Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Lıe Groups and Lıe Algebras I | MAT 590 | 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 I course aims to give the fundamental knowledge for the studies of graduate students who study at topology, algebra and geometry branch. |
Dersin İçeriği | Introduction, Definition of a Group and Basic Properties, Examples, Homomorphisms and Isomorphisms, Matrix Lie Groups, Definition, Examples, Lie Groups and Examples, Lie Algebras, The exponential Matrix, Matrix Logarithm, Properties, One-parameter Groups and Subgroups, The Lie Algebra of a Matrix Lie Group, The General Lie Groups, Properties of the Lie Algebra, The Adjoint Mapping, The Exponential Mapping and Related Theorems, Lie Algebras, Lie Algebra Homomorphism, The Complexification of a Real Lie Algebra, Subgroups and Subalgebras, Representations: Standard and Adjoint Representation, Representations of Semisimple Groups/Lie Algebras, The relatinship between O(3) and SU(2) Lie groups, Examples of Representations: su(2) and su(3) |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He/She learns concepts of group and homomorphism | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Homework, |
2 | He/She defines lie groups | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Homework, |
3 | He/She solves examples of lie groups | Lecture, Question-Answer, Drilland Practice, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
4 | He/She learns the exponential mapping and related theorems | Lecture, Question-Answer, Drilland Practice, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
5 | He/She analyzes subgroups and subalgebras | Lecture, Drilland Practice, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
6 | He/She realizes the relationship between O(3) and SU(2) Lie groups | Lecture, Question-Answer, Drilland Practice, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
7 | He/She expresses Examples of Representations: su(2) and su(3) | Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | Introduction, Definition of a Group and Basic Properties, Examples, Homomorphisms and Isomorphisms | |
2 | Lie groups and properties | |
3 | Lie algebra and exponential matrix | |
4 | Definition , Examples and Matrix of Lie Groups | |
5 | Matrix Logarithm, Properties, One-parameter Groups and Subgroups | |
6 | The Lie Algebra of a Matrix Lie Group, The General Lie Groups | |
7 | Properties of the Lie Algebra, The Adjoint Mapping | |
8 | The Exponential Mapping and Related Theorems | |
9 | Lie Algebras, Lie Algebra Homomorphism, The Complexification of a Real Lie Algebra | |
10 | Subgroups and Subalgebras | |
11 | Representations: Standard and Adjoint Representation, | |
12 | Representations of Semisimple Groups/Lie Algebras | |
13 | The relatinship between O(3) and SU(2) Lie groups, | |
14 | Examples of Representations: su(2) and su(3) |
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 |