Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis for deriving accurate asymptotics from the GF equations.

Analytic Combinatorics is based on formal methods for deriving functional relationships on generating functions and asymptotic analysis treating those functions as functions in the complex plane. This course covers the symbolic method for defining generating functions immediately from combinatorial constructions, then develops methods for directly deriving asymptotic results from those generating functions, using complex asymptotics, singularity analysis, saddle-point asymptotics, and limit laws. The course teaches the precept "if you can specify it, you can analyze it".No certificates, statements of accomplishment, or other credentials will be awarded in connection with this course.

会期:

- 2015年11月06日, 6 星期
- 2015年3月20日, 6 星期
- 2014年10月31日, 6 星期
- 2014年3月28日, 6 星期
- 2013年11月01日, 6 星期

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Algorithms

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Algorithms and data structures from the beginning to advanced analysis.

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