Syllabus ( MATH 549 )
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Basic information
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| Course title: |
Theory Of Univalent Functions |
| Course code: |
MATH 549 |
| Lecturer: |
Prof. Dr. Serkan SÜTLÜ
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| ECTS credits: |
7.5 |
| GTU credits: |
3 (3+0+0) |
| Year, Semester: |
1/2, Fall and Spring |
| Level of course: |
Second Cycle (Master's) |
| Type of course: |
Area Elective
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| Language of instruction: |
Turkish
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| Mode of delivery: |
Face to face
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| Pre- and co-requisites: |
MATH 501, MATH 502 |
| Professional practice: |
No |
| Purpose of the course: |
In this course the basic results of the univalent functions theory, such as: the area theorem, Koebes one-quarter theorem and the growth and distortion theorems and proof of the famous Bieberbach conjecture by dBranges , will be learned. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Explain the area theorem and Koebe one-quarter theorem.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Develop mathematical, communicative, problem-solving, brainstorming skills.
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Effectively express his/her research ideas and findings both orally and in writing
Method of assessment
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Written exam
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Explain growth and distortion theorems about univalent functions.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Develop mathematical, communicative, problem-solving, brainstorming skills.
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Effectively express his/her research ideas and findings both orally and in writing
Method of assessment
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Written exam
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Explain the proof of the famous Bieberbach Conjecture given by deDranges.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Develop mathematical, communicative, problem-solving, brainstorming skills.
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Effectively express his/her research ideas and findings both orally and in writing
Method of assessment
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Written exam
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Contents
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| Week 1: |
Fundamental Distortion Theorems for Univalent Functions |
| Week 2: |
Fundamental Inequalities of Coefficient for Univalent Functions. |
| Week 3: |
Some Special Classes of Univalent Functions. |
| Week 4: |
Some Special Classes of Univalent Functions. |
| Week 5: |
Parametric Representation of Loewner. |
| Week 6: |
Faber Polynomials and Generalization of Area Principle. |
| Week 7: |
Faber Transform. |
| Week 8: |
Subordination. |
| Week 9: |
Integral Means.
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| Week 10: |
Variational Tecniques. |
| Week 11: |
Extreme points of Some Special Class of Functions. |
| Week 12: |
Extreme points of Some Special Class of Functions. |
| Week 13: |
Proof of Bieberbach Conjecture. |
| Week 14: |
Proof of Bieberbach Conjecture. |
| Week 15*: |
- |
| Week 16*: |
Final Exam. |
| Textbooks and materials: |
Peter L. Duren, "Univalent Functions", Springer-Verlag, 1983.
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| Recommended readings: |
Pommerenke, Ch.,"Univalent Functions", Vandenhoeck und Ruprecht, GÄottingen, 1975. |
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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| Method of assessment |
Week number |
Weight (%) |
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| Mid-terms: |
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0 |
| Other in-term studies: |
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0 |
| Project: |
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0 |
| Homework: |
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0 |
| Quiz: |
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0 |
| Final exam: |
16 |
100 |
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Total weight: |
(%) |
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Workload
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| Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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| Courses (Face-to-face teaching): |
3 |
14 |
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| Own studies outside class: |
3 |
14 |
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| Practice, Recitation: |
0 |
0 |
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| Homework: |
0 |
0 |
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| Term project: |
0 |
0 |
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| Term project presentation: |
0 |
0 |
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| Quiz: |
0 |
0 |
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| Own study for mid-term exam: |
0 |
0 |
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| Mid-term: |
0 |
0 |
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| Personal studies for final exam: |
20 |
5 |
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| Final exam: |
3 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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