Function (nLab)
nLab
Wiki entry defining a function as a rule sending each domain element to a unique codomain element, then comparing set-theoretic, type-theoretic and category-theoretic formulations, total versus partial functions, and function sets. Readers see how the elementary notion generalises to morphisms in arbitrary categories.
More resources on Functions
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.
Discrete Math Full Course: Sets, Logic, Proofs, Functions and Relations
A one-semester university course on video. The sets-and-functions segment walks through domain and codomain, injective and surjective proofs, composition and inverses at whiteboard pace, giving a visual first pass before tackling a proof textbook.
Set Theory: An Open Introduction
Free CC BY textbook from the Open Logic Project. Chapter 4 covers function basics, kinds of functions, functions reduced to relations, inverses and composition; Chapter 5 uses bijections for enumerability, Cantor's theorem and Schroder-Bernstein.
How to Prove It: A Structured Approach (3rd Edition)
Velleman's structured method builds proofs from logical form outward. Chapter 5 treats functions as relations, then one-to-one and onto, composition, inverse images and inverse functions, with exercises that force explicit proof scaffolding rather than pattern matching.
Introduction to Mathematical Thinking
Stanford course by Keith Devlin on how mathematicians reason, starting with the logic of language (and, or, not, implication, quantifiers) and moving to the structure of proofs, including contradiction and induction. Learners become able to read, construct and critique simple mathematical proofs.