Best resources to learnRecurrence Relations

Q: What are the best free resources to learn Recurrence Relations?

Dantes has curated 9 resources for Recurrence Relations. All resources are hand-picked for quality — no algorithmic filler. Visit dantes.io/subject/recurrence-relations to browse the full curated list.

Study sheet

Recurrence relations are equations that define sequences recursively using previous terms. Learners will understand how to solve these relations using characteristic equations and generating functions to model algorithmic complexity and population growth.

Where to start

Start with Art of Problem Solving, whose free wiki and forum threads work through recurrences in combinatorics problems at a beginner level. If you only use one resource, make it Mathematics for Computer Science (MIT 6.042J) by Tom Leighton and Marten van Dijk, a full free course with lecture videos, problem sets and exams on discrete mathematics, including asymptotics and counting.

9 resources · Reviewed Oct 2026 · How we curate

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🎓Courses(3)

course

Mathematics for Computer Science (MIT 6.042J)

Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs.

intermediate🇬🇧

course

Analysis of Algorithms (Coursera)

Princeton course by Robert Sedgewick, free to audit, based on the Sedgewick-Flajolet textbook. Lectures cover recurrence relations, generating functions, and asymptotics applied to sorting, trees, and strings. Chapter 2 notes are on the aofa.cs.princeton.edu booksite. Shows recurrences doing real work in algorithm analysis, from first-order recurrences to generating-function solutions.

advanced🇬🇧

course

Discrete Mathematics

Dominik Scheder's proof-based course on sets, functions and relations, enumerative combinatorics, graph theory, and network flows and matchings, each concept paired with a fully proved non-trivial result. Learners read formal statements and write rigorous proofs of their own.

intermediate🇬🇧

📚Books(4)

book

generatingfunctionology

Wilf's text on generating functions, with the second edition free to download from his Penn page. Chapter 1 converts recurrences into generating functions and solves them, then the book covers formal power series, counting, and asymptotic estimates. Standard next step after characteristic roots: solving recurrences with generating functions.

advanced🇬🇧

bookPaid

Concrete Mathematics: A Foundation for Computer Science (2nd Edition)

Canonical book for recurrence-solving technique, built from Knuth's Stanford course. Chapter 1 solves recurrent problems such as the Tower of Hanoi and the Josephus problem; Chapter 7 solves recurrences with generating functions. Includes hundreds of exercises with answers.

advanced🇬🇧

book

Mathematics for Computer Science (Recurrences chapter)

Free MIT 6.042J textbook. Its Recurrences chapter covers the Towers of Hanoi, merge sort, linear recurrences solved by characteristic roots, divide-and-conquer recurrences and the Akra-Bazzi method, and guessing-and-verifying by induction; a later chapter covers generating functions. Bridges recurrences to algorithmic complexity with proofs and problem sets.

intermediate🇬🇧

book

Discrete Mathematics: An Open Introduction — Section 2.4: Solving Recurrence Relations

Free open-textbook section covering telescoping, iteration, and the characteristic root technique for linear homogeneous recurrences, including the repeated-root case, with worked examples, checks of closed formulas, and exercises with hints.

beginner🇬🇧

🌐Websites(2)

website

Art of Problem Solving

Art of Problem Solving wiki article defining recurrence relations and showing how to solve linear recurrences with constant coefficients through the characteristic polynomial, using examples such as the Fibonacci sequence. Prepares readers to find closed forms for recurrences that arise in competition counting problems.

beginner🇬🇧

website

Wolfram MathWorld

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

intermediate🇬🇧

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Frequently Asked Questions

Where should I start learning Recurrence Relations?

What are the best free resources to learn Recurrence Relations?

Dantes has curated 9 resources for Recurrence Relations, including 4 books, 3 courses, 2 websites. All resources are hand-picked for quality — no algorithmic filler. Browse the full list above to find the format that works best for you.

Is Recurrence Relations hard to learn?

Recurrence Relations is approachable at the beginner level — there are resources here specifically for those starting from scratch. As you progress, intermediate and advanced material is also available to take your skills further.

What types of Recurrence Relations learning resources are available on Dantes?

For Recurrence Relations, Dantes has curated 4 books, 3 courses, 2 websites. Each resource type serves a different learning style: videos and YouTube for visual learners, books for depth, courses for structured progression, and websites for quick reference.

How does Dantes select Recurrence Relations resources?

Dantes is an algorithm-free learning directory. Resources are hand-curated based on quality, accuracy, and usefulness — not engagement metrics or paid placements. The goal is to surface the best learning material for Recurrence Relations, whether it's a free YouTube series, a classic textbook, or an open courseware from a top university.

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