson arvosana määrätyy kurssitentistä ja harjoituksista saatujen pisteiden perusteella.

**Language:**

Finnish

**Study methods:**

28 h luentoja, 7 laskuharjoituskertaa

#### Teaching

##### 8/29–10/23/2022 Lectures

##### 10/26–10/26/2022 Exam

##### 11/16–11/16/2022 Exam

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Evaluation criteria:**

The grade is based on the number of points in the final exam.

**Language:**

English, Finnish