Group Theory

Uitgebreide vaknaam	Group Theory
Leerdoelen	The student has/is able to 1. a firm knowledge of definitions of and relations between basic notions and structures in abstract group theory, combined with an ability to recognize (a necessity of the use of) such concepts. 2. follow and reproduce the proofs which are given during the lectures. 3. design own proofs of hypotheses which are offered in exercises or which are elaborated individually by a student. 4. apply this knowledge to calculation of mathematical properties of the structures within this course.
Omschrijving	Abstract groups are one of the basic concepts in linear algebra but they are also used, e.g., in cryptography in the context of decomposition of large numbers into prime factors. However, the notion of a group is essential in almost all branches of abstract mathematics. It also has many applications in fundamental physics, where groups arise in the context of symmetry or invariance of models for elementary particles. The crystallographic groups are of interest in chemistry, physical chemistry, and solid state physics. Regarding applications in physics, it must be noted that group theory is not the same as their representation theory, which is a separate subject. Besides giving students a solid background in the theory of groups and how to apply it to solve specific problems, the aim of this course is to develop the students' ability to design their own rigorous proofs of abstract statements.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
Toetsvorm	Opdracht (AST), Schriftelijk tentamen (WE) (The final grade is determined by the exam grade E and the average homework grade H. Specifically, the grade is Max(E, 0.80*E+0.20*H). A student fails the course if this is less than 5.5, otherwise they pass.)
Vaksoort	bachelor
Coördinator	P. Kilicer, PhD.
Docent(en)	P. Kilicer, PhD.
Verplichte literatuur	Titel Auteur ISBN Prijs Reader Group Theory, 2016 Top
Entreevoorwaarden	Background knowledge from Linear Algebra is required.
Opmerkingen	The course prepares for the courses Algebraic Structures, Advanced Algebraic Structures, Security & Coding and Caput Algebra and Geometry.
Opgenomen in	Opleiding Jaar Periode Type BSc Applied Mathematics 2 semester I a verplicht BSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I a BSc Mathematics and Physics (double degree) 2 semester I a verplicht BSc Mathematics: General Mathematics  ( Major track General Mathematics) 2 semester I a verplicht BSc Mathematics: Probability and Statistics 2 semester I a verplicht Pre-master/Fast-track for MSc AI - CCS – CS - Math  ((Applied) Mathematics) - semester I a -