Discrete Mathematics

Learn Order Theory

Height, width and Dilworth, product against lexicographic order, complete lattices and the Knaster-Tarski fixed-point theorem, closure operators and Galois connections, formal concept analysis, the distributive and modular hierarchies with their two forbidden diagrams, Birkhoff representation, Heyting algebras and Stone duality, Scott continuity and the fixed-point semantics of recursion, and the Dedekind-MacNeille completion.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Order Theory

Height, width and DilworthProduct and lexicographic ordersComplete latticesKnaster-Tarski and least fixed pointsClosure operatorsGalois connectionsFormal concept analysisDistributive latticesModular latticesBirkhoff's representation theoremHeyting algebrasStone duality, the finite caseScott continuityCPOs and domain theoryFixed-point semantics of recursionInterval ordersThe dominance order on partitionsThe Dedekind-MacNeille completion
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Order Theory exactly where it's useful.

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