Course Code:
MATH 413
Course Type:
Area Elective
P:
3
Lab:
0
Laboratuvar Saati:
0
Credits:
3
ECTS:
7
Course Language:
English
Course Objectives:
To introduce the basics of the theory of Lie groups and Lie algebras within the framework of matrix groups.
Course Content:

General linear groups, Matrix groups, example : orthogonal groups, Tangent space and the dimension of matrix groups, smooth homomorphisms, Exponential and the logarithm of a matrix, Center, Maximal tori, Clifford algebras, Normalizers, Weyl groups, Reflections and roots.

Course Methodology:
1: Lecture, 2: Problem Solving
Course Evaluation Methods:
A: Written examination, B: Homework

## Vertical Tabs

### Course Learning Outcomes

 Learning Outcomes Teaching Methods Assessment Methods 1) Applies linear algebraic methods 1 A,B 2) Knows the basic properties and examples of matrix groups 1 A,B 3) Determines the tangent space to a matrix group 1 A,B 4) Computes the exponential and the logarithm of matrices 1 A,B 5) Knows the definition and basic properties of a maximal torus in a matrix groups 1 A,B 6) Knows the definition and very basic properties of general Lie groups and Lie algebras 1 A,B

### Course Flow

 Week Topics Study Materials 1 General linear groups Textbook 2 Orthogonal groups Textbook 3 Homomorphisms Textbook 4 Exponential of a matrix, logarithm of a matrix Textbook 5 Lie algebras Textbook 6 Manifolds Textbook 7 Maximal tori Textbook 8 Covering by maximal tori Textbook 9 Conjugacy of maximal tori Textbook 10 Simply connected groups Textbook 11 Spin(k) Textbook 12 Normalizers, Weyl groups Textbook 13 Lie groups Textbook 14 Reflections, roots Textbook

### Recommended Sources

 Textbook Matrix Groups, M. Curtis, 2nd. Ed., Springer-Verlag, 1984. Additional Resources

### Material Sharing

 Documents Assignments Exams

### Assessment

 IN-TERM STUDIES NUMBER PERCENTAGE Mid-terms Quizzes Assignments 7 100 Total 100 CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 40 CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE 60 Total 100

 COURSE CATEGORY Expertise/ Field Courses

### Course’s Contribution to Program

 No Program Learning Outcomes Contribution 1 2 3 4 5 1 The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) x 2 Acquiring fundamental knowledge on fundamental research fields in mathematics x 3 Ability form and interpret the relations between research topics in mathematics x 4 Ability to define, formulate and solve mathematical problems x 5 Consciousness of professional ethics and responsibilty x 6 Ability to communicate actively x 7 Ability of self-development in fields of interest x 8 Ability to learn, choose and use necessary information technologies x 9 Lifelong education x

### ECTS

 Activities Quantity Duration (Hour) Total Workload (Hour) Course Duration (14x Total course hours) 14 3 42 Hours for off-the-classroom study (Pre-study, practice) 14 4 56 Mid-terms (Including self study) Quizzes Assignements 7 8 56 Final examination (Including self study) 1 20 20 Total Work Load 174 Total Work Load / 25 (h) 6.96 ECTS Credit of the Course 7.00