Stony Brook University

Office: 4-112 Mathematics Building

Phone: (631)-632-8274

Dept. Phone: (631)-632-8290

FAX: (631)-632-7631

Complex Analysis, 1st edition, by Donald Marshall, Cambridge University Press. We will attempt to cover the whole book (minus a few sections).

Currently, I expect the class to meet Mondays and Wednesdays from 10:00am to 11:20am. Room P-127 in Physics.

Grades will be determined by a combination of problem sets, a midterm and a final exam, each counted as one third of the total score. The midterm will be in class on Wed March 20. The final exam will be Friday, May 10 from 11:15am to 1:45pm, in Physics P-127, our usual room. Each exam will consist of a section involving true/false questions knowledge of the definitions and results from class, followed a several short proofs, usually with some choice given to the student.

Alex Rodriguez (grader): Wednesday, 4-5pm.

Will be assigned weekly from the textbook and posted here.
Hand solutions in during class on Mondays; we will attempt to return on
Wednesday. Hand written or LaTeX is acceptable. Handwritten problems sets
should be very legible; I won't require the grader to try to decipher poor
penmanship. If you use a non-textbook source,( e.g., a webpage or another
textbook), you should cite this in your solution, although most problems
will not require any research like this.
I will generally try to post
problem sets at least a week before they are due.

Due Mon Jan 29:
Problem Set 1

Due Mon Feb 5:
Problem Set 2

Due Mon Feb 12:
Problem Set 3

Due Mon Feb 19:
Problem Set 4

Due Mon Feb 26:
Problem Set 5

Due Mon Mar 4:
Problem Set 6

No problem set for Mar 11 (Spring Break)

No problem set for Mar 18 (Spring Break)

No problem set for Mar 25 (Midterm week)

Due Wed Apr 3:
Problem Set 7

No problem set for Apr 8 (Algebra II midterm):

Due Mon Apr 15:
Problem Set 8

Due Mon Apr 22:
Problem Set 9

Sample final,
solutions . (updated 5-6-24, correcting
an error in Part 1, number 7)

solutions to final exam

Slide for lectures will be posted here. These generally follow the textbook, with some
additions and deletions. Slides will be updated throughout the semester.

Slides for Course Introduction and Chapter 1.
Used on Mon Jan 22.

Slides for Chapter 2.

Slides for Chapter 3.

Slides for Chapter 4.

Slides for Chapter 5.

Slides for Chapter 7.

Slides for Chapter 10.

Slides for Chapter 12.

Slides for Chapter 13.

Slides for Chapter 14.

Slides for Chapter 15.

Slides for Chapter 9.

Slides for Chapter 11.

Slides for Trees, Triangles and Tracts, Part I

Slides for Trees, Triangles and Tracts, Part II .

Link to
Video Recording .
(one YouTube video covers both talks).

Link to conference website:
Transcendental Dynamics and Beyond: topics in complex dynamics 2021,
(Centre de Recerca Matemàtica, Barcelona, April 19-23, 2021,

Class recordings are posted HERE.

Mon Jan 21: Introduction to class, Chapter 1

Wed Jan 23: Chapter 2, Polynomials 2.1, Fund. Thm. 2.2, Power series 2.3

Mon Jan 29 Chapter 2, Analytic functions 2.3 Elementary oeprations 2.5, Maximum Prin 3.1

Wed Jan 31: Chapter 3, Local behavior 3.2, Growth 3.3

Mon Feb 5: Chapter 4, Integration on Curves 4.1, Equivalence of analytic and holomoprhic 4.2

Wed Feb 7: Chapter 4, Morera's theorem, Runge's theorem

Mon Feb 12: Finish chapter 4, uniform limits of analytic functions,
applications of Runge's theore, Chapter 5, Cauchy's theorem 5.1, Winding numbers 5.2

Wed Feb 14: Chapter 5, Removable singularities 5.3, Laurent Series 5.4, The argument prinicple 5.5

Mon Feb 19: Finish Chapter 5, Laurant series, argument principle

Wed Feb 21: No class

Mon Feb 26: Chapter 7, harmonic functions, Cauchy-Riemann equattions

Wed Feb 28: Chapter 7, Harmonic conjugates, Lindelof's maximum principle, Harnack's inequality

Mon Mar 4: Chapter 10, normal families, spherical derivatives, Marty's theorem

Wed Mar 6: Chapter 10, Hurtwitz's theorem, Rieman mapping theorem, Zalcman's lemma

Mon Mar 11: Spring Break

Wed Mar 13: Spring Break

Mon Mar 18: Chapter 10, Montel's theorem, Picard's theorem, Julia and Fatou sets

Wed Mar 20: Midterm

Mon Mar 25: Chapter 12, Jordan curve theorem

Wed Mar 27: Chapter 12 and Chapter 13, Caratheodory's therorem, Perron families

Mon Apr 1: No class

Wed Apr 3: Chapter 13, local barriers, 2nd proof of Riemann mapping theorem

Mon Apr 8: Chapters 14, the monodromy theorem

Wed Apr 10: Chapter 14, universal covers, deck transformations

Mon Apr 15: Chapter 15, the moduluar function, Green's function

Wed Apr 17: Chapter 15, the uniformization theorem

Mon Apr 22: Chapter 9, Residue calculus, computing integrals

Wed Apr 24: Chapter 11, Mittag-Leffer's theorem, Blaschke products, factorization

Mon Apr 29: Brief introduction to some recent results: harmonic
measures, dessins d'enfants, triangulations of Riemann surfaces

Wed May 1: Last class

Friday May 10: Final Exam 11:15am-1:45pm, Physics P-127
(usual lecture toom).

Although it is not required, you may wish to consider writing up your solution in TeX, since eventually you will probably use this to write your thesis and papers.

The not too short introduction to LaTex

Link to Mathematical Biographies

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