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Go to Learning InterfaceKnow computer science the way you know arithmetic.
Spaced repetition for the ideas most curricula skip—logic, lambda calculus, type theory, and the math that underlies everything.
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Subjects
Abstract Algebra
Group theory, rings, and fields - the mathematics of symmetry and structure.
Available NowAdversarial Organizational Dynamics
Red-teaming organizations: attack patterns, sabotage mechanics, information warfare, and organizational exploitation—understanding how institutions are compromised from within and without.
Available NowAutomata Theory
Explore the mathematical foundations of computation through finite automata, regular languages, and the limits of pattern recognition.
Available NowBoolean Logic
Master the foundations of symbolic reasoning - truth values, logical operations, and the algebra that underlies all digital computation.
Available NowCategory Theory
The mathematics of structure and structure-preserving maps. Categories, functors, natural transformations, universal properties, and the Yoneda perspective.
Available NowCombinatorial Games
Analyze games with perfect information: recursive decomposition, Sprague-Grundy theory, partisan games, and the discovery that games ARE numbers.
Available NowCombinatorics
The mathematics of counting - permutations, combinations, and the art of systematic enumeration.
Available NowCommunication Complexity
The mathematical study of information exchange requirements for distributed computation.
Available NowComplexity Theory
The cost of computation. P, NP, NP-completeness, and the structural landscape of computational difficulty.
Available NowComputability Theory
Explore the fundamental limits of computation—what machines can and cannot do, from Turing machines to undecidability to the landscape of impossible problems.
Available NowConcurrency
Shared-memory concurrency: interleaving semantics, synchronization, correctness, consensus, and process algebra.
Available NowConstructive Logic
The logic of evidence and construction. Covers the BHK interpretation, intuitionistic propositional calculus, decidability, Kripke semantics, and the Curry-Howard correspondence. Nothing exists until you build it.
Available NowDatabase Theory
The theoretical foundations of relational databases. Relational algebra and calculus, Codd's theorem, functional dependencies, normalization, and Datalog. The Cartographer's Bureau maps territories from survey data — assembling, cross-referencing, and organizing observations into faithful maps.
Available NowDependent Types
Types that depend on values—Pi types, Sigma types, and the full Curry-Howard correspondence for quantifiers.
Available NowDescriptive Complexity
Characterizing complexity classes with logic — the correspondence between definability and computational power.
Available NowDistributed Systems
Message-passing systems with partial failure: system models, time and ordering, impossibility results, consensus, consistency models, replication, and distributed transactions. The Lighthouse Network — isolated keepers communicating through fog, where silence tells you nothing.
Available NowGame Theory
Strategic decision-making under interdependence - from dominant strategies to Nash equilibrium to sequential games.
Available NowGraph Theory
Vertices, edges, paths, and algorithms - the mathematics of connections, networks, and relationships.
Available NowInformation Theory
Quantifying, encoding, and protecting information—from Shannon entropy to channel capacity.
Available NowLambda Calculus
Patterns with slots, filled in by substitution. From this single operation: booleans, numbers, data structures, recursion — all of computation.
Available NowLambda Implementation
How lambda calculus runs: De Bruijn indices, nameless operations, advanced encodings, environments, closures, abstract machines, and optimal reduction.
Available NowLisp
Master recursive thinking through Lisp—the language that treats code as data. Build programs from five primitives, explore list processing with an adventure game theme, and discover how evaluators work.
Available NowLogic Programming
Master declarative programming through logic—the paradigm where you declare what is true and let the engine derive consequences. Build knowledge bases with facts and rules, ask queries, and watch unification and resolution work their magic. Experience logic programming through the lens of a sorcerer conjuring a text adventure world: speak things into existence, decree the laws of nature, and ask the spirits what is true in your creation.
Available NowMechanism Design
Designing rules so self-interested agents produce good outcomes: auctions, voting, matching, contracts, and the art of incentive alignment.
Available NowModal Logic
Logic of necessity and possibility. Covers modal operators, Kripke semantics, axiom systems (K, T, S4, S5), proof theory, epistemic logic, and temporal logic. The investigation continues—in precincts where doors open onto other worlds.
Available NowNumber Theory
The mathematics of integers - divisibility, primes, congruences, and the foundations of modern cryptography.
Available NowOrder Theory
Partial orders, lattices, and fixed-point theorems - the mathematics of hierarchy and structure.
Available NowOrganizational Dynamics
Systems reasoning applied to institutions: how authority, incentives, and controls shape behavior; how systems fail and recover; pattern recognition for incidents and organizational pathology.
Available NowPredicate Logic
First-order logic with quantifiers and predicates. Covers syntax (terms, predicates, quantifiers), semantics (structures, satisfaction), translation (English to FOL), natural deduction proofs, identity/equality, and meta-theory (completeness, undecidability).
Available NowProbability
Chance, expectation, and reasoning under uncertainty - from sample spaces to Bayesian inference.
Available NowPropositional Logic
Formal logic of propositions and proof systems. Covers syntax (well-formed formulas), semantics (truth and validity), proof methods (natural deduction, tableaux, resolution), and meta-theory (soundness, completeness).
Available NowRewriting Systems
Term rewriting systems, abstract reduction, confluence, and termination - the formal foundation underlying lambda calculus and symbolic computation.
Available NowSet Theory
The mathematical study of collections — from membership and operations through relations and functions to Cantor's infinite hierarchies and the axiomatic foundations of mathematics.
Available NowType Theory
Types as a foundation for programming and logic - from simply typed lambda calculus through polymorphism to Curry-Howard.
Available NowTopology
Point-set topology: open and closed sets, continuity, compactness, connectedness, metric spaces, separation axioms. The study of structure preserved under continuous maps.
BetaAlgebraic Foundations
Algebraic fluency from first principles — expressions, equations, functions, and the art of equivalence.
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