Reference
Mastery graph
87 topics and 148 declared prerequisite edges, laid out left to right so that every topic sits to the right of everything it assumes. Nodes you have marked studied turn green; nodes whose prerequisites are all met are highlighted as ready.
Nothing here is locked in the sense of being unavailable: every link works whatever your progress. A prerequisite is a claim about what a page assumes you can already do, which is information you can act on — not a gate.
studiedready — prerequisites metprerequisites outstanding· 16 dependency layers
Linear Algebra for Machine LearningFoundations · FoundationsMultivariable and Matrix CalculusFoundations · FoundationsAnalysis PrerequisitesFoundations · FoundationsProbability Spaces and Random VariablesProbability · FoundationsExpectation, Variance and Conditional ExpectationProbability · CoreModes of Convergence, LLN and CLTProbability · CoreSub-Gaussian and Sub-Exponential Random VariablesHigh-Dim Probability · AdvancedConcentration InequalitiesHigh-Dim Probability · AdvancedHigh-Dimensional Geometry and Concentration of the NormHigh-Dim Probability · AdvancedNets, Covering Numbers and Metric EntropyHigh-Dim Probability · GraduateThe Johnson–Lindenstrauss LemmaHigh-Dim Probability · GraduateSpectral Norm of Random MatricesRandom Matrices · GraduateSample Covariance and the Marchenko–Pastur LawRandom Matrices · GraduateCovariance Estimation and Sample ComplexityHigh-Dim Statistics · GraduateSparse Recovery, Compressed Sensing and the LassoHigh-Dim Statistics · ResearchConvex Sets, Convex Functions, Smoothness and Strong ConvexityOptimization · CoreGradient Descent and Its Convergence RatesOptimization · AdvancedLagrangian Duality and the KKT ConditionsAdvanced Optimization · AdvancedProjected, Proximal and Constrained First-Order MethodsAdvanced Optimization · GraduateMomentum and Nesterov AccelerationAdvanced Optimization · GraduateNewton, Quasi-Newton and Conjugate GradientAdvanced Optimization · GraduateSGD — Convergence Under Every Standard AssumptionSGD · GraduateAdaptive Methods and Variance ReductionSGD · GraduateEmpirical Risk Minimisation and Uniform ConvergenceLearning Theory · GraduateVC Dimension, Sauer's Lemma and Rademacher ComplexityLearning Theory · GraduateBias–Variance, Interpolation and Double DescentLearning Theory · GraduateLinear, Ridge and Lasso RegressionClassical ML · CoreLogistic RegressionClassical ML · CoreNearest Neighbours and the Curse of DimensionalityClassical ML · AdvancedTrees, Bagging and BoostingClassical ML · AdvancedKernels, RKHS and the Representer TheoremClassical ML · GraduateSupport Vector Machines — Complete DerivationClassical ML · GraduateApproximation Theory and BackpropagationDeep Learning · AdvancedConvolution, Recurrence and NormalisationDeep Learning · AdvancedThe Mathematics of TransformersDeep Learning · GraduateWhy Does Deep Learning Optimization Work?DL Theory · ResearchLanguage Modelling, Cross Entropy and PerplexityLLMs · GraduateRLHF, Bradley–Terry and DPOLLMs · ResearchScaling Laws, Fine-Tuning and In-Context LearningLLMs · ResearchLow-Rank AdaptationFine-Tuning · AdvancedThe Memory Arithmetic of TrainingFine-Tuning · AdvancedForgetting and RegularisationFine-Tuning · GraduateUniform Quantization and Its ErrorQuantization · AdvancedHessian-Aware RoundingQuantization · GraduateOutlier Features and Scale MigrationQuantization · GraduateInference Arithmetic and the RooflineLLM Ops · AdvancedKV Cache, Batching and Little's LawLLM Ops · AdvancedSpeculative DecodingLLM Ops · GraduateWhat a Serving System Must GuaranteeAI Systems · CoreLittle's Law and the Capacity of a Serving SystemAI Systems · CoreQueueing and the Utilisation WallAI Systems · AdvancedTail Latency and Fan-Out AmplificationAI Systems · AdvancedScaling Limits — Amdahl, Gustafson and the Coherency PenaltyAI Systems · AdvancedSizing a Serving Cluster End to EndAI Systems · AdvancedCaching — Hit Rates, Zipf and the Working SetAI Systems · AdvancedLoad Balancing and the Power of Two ChoicesAI Systems · AdvancedAvailability, Redundancy and Correlated FailureAI Systems · AdvancedThe Economics of Serving — Cost per TokenAI Systems · AdvancedThe Cost of Collective CommunicationAI Systems · GraduateSplitting a Model Across DevicesAI Systems · GraduateScheduling, Admission Control and FairnessAI Systems · GraduateAutoscaling — Delay, Overshoot and Standing HeadroomAI Systems · GraduateRollout, Canaries and Online ExperimentsAI Systems · GraduateThe Anatomy of an AI SystemAI Engineering · CoreAPI Design for Model EndpointsAI Engineering · CoreGateways, Authentication and QuotaAI Engineering · AdvancedRate Limiting AlgorithmsAI Engineering · AdvancedThe Model Context ProtocolAI Engineering · AdvancedSemantic CachingAI Engineering · AdvancedAutoscaling and Cold StartsAI Engineering · AdvancedGuardrails and Safety LayersAI Engineering · AdvancedData Pipelines and LineageAI Engineering · AdvancedReliability PatternsAI Engineering · AdvancedObservability for AI SystemsAI Engineering · AdvancedVector Search InfrastructureAI Engineering · AdvancedDeployment and RolloutAI Engineering · AdvancedTool Loops in ProductionAI Engineering · GraduateGPU Routing and Cache AffinityAI Engineering · GraduateInference Server ArchitectureAI Engineering · GraduateDrift DetectionAI Engineering · GraduateEvaluation HarnessesAI Engineering · GraduateEmbedding Geometry and SimilarityRAG · GraduateVector Search — Exact and Approximate Nearest NeighboursRAG · GraduateRetrieval as a Latent-Variable ModelRAG · ResearchError Compounding in Agent TrajectoriesAgents · AdvancedInference-Time Search and Best-of-nAgents · GraduateTool Selection and RegretAgents · Graduate