Information Package / Course Catalogue
Divergent Series I
Course Code: MTK552
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

The aim of this course is to introduce well known summability methods.

Course Content

Abel convergence, Cesaro convergence, Euler-Maclaurin sum Formula, Abel’s inequality, the Silverman-Toeplitz theorem, Nörlund and Nörlund type transformations, Hölder and Cesaro means, Euler, Taylor and Borel exponential transformations, Hausdorff means.

Name of Lecturer(s)
Learning Outcomes
1.To be able to see the relationships among the several summability methods
2.To be able to develop the capacity of posing and solving problems
3.To be able to gain the skill of interpreting some interrelations among these concepts
4.To be able to use mathematical concepts in solving certain types of problems
5.To be able to develop analytical skills and apply to problems
Recommended or Required Reading
1.Divergent Series, G. H. Hardy
Weekly Detailed Course Contents
Week 1 - Theoretical
Abel convergence
Week 2 - Theoretical
Cesaro convergence
Week 3 - Theoretical
Euler-Maclaurin sum formula
Week 4 - Theoretical
Abel’s inequality
Week 5 - Theoretical
Silverman-Toeplitz theorem
Week 6 - Theoretical
Silverman-Toeplitz theorem
Week 7 - Theoretical
Nörlund and Nörlund type transformations
Week 8 - Theoretical
Nörlund and Nörlund type transformations
Week 9 - Theoretical
Hölder and Cesaro means
Week 10 - Theoretical
Hölder and Cesaro means
Week 11 - Theoretical
Euler, Taylor and Borel exponential transformations
Week 12 - Theoretical
Euler, Taylor and Borel exponential transformations
Week 13 - Theoretical
Hausdorff means
Week 14 - Theoretical
Hausdorff means
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Term Assignment1%5
Midterm Examination1%20
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory141356
Assignment110212
Term Project110212
Individual Work140114
Midterm Examination120222
Final Examination132234
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
4
5
4
4
OÇ-2
4
4
4
2
OÇ-3
4
5
4
4
4
2
OÇ-4
4
5
4
4
4
2
OÇ-5
4
5
4
4
4
2
Adnan Menderes University - Information Package / Course Catalogue
2026