Caput Algebra and Geometry 20/21
Faculteit  Science and Engineering 
Jaar  2020/21 
Vakcode  WMMA02705 
Vaknaam  Caput Algebra and Geometry 20/21 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Caput Algebra and Geometry 20/21  
Leerdoelen  The student is able to 1. apply the bachelor's topics treated in abstract algebra in more advanced examples relevant to the course in question. 2. apply the theory presented in the course in concrete examples. 3. explain the basics of representation theory, irreducible representations, and character theory. 4. Explicitly construct the irreducible representations of small finite groups and be able to work with the irreps of S_n 

Omschrijving  The subject of the course varies with the national Mastermath program. This course intends to bridge the gap between the algebra taught in our bachelor program (Group Theory, Rings, (Finite) Fields, Modules), and various courses in Algebra and Geometry offered regularly in the national Mastermath program. 20/21: Representation Theory of Finite Groups We will study complex representations of a finite group, i.e., homomorphisms from a finite group to the group of invertible linear maps of a complex vector space. Properties of irreducible representations, character theory, and many examples including the irreducible representations of the symmetric groups S_n will be treated In previous years, the following topics were discussed: 19/20: Theory of Complex Multiplication 18/19: Computational algebraic number theory 17/18: The arithmetic of hyperelliptic curves 16/17: Galois Theory and applications 15/16: JP. Serre's book "A Course in Arithmetic". 

Uren per week  
Onderwijsvorm 
Hoorcollege (LC)
(Depending on the number of participants, the course is given as a series of lectures or as a seminar in which the participants each prepare and present a chapter from a chosen textbook.) 

Toetsvorm 
Mondeling tentamen (OR)
(Final grade is based on the answers of a homework set and the ability to discuss these during the oral examination) 

Vaksoort  master  
Coördinator  prof. dr. J. Top  
Docent(en)  prof. dr. J. Top  
Verplichte literatuur 


Entreevoorwaarden  Linear Algebra, Group Theory, and Algebraic Structures are required.  
Opmerkingen  The course unit prepares students for various mastermath courses in which the learning objectives attained are required as prior knowledge. This course was registered last year with course code WMMA1920C 

Opgenomen in 
