# 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

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