Princeton University - Analytic Combinatorics
- Offered byCoursera
- Public/Government Institute
Analytic Combinatorics at Coursera Overview
Duration | 17 hours |
Total fee | Free |
Mode of learning | Online |
Schedule type | Self paced |
Difficulty level | Intermediate |
Official Website | Explore Free Course  |
Credential | Certificate |
- Overview
- Highlights
- Course Details
- Curriculum
Analytic Combinatorics at Coursera Highlights
- 100% online Start instantly and learn at your own schedule.
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Intermediate Level
- Approx. 17 hours to complete
- English Subtitles: French, Portuguese (European), Russian, English, Spanish
Analytic Combinatorics at Coursera Course details
- 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.
Analytic Combinatorics at Coursera Curriculum
Combinatorial Structures and OGFs
Brief History
Symbolic Method
Trees and Strings
Powersets and Multisets
Compositions and Partitions
Substitution
Exercises
Getting Started
Exercises from Lecture 1
Combinatorial Structures and OGFs
Labelled Structures and EGFs
Basics
Symbolic Method for Labelled Classes
Words and Strings
Labelled trees
Mappings
Summary
Exercises
Exercises from Lecture 2
Labeled Structures and EGFs
Combinatorial Parameters and MGFs
Basics
Moment Calculations
OBGF examples
Labelled Classes
Exercises
Exercises from Lecture 3
Combinatorial Parameters and MGFs
Complex Analysis, Rational and Meromorphic Asymptotics
Roadmap
Complex Functions
Rational Functions
Analytic Functions and Complex Integration
Meromorphic Functions
Exercises
Exercises from Lecture 4
Complex Analysis, Rational and Meromorphic Asymptotics
Applications of Rational and Meromorphic Asymptotics
Bitstrings
Other Familiar Examples
Restricted Compositions
Supercritical Sequence Schema
Summary
Exercises
Exercises from Lecture 5
Applications of Complex Analysis, Rational and Meromorphic Asymptotics
Singularity Analysis
Prelude
Standard Function Scale
Singularity Analysis
Schemas and Transfer Theorems
Exercises
Exercises from Lecture 6
Singularity Analysis of Generating Functions
Applications of Singularity Analysis
Simple Varieties of Trees
Labelled Sets
Mappings
Tree-like Classes
Summary
Exercises
Exercises from Lecture 7
Applications of Singularity Analysis
Saddle Point Asymptotics
Modulus Surfaces
Saddle Point Bounds
Saddle Point Asymptotics
Applications
AC Wrap-up
Saddle-Point Asymptotics
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