Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

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Real and Complex Analysis I

Course Code	: MTK501
Course Type	: Area Elective
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 6

Objectives of the Course

This course aims to acquaint students with the fundamental notions of Real and Complex analysis including abstract integration, positive Borel measures,L^p -spaces, elementary Hilbert theory, examples of Banach spaces techniques, complex measures, differentiation and integration on product spaces.

Course Content

Abstract integration, positive Borel measures,L^p -spaces, elementary Hilbert theory, examples of Banach spaces techniques, complex measures, differentiation and integration on product spaces.

Name of Lecturer(s)

Learning Outcomes

1.	To be able to comprehend the basic concept of real and complex analysis.
2.	To be able to develop mathematical sense
3.	To be able to develop the capacity of posing and solving problems
4.	To be able to use mathematical concepts in solving certain types of problems
5.	To be able to gain the skill of interpreting some interrelations among these concepts

Recommended or Required Reading

1.	Real and Complex Analysis, Walter Rudin, 1987.

Weekly Detailed Course Contents

Week 1 - Theoretical

Abstract integration

Week 2 - Theoretical

Abstract integration

Week 3 - Theoretical

Abstract integration

Week 4 - Theoretical

Positive Borel measures

Week 5 - Theoretical

Positive Borel measures

Week 6 - Theoretical

L^p-spaces

Week 7 - Theoretical

L^p -spaces

Week 8 - Theoretical

Elementary Hilbert theory (Midterm Exam)

Week 9 - Theoretical

Elementary Hilbert theory

Week 10 - Theoretical

Examples of Banach spaces techniques

Week 11 - Theoretical

Examples of Banach spaces techniques

Week 12 - Theoretical

Complex measures

Week 13 - Theoretical

Complex measures

Week 14 - Theoretical

Differentiation and integration on product spaces

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Term Assignment	1	%5
Assignment Examination	1	%5
Midterm Examination	1	%20
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	1	3	56
Assignment	1	10	2	12
Term Project	1	10	2	12
Individual Work	14	0	1	14
Midterm Examination	1	20	2	22
Final Examination	1	32	2	34
TOTAL WORKLOAD (hours)				150

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13	PÇ-14	PÇ-15
OÇ-1	5		4				4
OÇ-2	5		4				4						2
OÇ-3			4		4								2
OÇ-4	4		4				4								1
OÇ-5	4		4				4								1

Person Responsible for Information Package