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 to your own forgetting.

What you'll learn

30 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 completionLinear extensions & SzpilrajnOrder dimensionWell-quasi-orders & Dickson's lemmaHigman's lemmaThe multiset order & terminationFrames & localesUltrafilters & Stone dualityThe partition latticeAntimatroids & convex geometriesMedian algebrasThe fixed-point propertyContinuous lattices & way-below
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 day its model predicts you would 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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