MATH 503 - Complex Analysis I
Fall 2012
Ali Sinan Sertöz
Faculty of Science, Department of Mathematics, Room: SA-121
Office Hours: Wednesday 13:40-15:30
Text Books:
An Introductıon to Complex Analysıs, Agarwal &
Perera & Pınelas, Springer, 2011.
Schedule:
MON | 13:40-15:30 | SAZ-19 | |
WED | 15:40-16:30 | SAZ-03 |
Syllabus:
Week |
Date |
Subjects to be covered | Chapters |
1 | 17, 19 Sep | Complex numbers and complex functions | 1-7 |
2 | 24, 26 Sep | Elementary functions | 8-11 |
3 | 1, 3 Oct | Complex integration | 12-18 |
4 | 8,10 Oct | Fundamental theorem of algebra | 19-20 |
5 | 15, 17 Oct | Taylor and Laurent series | 21-26 |
6 | 22 Oct | Analytic continuation | 27 |
7 | 31 Oct | Reflection principle | 28 |
8 | 5, 7 Nov | Poles and residues | 29-31 |
9 | 12, 14 Nov | Cauchy Integral Formula and applications | 32-35 |
10 | 19, 21 Nov | Applications of residues | 36-38 |
11 | 26, 28 Nov | Riemann mapping theorem | 39 |
12 | 3, 5 Dec | Harmonic functions | 40 |
13 | 10, 12 Dec | Infinite products | 42-44 |
14 | 17, 19 Dec | Riemann zeta function | 46 |
15 | 24, 26 Dec | Riemann surfaces | 48 |
Exams and Grading:
Presentation | 25% |
Written Report | 15% |
Exams | 50% |
Homework | 10% |
Old Exams are on Old Courses Web Page
List of Oral Presentations:
10 October 2012 | Wednesday | BÜYÜKÇOLAK Yasemin | Riemann surfaces |
15 October 2012 | Monday | DANIŞ Bekir | Runge's Theorem |
17 October 2012 | Wednesday | Exam 1 | Solutions |
22 October 2012 | Monday | DEMİREL Merve | Mittag-Leffler theorem |
31 October 2012 | Wednesday | Exam 2 | Solutions |
5 November 2012 | Monday | DOĞAN Elif | Bieberbach conjecture |
7 November 2012 | Wednesday | Exam 3 | Solutions |
12 November 2012 | Monday | GEZMİŞ Oğuz | Space of analytic functions |
14 November 2012 | Wednesday | Exam 4 | Solutions |
19 November 2012 | Monday | HATİNOĞLU Burak | Harmonic functions |
21 November 2012 | Wednesday | Exam 5 | Solutions |
26 November 2012 | Monday | KAYA Merve | Periodic functions |
28 November 2012 | Wednesday | Exam 6 | Solutions |
3 December 2012 | Monday | ÖĞÜT İsmail Alperen | Riemann zeta function |
5 December 2012 | Wednesday | Exam 7 | Solutions |
10 December 2012 | Monday | ÖNER Abdullah | Complex Gamma function |
12 December 2012 | Wednesday | Exam 8 | Solutions |
17 December 2012 | Monday | ÖZKAN Recep | Weierstrass factorization theorem |
19 December 2012 | Wednesday | Exam 9 | Solutions |
24 December 2012 | Monday | Sinan Sertöz | An alternate description of the Gamma function |
28 December 2012 | Friday | Exam 10 | Solutions |
28 December 2012 | Friday | Exam 11 | Solutions |
Notes on Presentations |
In MATH 503 you will prepare a topic and present it in class. You will prepare a (La)TeX output for the class before you begin your talk. You will have two class hours to complete your talk on Monday class time. On Wednesday class time I will give an open book exam to class on your topic. Therefore the class will probably ask you lots of details during your Monday talk so that they can answer my questions on Wednesday. Your presentation, and also your written report, should begin with explaining the main purpose of your talk. Give some historical background to place your topic into perspective. In this introduction talk about your main theorems and results in plain words, without formulas, and explain where they apply, what sort of problems they solve. Again do not use any formulas. After the introduction you should develop your terminology, make necessary definitions. This is where you prove or simply quote some technical lemmas which you will be using later. Give examples of the concepts you are discussing. If you give a definition give examples of that object. Also give some examples which almost make the definition but fail so that we can place the object of your definition in our mind along other concepts we know. After these preparatory steps you can now quote and prove your main results. Finally give us some interesting applications of your main results so that we feel that two hours spent listening to your talk was in fact worth it. Also discuss at this point what might be some questions that the audience must be able to answer about this talk so that they can test their understanding of your topic. I may use some of your questions on the Wednesday exam. I am always ready to give you advise and willing to guide you through your presentations but remember that the final responsibility of your presentation lies on you. If you do not like my comments you should not use them just because hoca said so! Hoca says a lot of things but it is your responsibility to pick up the ones that match your own style. Good luck and enjoy your work. |
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