| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Lıe Groups and Lıe Algebras II | MAT 591 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. MAHMUT AKYİĞİT |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | The lie groups and lie algebras II course aims to give the fundamental knowledge for the studies of graduate students who study at topology, algebra and geometry branch. |
| Dersin İçeriği | sl(2) and its Representations, The Lie algebra of an algebraic group, Reel and Complex Lie groups and Algebras, Split Complex and Dual Lie Groups, Topology of Lie Groups, Compact Lie groups, Compactness , Connectedness, The maximal torus of a compact Lie group, Nillpotent Lie Groups, Matrix groups and transformation groups, Dynkin Diagrams Cartan Matrices, Classification of Dynkin diagrams, Casimir elements and Weyl teorems, Simple roots, Properties of root systems, Actions of Lie groups and Lie algebras |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She realizes the lie algebra of an algebraic group | Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
| 2 | He/She learns split complex and dual lie groups | Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
| 3 | He/She realizes nillpotent lie groups | Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
| 4 | He/She realizes Dynkin diagrams cartan matrices | Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
| 5 | He/She learns actions of lie groups and lie algebras | Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | sl(2) and its Representations | |
| 2 | The Lie algebra of an algebraic group | |
| 3 | Reel and Complex Lie groups and Algebras | |
| 4 | Split Complex and Dual Lie Groups | |
| 5 | Topology of Lie Groups | |
| 6 | Compact Lie groups, Compactness , Connectedness | |
| 7 | The maximal torus of a compact Lie group | |
| 8 | Nillpotent Lie Groups | |
| 9 | Matrix groups and transformation groups | |
| 10 | Dynkin Diagrams Cartan Matrices | |
| 11 | Classification of Dynkin diagrams | |
| 12 | Casimir elements and Weyl teorems | |
| 13 | Simple roots, Properties of root systems | |
| 14 | Actions of Lie groups and Lie algebras |
| Kaynaklar | |
|---|---|
| Ders Notu | 1.) Lie Groups, Lie Algebras and Representation Theory: An Introduction, Brian C. Hall, (2005) Graduate Texts in Mathematics, Springer Verlag 2.) Lie Groups: An Introduction through Linear Groups, W. Rossman, (2005) Oxford Graduate Texts in Mathematics, Oxford Science Publications |
| Ders Kaynakları | |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | ||||||
| 2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
| 3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
| 7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
| 8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
| 9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
| 10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
| 11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 70 |
| 1. Kısa Sınav | 10 |
| 1. Ödev | 10 |
| 2. Ödev | 10 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 10 | 10 |
| Quiz | 1 | 10 | 10 |
| Assignment | 2 | 16 | 32 |
| Final examination | 1 | 10 | 10 |
| Toplam İş Yükü | 158 | ||
| Toplam İş Yükü / 25 (Saat) | 6,32 | ||
| Dersin AKTS Kredisi | 6 | ||