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Course module: 202001362
202001362
Algebra
Course info
Course module202001362
Credits (ECTS)3.5
Course typeStudy Unit
Language of instructionEnglish
Contact persondr. G. Loho
E-mailg.loho@utwente.nl
Lecturer(s)
Lecturer
dr. G. Loho
Contactperson for the course
dr. G. Loho
Examiner
dr. G. Loho
Lecturer
dr. L. Pehlivan
Lecturer
S. Piceghello
Academic year2022
Starting block
2A
RemarksPart of module 7 AM/TCS. Minor students: please register for the minor!
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
Aims
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
Content
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, 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 structure-preserving transformations
Assumed previous knowledge
Linear maps between vector spaces; calculations with matrices; properties of real and complex numbers; working with functions and relations
Module
Module 7
Participating study
Bachelor Applied Mathematics
Participating study
Bachelor Technical Computer Science
Required materials
Canvas
Lecture Notes, to be provided online
Recommended materials
-
Instructional modes
Assessment

Assignment
Presence dutyYes

Lecture

Tutorial

Tests
Algebra

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Kies de Nederlandse taal