Foundations

A notation for describing how an algorithm's cost grows as its input grows — the standard way computer scientists compare algorithms.

A way of writing whole numbers using only two digits, 0 and 1 — the native number system of digital computers.

A bit is the smallest unit of information in computing — a single value that is either 0 or 1.

The algebra of true and false — the simple rules (AND, OR, NOT) from which every digital decision is built.

A way of organising values in memory so that the operations you care about — find, insert, delete, sort — are efficient.

A way of solving a problem by having a function call itself on a smaller version of the same problem, until the base case is trivial.

A precise, finite recipe for solving a problem — the central idea of computer science.

Hiding complexity behind a simpler interface — the core technique that lets us build and reason about large systems by ignoring lower-level details until we need them.

The standard that maps characters to numbers so text can be stored and transmitted as bits — from ASCII's original 128 code points to Unicode's 150,000 and UTF-8's dominant variable-length encoding.

A data structure that maps keys to values with average O(1) lookup, insert, and delete — the workhorse of dictionaries, sets, caches, and indexes.

A base-16 numbering system used throughout computing because each hex digit corresponds exactly to 4 binary digits.

A data structure built from nodes that each point to the next, allowing O(1) insert and remove at any known node — and notably awful cache behaviour.

Two of the simplest data structures — a stack is last-in-first-out, a queue is first-in-first-out. Both show up everywhere from CPU instructions to background job systems.

A hierarchical data structure where each node has children but only one parent — the basis of file systems, search structures, DOMs, and ASTs.

A self-balancing tree optimised for block storage — wide, shallow, and designed so every search, insert, and delete touches only O(log n) pages, which is why it powers almost every database index.

The branch of mathematics dealing with distinct, separate values — logic, sets, combinatorics, graphs, and proof — that forms the mathematical foundation of computer science.

The standard way computers represent real numbers — a finite binary approximation with a sign, an exponent, and a significand that makes most arithmetic fast but never perfectly exact.

The study of graphs — collections of nodes connected by edges — which model networks, relationships, and dependencies across computing and beyond.

Abstract machines that read input and move between states according to fixed rules — the mathematical models of computation, from simple finite-state machines up to the Turing machine.

The study of how the resources a problem requires — time and memory — grow with input size, and how problems are classified by how hard they are to solve.

The study of what can be computed by an algorithm at all — and the proof that some problems, like the halting problem, can never be solved by any computer.

A precisely-defined set of strings built from an alphabet according to formal rules (a grammar) — the mathematical foundation for parsing, programming languages, and computation theory.

A formal notation for describing patterns in text — based on the theory of finite automata and regular languages, implemented in every programming language for string matching, validation, and parsing.

An abstract mathematical framework studying structures and the structure-preserving maps between them — the algebraic language behind Haskell's monads, functional programming abstractions, and the compositional design of software.

A minimal formal system for expressing computation through function abstraction and application — the mathematical foundation of functional programming, type theory, and the theoretical basis for what is computable.

A formal framework for classifying values by their kind — preventing invalid operations, enabling type inference, and at its most powerful, encoding mathematical proofs as programs through the Curry-Howard correspondence.