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.
About this Course
Offered by

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.
Syllabus - What you will learn from this course
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.
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.
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.
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.
Reviews
TOP REVIEWS FROM ANALYSIS OF ALGORITHMS
This course is more about mathematic than algorithms, it teaches how to solve tricky combinatorial problems
I enjoyed problems given in the quizzes. The course is one of the best presentations I have seen.
clear explanation, and amazing tools to analyze algorithms through a scientific approach.
Wonderful insights about the study of the algorithm's complexity and combinatoric logic.
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