# MATS215 Algebraic Topology (9 cr)

**Study level:**

Advanced studies

**Grading scale:**

0-5

**Language:**

English

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

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

## Description

Basics of the theory of algebraic topology: Fundamental group and homology (Chapters 1 and 2 in Hatcher’s book)

## Learning outcomes

After completing the course, students are familiar with

- basic properties of the fundamental group, covering spaces, and homology groups
- basic techniques for calculating fundamental and homology groups
- classical applications of algebraic topology

## Description of prerequisites

Algebra 1: groups, Metric spaces, Topology. Complex Analysis is also useful.

## Literature

- Hatcher: Algebraic topology; ISBN: 0-521-79540-0
- Munkres: Topology; ISBN: 0-131-81629-2
- Munkres: Elements of algebraic topology; ISBN: 0-201-62728-0

## Completion methods

### Method 1

**Evaluation criteria:**

Course exam, written homework problems

Select all marked parts

### Method 2

**Evaluation criteria:**

Final exam

Select all marked parts

**Parts of the completion methods**

x

### Teaching (9 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Language:**

English

#### Teaching

##### 1/11–5/10/2024 Lectures

##### 5/23–5/23/2024 Course Exam

##### 6/5–6/5/2024 Course Exam

x

### Exam (9 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Language:**

English