| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6006 | Lie Groups and Lie Algebras | Spring | 3 | 0 | 3 | 8 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ATABEY KAYGUN |
| Course Objectives: | The aim of the course is to give the improvements in Lie Algebras to the students. |
|
The students who have succeeded in this course; Ability to define of Semisimple Lie Algebras Ability to create of Root Systems Ability to use of Isomorphism and Conjugacy Theorems Ability to use of Existence Theorem and Representation Theory Ability to define of Chevalley Algebras and Groups |
| • Basic Concepts • Semisimple Lie Algebras • Root Systems • Isomorphism and Conjugacy Theorems • Existence Theorem • Representation Theory • Chevalley Algebras and Groups |
| Week | Subject | Related Preparation | |
| 1) | Basic Concepts | ||
| 2) | Semisimple Lie Algebras | ||
| 3) | Semisimple Lie Algebras | ||
| 4) | Root Systems | ||
| 5) | Root Systems | ||
| 6) | Isomorphism and Conjugacy Theorems | ||
| 7) | Isomorphism and Conjugacy Theorems | ||
| 8) | Existence Theorem | ||
| 9) | Existence Theorem | ||
| 10) | Existence Theorem | ||
| 11) | Representation Theory | ||
| 12) | Representation Theory | ||
| 13) | Chevalley Algebras and Groups | ||
| 14) | Chevalley Algebras and Groups | ||
| Course Notes: | Humphyres, J. E., “ Introduction to Lie Algebras and Representation Theory”, Springer-Verlag, Third Printing, Revised, (1980) |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | 3 | % 10 |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | % 0 | |
| Seminar | % 0 | |
| Midterms | 2 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 5 | 70 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 3 | 2 | 6 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 20 | 40 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 42 | 42 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | |
| 2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | |
| 3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | |
| 4) | Ability to make individual and team work on issues related to working and social life. | |
| 5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | |
| 6) | Ability to use mathematical knowledge in technology. | |
| 7) | To apply mathematical principles to real world problems. | |
| 8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | |
| 9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | |
| 10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | |
| 11) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | |
| 12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |