The mathematical foundations of computation. Discover the algebra, combinatorics, and analysis that power efficient algorithms through 39 interactive demonstrations.
This is not interview prep — it's the deep mathematics behind why algorithms work: monoids, generating functions, information-theoretic bounds, and probabilistic analysis.
See also: Graph Theory for the graph problems many algorithms solve, Combinatorics for the recurrences governing complexity, and Optimization for the dynamic-programming and greedy strategies that find optima.
Discover the hidden algebraic structures in algorithms: monoids, semigroups, and how they power segment trees and parallel computation
Explore Catalan numbers, generating functions, and the surprising connections between binary trees, Dyck paths, and parenthesizations
Master the analysis of divide-and-conquer algorithms through recursion trees, the Master Theorem, and geometric series
Understand fundamental limits: decision trees, entropy, and why comparison-based sorting requires Omega(n log n) comparisons
Explore skip lists, Bloom filters, and HyperLogLog—structures that trade exactness for remarkable efficiency using probability
Learn to analyze sequences of operations using potential functions, proving that expensive operations are rare enough to be efficient
Discover Union-Find with path compression and union by rank, achieving the almost-impossible O(α(n)) bound
Explore the most important algorithm in signal processing: how roots of unity enable O(n log n) polynomial multiplication
Study B-trees for disk optimization, persistent trees for version control, and van Emde Boas trees for integer keys