Course Summary
Learn the art of analytic combinatorics and apply it in real-world scenarios with this comprehensive course. This course offers a deep dive into combinatorial structures, generating functions, and asymptotic analysis.Key Learning Points
- Understand the fundamentals of combinatorics and generating functions
- Learn how to apply analytic combinatorics in real-world scenarios
- Develop skills in asymptotic analysis and singularity analysis
Related Topics for further study
Learning Outcomes
- Develop a strong understanding of combinatorial structures
- Learn how to use generating functions to solve combinatorial problems
- Master the art of asymptotic analysis and singularity analysis
Prerequisites or good to have knowledge before taking this course
- Basic understanding of calculus
- Familiarity with discrete mathematics
Course Difficulty Level
IntermediateCourse Format
- Online Self-paced Course
- Video Lectures
- Assignments and Quizzes
Similar Courses
- Applied Combinatorics
- Discrete Optimization
Related Education Paths
Notable People in This Field
- Herbert S. Wilf
- Donald E. Knuth
Related Books
Description
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.
Outline
- 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
Summary of User Reviews
This course on analytic combinatorics has received positive reviews from many users. It covers a range of topics related to combinatorial analysis and is taught by experienced instructors. One key aspect that many users found good is the clear and concise explanations of complex concepts.Pros from User Reviews
- Experienced instructors with in-depth knowledge of the subject matter
- Clear and concise explanations of complex concepts
- Well-structured course content with good pacing
- Engaging assignments and quizzes that reinforce learning
- Access to a supportive community of fellow learners
Cons from User Reviews
- Requires a strong background in mathematics and computer science
- Some users found the course content to be too theoretical
- Limited interaction with instructors
- Some users found the course to be too challenging
- Not suitable for beginners in combinatorics
Robert Sedgewick
4.6 Raiting
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