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


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, topological data analysis, and homotopy type theory. The learning and understanding of abstract algebraic structures will be supported by mandatory Grasple exercises.
Topics covered in this course are:
 Constructions of groups: Integers and integers modulo n, matrix groups, symmetry groups and groups of functions
 Group Theory: group operations, cosets & Lagrange Theorem, group homomorphism, crucial structures in groups
 Rings and Fields
 Applications of Algebra including encryption, data analysis and the recognition of structurepreserving transformations




 Assumed previous knowledgeLinear 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 
  Required materialsCanvasLecture Notes, to be provided online 

 Recommended materialsInstructional modesAssessment
 AssignmentPresence duty   Yes 
 Lecture
 Tutorial

 TestsAlgebra


 