Course Name Code Semester T+U Hours Credit ECTS
Lie Groups and Lie Algebras I MAT 590 0 3 + 0 3 6
 Precondition Courses Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Doç.Dr. MAHMUT AKYİĞİT Course Lecturers Course Assistants Course Category Course Objective 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. Course Content 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)
# Course Learning Outcomes Teaching Methods Assessment Methods
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,
Week Course Topics Preliminary Preparation
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)
Resources
Course Notes 1.) Lie Groups, Lie Algebras and Representation Theory: An Introduction, Brian C. Hall, (2005) Graduate Texts in Mathematics, Springer Verlag<br>2.) Lie Groups: An Introduction through Linear Groups, W. Rossman, (2005) Oxford Graduate Texts in Mathematics, Oxford Science Publications
Course Resources
Order Program Outcomes Level of Contribution
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
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
1. Ödev 10
2. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100