This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. In addition, this course covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings.
All the features of this course are available for free. It does not offer a certificate upon completion.
Offered By
20,398 already enrolled!
Princeton University
Syllabus - What you will learn from this course
Week
12 hours to complete
Analysis of Algorithms
We begin by considering historical context and motivation for the scientific study of algorithm performance. Then we consider a classic example that illustrates the key ingredients of the process: the analysis of Quicksort. The lecture concludes with a discussion of some resources that you might find useful during this course.
4 videos (Total 76 min), 2 readings, 1 quiz
2 readings
Getting Started10m
Exercises from Lecture 110m
1 practice exercise
Analysis of Algorithms4m
Week
22 hours to complete
Recurrences
We begin this lecture with an overview of recurrence relations, which provides us with a direct mathematical model for the analysis of algorithms. We finish by examining the fascinating oscillatory behavior of the divide-and-conquer recurrence corresponding to the mergesort algorithm and the general "master theorem" for related recurrences.
5 videos (Total 71 min), 1 reading, 3 quizzes
1 reading
Exercises from Lecture 210m
3 practice exercises
Pop Quiz on Telescoping2m
Pop Quiz on the Master Theorem2m
Recurrences4m
Week
32 hours to complete
Generating Functions
Since the 17th century, scientists have been using generating functions to solve recurrences, so we continue with an overview of generating functions, emphasizing their utility in solving problems like counting the number of binary trees with N nodes.
5 videos (Total 84 min), 1 reading, 1 quiz
5 videos
Counting with Generating Functions27m
Catalan Numbers14m
Solving Recurrences18m
Exponential Generating Functions7m
1 reading
Exercises from Lecture 310m
1 practice exercise
Generating Functions6m
Week
42 hours to complete
Asymptotics
Exact answers are often cumbersome, so we next consider a scientific approach to developing approximate answers that, again, mathematicians and scientists have used for centuries.
4 videos (Total 83 min), 1 reading, 1 quiz
4 videos
Manipulating Expansions 19m
Asymptotics of Finite Sums 16m
Bivariate Asymptotics 28m
1 reading
Exercises from Lecture 410m
1 practice exercise
Asymptotics4m
4.7
6 ReviewsTop Reviews
This course is more about mathematic than algorithms, it teaches how to solve tricky combinatorial problems
This is great course if you already done some algorithms courses and want to go deeper.
Instructor
Robert Sedgewick
William O. Baker *39 Professor of Computer ScienceComputer Science
About Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. It is one of the eight universities of the Ivy League, and one of the nine Colonial Colleges founded before the American Revolution.
Frequently Asked Questions
When will I have access to the lectures and assignments?
Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.
Can I earn a certificate in this course?
No. As per Princeton University policy, no certificates, credentials, or reports are awarded in connection with this course.
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