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Analytic Combinatorics
  • Level Professional
  • Duration 17 hours
  • Course by Princeton University
  • Offered by

About

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. All the features of this course are available for free. It does not offer a certificate upon completion.

Modules

Overview

    • 1 Videos
    • 1 Readings
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1 Videos

  • Brief History

1 Readings

  • Getting Started

Combinatorial structures and OGFs

    • 6 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Combinatorial Structures and OGFs

1 Discussions

  • Exercises from Lecture 1

6 Videos

  • Symbolic Method
  • Trees and Strings
  • Powersets and Multisets
  • Compositions and Partitions
  • Substitution
  • Exercises

1 Readings

  • Exercises from Lecture 1

Labelled Structures and EGFs

    • 7 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Labeled Structures and EGFs

1 Discussions

  • Exercises from Lecture 2

7 Videos

  • Basics
  • Symbolic Method for Labelled Classes
  • Words and Strings
  • Labelled trees
  • Mappings
  • Summary
  • Exercises

1 Readings

  • Exercises from Lecture 2

Combinatorial Parameters and MGFs

    • 5 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Combinatorial Parameters and MGFs

1 Discussions

  • Exercises from Lecture 3

5 Videos

  • Basics
  • Moment Calculations
  • OBGF examples
  • Labelled Classes
  • Exercises

1 Readings

  • Exercises from Lecture 3

Complex Analysis, Rational and Meromorphic Asymptotics

    • 6 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Complex Analysis, Rational and Meromorphic Asymptotics

1 Discussions

  • Exercises from Lecture 4

6 Videos

  • Roadmap
  • Complex Functions
  • Rational Functions
  • Analytic Functions and Complex Integration
  • Meromorphic Functions
  • Exercises

1 Readings

  • Exercises from Lecture 4

Applications of Rational and Meromorphic Asymptotics

    • 6 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Applications of Complex Analysis, Rational and Meromorphic Asymptotics

1 Discussions

  • Exercises from Lecture 5

6 Videos

  • Bitstrings
  • Other Familiar Examples
  • Restricted Compositions
  • Supercritical Sequence Schema
  • Summary
  • Exercises

1 Readings

  • Exercises from Lecture 5

Singularity Analysis

    • 5 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Singularity Analysis of Generating Functions

1 Discussions

  • Exercises from Lecture 6

5 Videos

  • Prelude
  • Standard Function Scale
  • Singularity Analysis
  • Schemas and Transfer Theorems
  • Exercises

1 Readings

  • Exercises from Lecture 6

Applications of Singularity Analysis

    • 6 Videos
    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Applications of Singularity Analysis

1 Discussions

  • Exercises from Lecture 7

6 Videos

  • Simple Varieties of Trees
  • Labelled Sets
  • Mappings
  • Tree-like Classes
  • Summary
  • Exercises

1 Readings

  • Exercises from Lecture 7

Saddle Point Asymptotics

    • 5 Videos
    • 1 Assignment
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1 Assignment

  • Saddle-Point Asymptotics

5 Videos

  • Modulus Surfaces
  • Saddle Point Bounds
  • Saddle Point Asymptotics
  • Applications
  • AC Wrap-up

Auto Summary

Analytic Combinatorics, offered by Coursera, delves into the calculus for predicting large combinatorial structures using symbolic methods and complex analysis. This professional-level course spans 1020 minutes and is ideal for those in Maths & Statistics. While all features are free, additional resources are available on the course website or via the textbook. Subscription options include Starter and Professional plans. Note that the course does not provide a completion certificate.

Robert Sedgewick
Instructor

Robert Sedgewick