Analytic Combinatorics, Part I

开始时间: 02/08/2013 持续时间: 5 weeks

所在平台: Coursera

课程类别: 数学

大学或机构: Princeton University(普林斯顿大学)

授课老师: Robert Sedgewick



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Analytic Combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the scientific analysis of algorithms in computer science and for the study of scientific models in many other disciplines, including probability theory, statistical physics, computational biology and information theory. Part I of this course covers recurrence relations, generating functions, asymptotics, and fundamental structures such as trees, permutations, strings, tries, words, and mappings, in the context of applications to the analysis of algorithms.


 Lecture  1  Analysis of Algorithms
 Lecture  2  Recurrences
 Lecture  3  Solving recurrences with GFs
 Lecture  4  Asymptotics
 Lecture  5  The symbolic method
 Lecture  6  Trees
 Lecture  7  Permutations
 Lecture  8  Strings and Tries
 Lecture  9  Words and Mappings





This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. Part I covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings.





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