CLASSICAL LIE GROUPS AND LIE ALGEBRAS

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	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) Applies linear algebraic methods	1,2,5	1	A,B
2) Knows the basic properties and examples of matrix groups	1,2,3,4,7,9	1	A,B
3) Determines the tangent space to a matrix group	1,2,5	1	A,B
4) Computes the exponential and the logarithm of matrices	1,2,3,5	1	A,B
5) Knows the definition and basic properties of a maximal torus in a matrix groups	1,2,3,5,7,9	1	A,B
6) Knows the definition and very basic properties of general Lie groups and Lie algebras	1,2,3,5,7,9	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
No	Program Learning Outcomes	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

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