
After completion of the course, the student is able to:
 recognise and apply properties of groups
 know and recognise several constructions of groups
 know and work with group homomorphisms and isomorphisms and understand their role in the more general context of mathematics
 work with rings and fields
 apply the (extended) Euclidean algorithm to integers and polynomials
 investigate and understand when two algebraic structures are isomorphic
 understand and describe several applications of Algebra, such as cryptography, the word problem, symmetries and isomorphisms of structures


This course provides an introduction to abstract algebra and some of its applications. Three families of algebraic structures are introduced and studied: groups, rings and fields. Roughly speaking, groups are generalisations of the set of integers equipped with addition; rings are generalisations of the set of integers equipped with both addition and multiplication; fields are generalisations of the set of rational numbers equipped with addition, multiplication and division by nonzero numbers. The generalisations go as far as finite structures and structures in which the operation(s) are noncommutative.
The backbones of the course are constructions for groups and the understanding of structurepreserving maps. As to applications of algebraic structures, the course addresses encryption based on RSA, the word problem, symmetries and isomorphisms in adjacent mathematical domains.
Topics covered in this course are:
 An overview of algebra and algebraic structures
 Constructions of groups: integers, integers modulo n, groups of matrices, groups of symmetry, groups of functions, finitely generated groups, cyclic groups
 Basics in group theory: group operations, cosets, the Lagrange Theorem, group homomorphisms and isomorphisms, quotients, free groups, group presentation
 Rings and ideals; fields
 Applications of algebra, including encryption, data analysis and the recognition of structurepreserving transformations




 VoorkennisLinear maps between vector spaces; calculations with matrices; properties of real and complex numbers; working with functions and relations 
Bachelor Applied Mathematics 
Bachelor Technical Computer Science 
  Verplicht materiaalCanvasLecture Notes, to be provided online 

 Aanbevolen materiaalWerkvormenAssessment
 Hoorcollege
 OpdrachtAanwezigheidsplicht   Ja 
 Werkcollege

 ToetsenAlgebra


 