Analytic Combinatorics
- Free
- No certificate
- Intermediate
- 2 weeks
Analytic Combinatorics is Robert Sedgewick's Princeton course on a calculus for making precise quantitative predictions about large combinatorial structures. It introduces the symbolic method for deriving functional relations among ordinary, exponential and multivariate generating functions, and then methods from complex analysis for extracting accurate asymptotics from those equations. The eight modules cover combinatorial structures and ordinary generating functions, labelled structures and exponential generating functions, combinatorial parameters and multivariate generating functions, complex analysis with rational and meromorphic asymptotics, applications of those asymptotics, singularity analysis, applications of singularity analysis, and saddle-point asymptotics.
Coursera labels the course intermediate level with a flexible schedule and estimates two weeks at ten hours a week. The page states that all features are available for free and that no certificates, credentials or reports are awarded. The textbook Analytic Combinatorics is optional.
What you’ll learn
- Derive ordinary, exponential and multivariate generating functions with the symbolic method
- Describe labelled and unlabelled combinatorial structures and their parameters
- Obtain asymptotics from rational and meromorphic generating functions
- Apply singularity analysis and saddle-point methods
Who it’s for
Mathematically prepared learners, ideally after Analysis of Algorithms, who want the full generating-function and complex-analysis toolkit.
Syllabus
8 sections as listed on coursera.org, 16 h 54 min in total.
- Combinatorial Structures and OGFs 2 h 13 min
- Labelled Structures and EGFs 2 h 15 min
- Combinatorial Parameters and MGFs 2 h 14 min
- Complex Analysis, Rational and Meromorphic Asymptotics 2 h 39 min
- Applications of Rational and Meromorphic Asymptotics 1 h 53 min
- Singularity Analysis 2 h 12 min
- Applications of Singularity Analysis 1 h 55 min
- Saddle Point Asymptotics 1 h 33 min
Instructor
- Robert Sedgewick William O. Baker *39 Professor in Computer Science, Emeritus, Computer Science, Princeton University
Course details
- Skills covered
- Mathematical Theory & Analysis
- Combinatorics
- Calculus
- Includes
- 8 modules · 8 assignments
- Prerequisites
- Some related experience required
- Subtitles
- 22 languages
On coursera.org
Rated 4.6 out of 5 by 76 learners; 27,260 enrolled, as shown on the course page on 20 Oct 2026. These are coursera.org’s own figures, not ours.
Source: Princeton Online (opens in a new tab) · Verified · Report a change
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