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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