Advanced Algebraic Structures

Uitgebreide vaknaam	Advanced Algebraic Structures
Leerdoelen	At the end of the course, the student is able to: 1. recognize, analyse, and calculate with examples the abstract notions ‘field extension’, `separability’, `normality’. The Galois correspondence can be formulated, and used in concrete examples. Moreover basic definitions, examples, and applications of the theory of modules over a commutative ring are understood (cyclic modules, Hom's, tensor products, exact sequences). 2. acquire skills in reproducing and designing proofs relevant in this theory.
Omschrijving	The first half of the course extends the field theory introduced in the course Algebraic Structures. Topics treated include Galois Theory, cyclotomic fields, quadratic reciprocity. The second half of the course treats some basic theory of modules over commutative rings (including tensor products).
Uren per week
Onderwijsvorm	Hoorcollege (LC), Werkcollege (T)
Toetsvorm	Schriftelijk tentamen (WE) (Final mark equals the grade for the final exam.)
Vaksoort	bachelor
Coördinator	prof. dr. J. Top
Docent(en)	prof. dr. J. Top
Verplichte literatuur	Titel Auteur ISBN Prijs Lecture notes Advanced Algebraic Structures L.N.M. van Geemen, H.W. Lenstra, F. Oort, and J. Top
Entreevoorwaarden	The course unit assumes prior knowledge acquired from Group Theory, Linear Algebra 1 and 2, and Algebraic Structures.
Opmerkingen
Opgenomen in	Opleiding Jaar Periode Type BSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I b BSc Mathematics and Physics (double degree) 3 semester I b keuzegroep BSc Mathematics: General Mathematics  ( Major track General Mathematics) 3 semester I b keuzegroep BSc Mathematics: General Mathematics  (Electives and Minor General Mathematics) 3 semester I b keuze BSc Mathematics: Probability and Statistics 3 semester I b keuze BSc Technische Wiskunde 3 semester I b keuze