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Course Description

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.

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This course is offered by Offered by Princeton University on the Coursera platform.
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Not many people realize that the literature you mention is the field of "analysis of algorithms", which is a sub-field of (or, in practice, somewhat different from) computational complexity theory / theory of algorithms. Robert Sedgewick (CS professor at Princeton, and an early PhD student of Knuth) has a great book with Flajolet on Analysis of Algorithms [1], and in one of the lectures from his course [2] makes a distinction between the complexity analysis usually taught in basic undergraduate algorithms courses (he calls O-notation not the scientific method, in a certain context in the lecture) and AofA (which involves saying "Running time is ~aN^c" instead of saying "Running time is O(N^c)", and also actually measuring against real programs) — watch the video or read the slides; it's an interesting distinction.

And the Purdue website [3] is even better at giving a sense of the field.


[2]: /


Its both. Here are some links:

Video Lectures are here:

and the book:

Also a youtube - short history of algorithm analysis by Sedgewick is worth a watch:

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