Analytic Combinatorics

Princeton University

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.

Analytic Combinatorics is based on formal methods for deriving functional relationships on generating functions and asymptotic analysis treating those functions as functions in the complex plane. This course covers the symbolic method for defining generating functions immediately from combinatorial constructions, then develops methods for directly deriving asymptotic results from those generating functions, using complex asymptotics, singularity analysis, saddle-point asymptotics, and limit laws. The course teaches the precept "if you can specify it, you can analyze it".

Syllabus

Lecture  1  Combinatorial Structures and OGFsLecture  2  Labelled Structures and EGFsLecture  3  Combinatorial Parameters and MGFsLecture  4  Complex Analysis, Rational and Meromorphic AsymptoticsLecture  5  Applications of Rational and Meromorphic AsymptoticsLecture  6  Singularity Analysis of Generating FunctionsLecture  7  Applications of Singularity AnalysisLecture  8  Saddle-Point Asymptotics

Recommended Background

Familiarity with recurrences, generating functions, asymptotics and basic combinatorics as taught in Analysis of Algorithms. Basic familiarity with programming in Java and the algorithms and data structures covered in Algorithms, Part I is helpful but not required. The video From Analysis of Algorithms to Analytic Combinatorics: A Journey with Philippe Flajolet, is an optional overview that tries to answer the question "What is Analytic Combinatorics" and to give some historical perspective.

Suggested Readings

This course is based on the textbook Analytic Combinatorics by Flajolet and Sedgewick. The (free) web materials associated with the course and the textbook can be found at http://ac.cs.princeton.edu/home/

Course Format

There will be one lecture (about 80 minutes) and a problem set each week.

FAQ

Does Princeton award credentials or reports regarding my work in this course?

No certificates, statements of accomplishment, or other credentials will be awarded in connection with this course.

Dates:
  • 6 November 2015, 6 weeks
  • 20 March 2015, 6 weeks
  • 31 October 2014, 6 weeks
  • 28 March 2014, 6 weeks
  • 1 November 2013, 6 weeks
Course properties:
  • Free:
  • Paid:
  • Certificate:
  • MOOC:
  • Video:
  • Audio:
  • Email-course:
  • Language: English Gb

Reviews

No reviews yet. Want to be the first?

Register to leave a review

Show?id=n3eliycplgk&bids=695438
Included in selections:
6-046jf05 Algorithms
Algorithms and data structures from the beginning to advanced analysis.
NVIDIA
More on this topic:
18-319f05 Geometric Combinatorics
This course offers an introduction to discrete and computational geometry. Emphasis...
21m-350s08 Musical Analysis
This class is an introduction to the analysis of tonal music. Students develop...
Extensionflag Industrial Ecology: Concepts and Practice
Industrial ecology is an interdisciplinary field focused on the sustainable...
Chp_set_rook Combinatorial Analysis
This course analyzes combinatorial problems and methods for their solution....
18-997s04 Topics in Combinatorial Optimization
In this graduate-level course, we will be covering advanced topics in combinatorial...
More from 'Computer Science':
D8d3c316-0e41-4083-93ff-733a7e9b16bb-46a802220de9.small Capstone Exam in Statistics and Data Science
Solidify and demonstrate your knowledge and abilities in probability, data analysis...
Logo2 Network Science
The course is an interdisciplinary course, focused on the emerging science of...
3734fd64-86ca-48d2-96cd-68012918b899-a001bb3f9d3d.small Gameplay Programming for Video Game Designers
Learn how to create the best gameplay by understanding algorithmic thinking...
Regular_1bb827eb-8ea2-482a-af4a-fd767b047713 Introducing Robotics: Making Robots Move
The world needs people who understand how to get robots moving.
Regular_cce76e9c-434e-42e9-a6b1-e2d402812376 Python in High Performance Computing
Learn how to analyse Python programmes and identify performance barriers to...
More from 'Coursera':
Success-from-the-start-2 First Year Teaching (Secondary Grades) - Success from the Start
Success with your students starts on Day 1. Learn from NTC's 25 years developing...
New-york-city-78181 Understanding 9/11: Why Did al Qai’da Attack America?
This course will explore the forces that led to the 9/11 attacks and the policies...
Small-icon.hover Aboriginal Worldviews and Education
This course will explore indigenous ways of knowing and how this knowledge can...
Talk_bubble_fin2 Accountable Talk®: Conversation that Works
Designed for teachers and learners in every setting - in school and out, in...
Coursera_accounting_460x259 An Introduction to Financial Accounting
This course will improve your fluency in financial accounting, the language...

© 2013-2019