Faculteit  Science and Engineering 
Jaar  2021/22 
Vakcode  WMMA02805 
Vaknaam  Caput Algebra and Geometry (21/22) 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Caput Algebra & Geometry (21/22)  
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. 

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. 21/2022: Algebraic Curves. We will study the (algebraic) geometry of algebraic curves, i.e., one dimensional algebraic varieties. In particular, we will give a brief introduction to affine and projective varieties, rational maps and function fields. We will also cover local properties of algebraic curves, smoothness, intersection theory, divisors and their linear spaces (RiemannRoch theorem). In previous years, the following topics were discussed: 20/21: Representation theory of finite groups 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". 2014/15 Representation Theory of Finite Groups 2013/14 Galois and Differential Galois Theory 2012/13 Algebraic structures of differential calculus in (non)commutative geometry. 2011/12 Group methods in the geometry of differential equations 2010/11 Galois correspondence 2009/10 Commutative Algebra 2008/09 Arithmetic of elliptic curves 2007/08 Algebraic geometry: cubic surfaces 2006/07 Representation Theory of Finite Groups 2005/06 Galois and Differential Galois Theory 

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. C. Salgado Guimarães da Silva  
Docent(en)  O. Lorscheid, PhD. ,prof. dr. C. Salgado Guimarães da Silva ,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. Students are encouraged to attend and participate in the lectures. If you need to miss some classes, please inform the course coordinator. 

Opgenomen in 
