FÄ°Z721 - GROUP THEORY
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| GROUP THEORY | FÄ°Z721 | Any Semester/Year | 3 | 0 | 3 | 8 |
| Prequisites | Quantum mechanics and Linear algebra are essential prerequisites of this course. A basic knowledge on groups can be usefull. | |||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Discussion | |||||
| Instructor (s) | Assigned by Department of Physics Engineering | |||||
| Course objective | Group theory provides the natural mathematical language to formulate symmetry principles and to derive their consequences in Mathematics and in Physics. | |||||
| Learning outcomes |
| |||||
| Course Content | Groups, structures within a group, Homomorphism, Isomorphism, Action of a Group on a manifold, Topological groups. Manifolds and their tangent spaces, Lie groups and their Lie algebras, Representation theory of finite groups, The structure of Lie Algebras, simple and semi-simple algebras, The structure of semi-simple Lie algebras, roots, simple roots, positive roots, Cartan basis, Dynkin diagrams, Classification of simple Lie algebras, Representation of Lie algebras. | |||||
| References | Lie algebras in particle physics, Howard Georgi Group theory for physicists | |||||
Course outline weekly
| Weeks | Topics |
|---|---|
| Week 1 | Groups, matrix groups, permutation and braid groups, generators and relations. |
| Week 2 | structures within a group, subgroups, classes, cosets, factor groups, centers of a group, normalizers. |
| Week 3 | Homomorphism, Isomorphism, the fundamental theorem of Isomorphisms. |
| Week 4 | Action of a group on a manifold, |
| Week 5 | The general linear Matrix group and its subgroups. |
| Week 6 | Midterm exam I |
| Week 7 | Topological groups. |
| Week 8 | Manifolds and their tangent spaces, Lie groups and their Lie algebras, |
| Week 9 | Representation theory of finite groups, |
| Week 10 | The structure of Lie Algebras, |
| Week 11 | The structure of semi-simple Lie algebras, roots, simple roots, positive roots, Cartan basis, Dynkin diagrams, |
| Week 12 | Midterm exam II |
| Week 13 | Classification of simple Lie algebras and its proof. |
| Week 14 | Representation of Lie algebras. |
| Week 15 | Preparation for final exam |
| Week 16 | Final exam |
Assesment methods
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 0 | 0 |
| Midterms | 2 | 50 |
| Final exam | 1 | 50 |
| Total | 100 | |
| Percentage of semester activities contributing grade succes | 0 | 50 |
| Percentage of final exam contributing grade succes | 0 | 50 |
| Total | 100 | |
WORKLOAD AND ECTS CALCULATION
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, ect) | 14 | 8 | 112 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 5 | 8 | 40 |
| Midterms (Study duration) | 2 | 8 | 16 |
| Final Exam (Study duration) | 1 | 30 | 30 |
| Total Workload | 36 | 57 | 240 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest