# MATA1420 Introduction to combinatorics (4 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2024-2025, 2025-2026, 2026-2027, 2027-2028

## Description

Introduction to combinatorics and linear recurrence relations.

The contents correspond to Anderson: "A First Course in Combinatorial Mathematics" and Bogart: "Discrete Mathematics", chapters 5-7.

## Learning outcomes

After completing the course, the student

- can apply the basic principles of combinatorics (addition principle, multiplication principle and inclusion-exclusion principle) and knows some of their applications.
- knows the the basic definitions of combinatorics, such as permutations and combinations.
- 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.
- can apply induction in proving results in combinatorics.
- is familiar with the generating functions.

## Additional information

The course is organized every second year alternating with the course "Introduction to graph theory". Introduction to combinatorics will be taught in autumn 2025 and autumn 2027.

## 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,

Anderson: A First Course in Combinatorial Mathematics,

Bogart: Discrete mathematics.

Erickson: Introduction to Combinatorics,

Berman & Fryer: Introduction to Combinatorics.

## Completion methods

### Method 1

**Evaluation criteria:**

Grade is based on weekly exercises and points from the exam.

Select all marked parts

### Method 2

**Evaluation criteria:**

Grade is based on the points from the final exam.

Select all marked parts

**Parts of the completion methods**

x

### Participation in teaching (4 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Language:**

Finnish

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Language:**

English, Finnish