이번 가을학기에 독일 TU Berlin에 계시는 강미현 박사님을 초청해서, 9월 12일에서 19일까지 

Analytic Combinatorics (해석적 조합론)

을 주제로 1주일간 1학점 과목(MAS581, Topics in Mathematics, Analytic Combinatorics)을 개설합니다.

강미현 박사님은 2001년 KAIST에서 박사를 받고 바로 독일로 가신 후 2007년에 하빌리타치온(Habilitation)을 받고, 현재는 Heisenberg Fellow로 TU Berlin에 계십니다.

아래에 그 과목의 syllabus를 첨부합니다.

MAS581, 2010 Fall, KAIST

Topics in Mathematics: Analytic Combinatorics

This course is a gentle introduction to Analytic Combinatorics. We will start with generating functions, which describe the enumerative information of combinatorial structures in terms of power series as formal algebraic objects. We will study how certain combinatorial structures can naturally be decomposed into smaller building blocks and how such decompositions can be interpreted as functional operations of generating functions. Next we will view generating functions as analytic functions that map the complex plane into itself and study their analytic properties, e.g. singularity and singular expansions, from which we will extract asymptotic estimates of counting sequences. Finally we will study how this approach can be applied to various classes of maps and graphs on surfaces, in particular planar graphs.

Lecture

• Sept. 12, 3:00PM-6:00 PM 
• Sept. 13-17, 4:00PM-6:00PM

Mihyun Kang, http://www.math.tu-berlin.de/~kang/

kang _at_ math.tu-berlin.de 

Office hours

Sept. 13-17, 3:00PM-4:00PM 

Textbook 

Flajolet and Sedgewick, Analytic Combinatorics, Cambridge University Press, 2009 

http://algo.inria.fr/flajolet/Publications/book.pdf 

Final exam

Sept. 19, oral exam 

Homework 

Homework will be given on Sept. 13 and 15 and collected at the beginning of class on Sept. 15 and 17. Students are encouraged to collaborate with one another. 

Grading

20% Homework, 80% Exam 

Plan 

• Sept. 12, Symbolic methods and basic combinatorial constructions 
• Sept. 13, Essentials from complex analysis 
• Sept. 14, Singularity analysis 
• Sept. 15, Enumeration of various types of trees
• Sept. 16, Enumeration of outerplanar graphs 
• Sept. 17, Enumeration of planar graphs
• Sept. 19, Oral exam