Information Package / Course Catalogue
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: 8
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 AssessmentCountPercent
Midterm Examination1%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Individual Work140684
Midterm Examination130232
Final Examination140242
TOTAL WORKLOAD (hours)200
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
4
4
4
4
4
4
4
OÇ-2
4
4
4
4
4
4
4
OÇ-3
4
4
4
4
4
4
4
4
OÇ-4
4
4
4
4
4
4
4
4
OÇ-5
4
4
4
4
4
4
4
4
Adnan Menderes University - Information Package / Course Catalogue
2026