Group Theory
Faculteit | Science and Engineering |
Jaar | 2020/21 |
Vakcode | WBMA005-05 |
Vaknaam | Group Theory |
Niveau(s) | bachelor |
Voertaal | Engels |
Periode | semester I a |
ECTS | 5 |
Rooster | rooster.rug.nl |
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. |
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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. |
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Uren per week | |||||||||||||||||||||||||
Onderwijsvorm | Hoorcollege (LC), 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, 0.75*E+0.25*H). A student fails the course if this is less than 5.5, otherwise they pass.) |
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Vaksoort | bachelor | ||||||||||||||||||||||||
Coördinator | P. Kilicer, PhD. | ||||||||||||||||||||||||
Docent(en) | P. Kilicer, PhD. | ||||||||||||||||||||||||
Verplichte literatuur |
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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 This course was registered last year with course code WIGT-07 |
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Opgenomen in |
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