# Homological algebra and algebraic topology, 7.5 ECTS

Second level## Facts

No available facts**Course code**MM8020

## Syllabus

## Description

Homological algebra: homomorphisms, kernels, cokernels, exact sequences and complexes, Snake lemma, functorial properties of Hom and the tensor product, Tor and Ext, Universal Coefficient Theorem.

Topology: Euclidian and projective spaces, singular homology, fundamental group.

Applications on for example Brouwer fix point theorem and non-vanishing vector fields on spheres.

## Area of interests: Information only in Swedish

## Subject

### Mathematics

As a mathematical theory always implies that certain conclusions hold under certain given conditions, it can in principle say nothing about the physical reality. None the less mathematics has become an indispensable tool for a large number of subjects like astronomy, physics, chemistry, statistics and the technical sciences and in later times also for economy, biology, various social sciences and computor science. The role of mathematics in the applied sciences is both to supply notions for exact and adequate formulations of empirical laws but also from these laws to derive consequences, which can be used to find better models of the reality one has to describe. These tasks have lately become more important. Mathematics is in continual progress by intensive international research, new theories are created and already existing theories are simplified and augmented.