Caput Algebra and Geometry
Faculteit  Science and Engineering 
Jaar  2018/19 
Vakcode  WMMA1516 
Vaknaam  Caput Algebra and Geometry 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Caput Algebra and Geometry  
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 (the specific theory varies each year. 3. apply computer algebra to problems in number theory 4. translate theoretical algorithms in algebraic number theory into efficient computer code and apply it to solve advanced problems in number theory. 

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. 18/19: Computational algebraic number theory We will discuss computer algorithms to solve the main computational task in algebraic number theory: compute efficiently in number fields, compute the maximal order, the class group, and generators of the unit group. The algorithms we will develop have many applications, both in number theory and in other fields. If time permits, we will discuss some of these applications, taking students' interests into account. In previous years, the following topics were discussed: 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 
Bijeenkomst (S)
(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 
Presentatie (P), Schriftelijk tentamen (WE)
(The course finishes with a take home exam and a group session in which all students present one of the solutions to the take home problems. Final grade is based on the answers of the take home exam, provided the final discussion confirms that the student understands his/her answers.) 

Vaksoort  master  
Coördinator  dr. J.S. Müller  
Docent(en)  dr. J.S. Müller  
Entreevoorwaarden  The course unit assumes prior knowledge acquired from Linear Algebra, Group Theory, Algebraic Structures and Advanced Algebraic Structures. In 2018/19 it is also assumed that the students have either taken the Mastermath course Algebraic Number Theory, or that they are taking it this year. Interested students missing any of these prerequisites should contact the lecturer as soon as possible.  
Opmerkingen  The course unit prepares students for various mastermath courses in which the learning objectives attained are required as prior knowledge.  
Opgenomen in 
