Analysis of Algorithms from Coursera

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. People who are interested in digging deeper into the content may wish to obtain the textbook Analysis of Algorithms, Second Edition (upon which the course is based) or to visit the website aofa.cs.princeton.edu for a wealth of additional material.

This course does not offer a certificate upon completion.

What's inside

Syllabus

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.

Analytic Combinatorics

Analytic Combinatorics. With a basic knowledge of recurrences, generating functions, and asymptotics, you are ready to learn and appreciate the basic features of analytic combinatorics, a systematic approach that avoids much of the detail of the classical methods that we have been considering. We introduce unlabeled and labelled combinatorial classes and motivate our basic approach to studying them, with numerous examples.

Trees

The quintessential recursive structure, trees of various sorts are ubiquitous in scientific enquiry, and they arise explicitly in countless computing applications. You can find broad coverage in the textbook, but the lecture focuses on the use of analytic combinatorics to enumerate various types of trees and study parameters.

Permutations

The study of sorting algorithms is the study of properties of permutations. We introduce analytic-combinatoric approaches to studying permutations in the context of this relationship.

Strings and Tries

From DNA sequences to web indices, strings (sequences of characters) are ubiquitous in modern computing applications, so we use analytic combinatorics to study their basic properties and then introduce the trie, an essential and fundamental structure not found in classical combinatorics.

Words and Mappings

We view strings as sets of characters or as functions from [1..N] to [1..M] to study classical occupancy problems and their application to fundamental hashing algorithms. Functions from [1..N] to [1..N] are mappings, which have an interesting and intricate structure that we can study with analytic combinatorics.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Covers core principles of analytic combinatorics

Instructed by Robert Sedgewick, a renowned professor and author in the field of algorithms and data structures

Designed for individuals with a strong foundation in calculus

Incorporates mathematical concepts and techniques to analyze algorithms and combinatorial structures

Reviews summary

Well received algorithms course

Learners say that Analysis of Algorithms is a well received course that largely features informative and engaging lectures, readings, homework, and quizzes. The instructors are knowledgeable and present the material in a clear and understandable way. Overall, students find this course to be helpful and enjoyable.

Challenging but rewarding

"Definitely a tough course. But very useful for algorithm analysis and set theory."

"Difficult, and mathematically demanding."

"it was nice learning but at some points it was difficult to understand at all, so had to watch multiple times"

Deep dives into mathematical concepts

"Excellent material and instruction, and the course readings do require matematical sophistication."

"Such a good class as an intro to Analytic Combinatorics and Analysis of Algorithms"

"Wonderful insights about the study of the algorithm's complexity and combinatoric logic."

Knowledgeable and engaging

"the material is delivered by great and experienced presenters"

"Professor Sedgewick was amazing to listen to."

"I think that professor Sedgewick does an excellent job making this material accessible at a deep level."

Valuable lessons on algorithm analysis

"This course offers an extensive coverage of mathematical material like tools and techniques, putting special emphasis on simple principles and never losing its focus on the general perspective of the topic."

"Such a Insightful course on algorithm analysis, this really improved my problem-solving skills significantly."

"Outstanding material, brilliantly conceived! It contains the essence of mathematics necessary for anyone serious about programming."

No certificate provided

"where can I get certificate"

"I am complete but did not certificate received."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Analysis of Algorithms with these activities:

Review Calculus

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Reacquaint yourself with the principles of calculus and their applications.

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Review your notes or textbooks.
Practice solving basic calculus problems.
Take a practice test or quiz.

Read 'Analytic Combinatorics'

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Supplement your learning with in-depth insights from the leading textbook.

View An Introduction to the Analysis of Algorithms on Amazon

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Obtain a copy of the book.
Read and take notes on the relevant chapters.
Work through the exercises and problems.

Explore Analytic Combinatorics

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Gain a solid foundation in a key topic from the course.

Browse courses on Analytic Combinatorics

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Find online tutorials or courses.
Follow along and take notes.
Practice solving problems and exercises.

Five other activities

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Practice Recurrence Relations

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Improve problem-solving skills and reinforce key concepts.

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Solve practice problems and review examples.
Analyze real-world scenarios.
Use online resources and tools.

Attend a Workshop on Combinatorial Analysis

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Deepen your knowledge and connect with experts in the field.

Browse courses on Combinatorics

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Find and register for a relevant workshop.
Attend the workshop and actively participate.
Network with other attendees and speakers.

Analyze an Algorithm Using Asymptotics

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Gain hands-on experience in evaluating algorithm performance.

Browse courses on Asymptotic Analysis

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Select an algorithm and problem instance.
Implement the algorithm.
Analyze the algorithm's running time.
Compare your findings with theoretical predictions.

Build a Generative Function Model

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Deepen your understanding by applying concepts to a practical project.

Browse courses on Generating Functions

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Choose a specific problem or dataset.
Develop a generative function model.
Test and evaluate your model.
Present your findings.

Develop a Trie Structure

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Reinforce concepts and apply skills by implementing a practical data structure.

Browse courses on Data Structures

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Design and plan the trie structure.
Implement the structure in a programming language.
Test and debug your implementation.
Integrate the trie into a larger project or application.

Career center

Learners who complete Analysis of Algorithms will develop knowledge and skills that may be useful to these careers:

Software Engineer

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Data Scientist

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Operations Research Analyst

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Financial Analyst

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Quantitative Analyst

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Actuary

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Economist

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Statistician

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Computer Scientist

Computer scientists design, develop, and implement software systems. This course can help you build a foundation in the mathematical and analytical skills necessary for this field. The course covers topics such as algorithm design, data structures, and software design patterns, which are essential for computer science. Additionally, the course's emphasis on problem-solving can help you develop the critical thinking skills necessary to solve complex computer science problems.

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Mathematician

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Data Analyst

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Operations Manager

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