Scientific Disciplinary Sector (SSD)
MAT/02 - ALGEBRA
Secondo semestre dal Mar 6, 2023 al Jun 16, 2023.
The course provides a first introduction to homological algebra and representation theory of quivers, an important branch of modern algebra with connections to geometry, topology, theoretical physics and data science.
Prerequisites and basic notions
Linear algebra, basic notions of group theory and ring theory
The first part of the course introduces to quivers and representations and covers fundamental notions and results from module theory. The second part provides some basic knowledge on categories and functors and introduces to homological algebra: homological functors, complexes, homology.
The course consists of front lessons and classroom exercises. Moreover optional tutoring activities are offered. In particular, weekly home exercises are given. They are individually corrected by a tutor and discussed during the exercise hours.
Learning assessment procedures
The exam consists of an oral examination. Each student may choose to either: 1. carry out a traditional oral examination on the contents of the course; or 2. present a topic chosen in agreement with the course coordinators.
The exam is aimed at verifying full maturity concerning demonstrative techniques and the ability to read and understand more advanced topics.
Criteria for the composition of the final grade
Additional points will be awarded to those students who achieve 50% or higher in the weekly exercise sheets.