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Cursus: 202001362
202001362
Algebra
Cursus informatie
Cursus202001362
Studiepunten (ECTS)3,5
CursustypeOnderwijseenheid
VoertaalEngels
ContactpersoonS. Piceghello
E-mails.piceghello@utwente.nl
Docenten
Docent
dr. M. Melistas
Docent
dr. L. Pehlivan
Examinator
S. Piceghello
Docent
S. Piceghello
Contactpersoon van de cursus
S. Piceghello
Collegejaar2023
Aanvangsblok
2A
OpmerkingPart of module 7 AM/TCS. Minor students: please register for the minor!
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
Cursusdoelen
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
Inhoud
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 non-commutative.

The backbones of the course are constructions for groups and the understanding of structure-preserving 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 structure-preserving transformations
Voorkennis
Linear maps between vector spaces; calculations with matrices; properties of real and complex numbers; working with functions and relations
Participating study
Bachelor Applied Mathematics
Participating study
Bachelor Technical Computer Science
Module
Module 7
Verplicht materiaal
Canvas
Lecture Notes, to be provided online
Aanbevolen materiaal
-
Werkvormen
Assessment

Hoorcollege

Opdracht
AanwezigheidsplichtJa

Werkcollege

Toetsen
Algebra

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