Browse 40 free AI courses
Other people’s courses, beginner to advanced — for when you want a second explanation, or a teacher who is not me.
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Learn mathematics for AI
A collection I keep of books, papers and video lecture courses for the mathematics machine learning rests on — linear algebra, calculus, probability. All of it free. It goes deeper than these pages do, so treat it as where to turn when a concept here leaves you wanting the real derivation.
Browse the resourcesWhere to begin
43 concepts rest on nothing
You can open any of these today without reading something else first. The rest of the map is reachable from them — every concept page shows how few pages it takes to get there.
Everything there is
12 domains, 60 modules, 425 concepts
All of it, on this page — click any concept to read it. Inside a module the order is not alphabetical: each concept comes after whatever it depends on, worked out from the notes themselves. Where several concepts build on the same idea it is marked, and those are the ones worth slowing down for.
Mathematical Foundations
77Discrete Mathematics4
Proof by Induction4 build on thisEstablishing a statement for all natural numbers by proving a base case and showing each case implies the next.Catalan NumbersA sequence counting many structurally similar objects — balanced parentheses, binary trees, non-crossing partitions — all in bijection with each other.Integer PartitionsThe ways of writing an integer as a sum of positive integers, ignoring order — a classic counting problem with surprisingly deep structure.Modular Arithmetic3 build on thisArithmetic on remainders after division by a fixed modulus, giving a finite cyclic structure that underpins hashing and cryptography.
Linear Algebra11
Vector Spaces and Rank10 build on thisA vector space is a set closed under addition and scaling; rank is the dimension of the space a matrix's columns actually span.Linear Transformations9 build on thisMaps that preserve addition and scalar multiplication.Tensors and Shapes12 build on thisMulti-dimensional arrays and the discipline of tracking their dimensions through a computation.Matrix Multiplication7 build on thisComposing two linear transformations by taking dot products of rows with columns.NumPy BroadcastingThe rule set that lets arrays of different shapes combine by implicitly expanding size-one dimensions, avoiding explicit loops and copies.Eigenvalues and EigenvectorsDirections a transformation merely stretches rather than rotates, and the factors by which it stretches them.Determinants and InversesThe determinant measures how much a transformation scales volume, and vanishes exactly when the transformation collapses dimensions.Orthogonality and ProjectionsTwo vectors are orthogonal when their dot product vanishes; a projection drops a vector perpendicularly onto a subspace.Singular Value DecompositionFactoring any matrix into a rotation, a scaling and another rotation.Gram-SchmidtA procedure that turns any linearly independent set into an orthonormal one by repeatedly subtracting off the components already accounted for.Normal Equations3 build on thisThe linear system whose solution is the least-squares fit, obtained by requiring the residual to be orthogonal to the column space of the design matrix.
Probability Theory5
Markov Decision Processes3 build on thisThe formal model of sequential decision-making: states, actions, transition probabilities, rewards and a discount factor, with the Markov property making history irrelevant given the present state.Sampling Distributions8 build on thisThe distribution of a statistic across repeated samples from the same population.Empirical CDFThe step function that jumps by 1/n at each observation, estimating the cumulative distribution directly from data with no parametric assumption.Concentration InequalitiesBounds showing that a random quantity stays close to its expectation with high probability.Fitting Distributions4 build on thisChoosing a parametric family and estimating its parameters from data, then checking whether the fit is adequate rather than assuming it.
Bayesian Methods3
Bayesian Inference and Decision Theory4 build on thisUpdating beliefs with Bayes' rule and then choosing the action that minimises expected loss under the resulting posterior.Fisher InformationA measure of how sharply the likelihood identifies a parameter, equivalently the curvature of the log-likelihood at its maximum.Information GeometryTreating families of probability distributions as curved manifolds, with divergences playing the role of distance and Fisher information as the metric.
Calculus4
Computational Graphs9 build on thisRepresenting a calculation as a directed graph of operations, so the forward pass evaluates it and the backward pass traverses it in reverse to accumulate gradients.Matrix Calculus and JacobiansDifferentiating functions whose inputs and outputs are vectors or matrices.Automatic Differentiation3 build on thisComputing exact derivatives by tracking elementary operations and applying the chain rule mechanically, distinct from both symbolic differentiation and finite differences.Gradient CheckingVerifying an analytic gradient against a finite-difference approximation, the standard sanity check before trusting a hand-written backward pass.
Graph Theory5
Topological SortOrdering the nodes of a directed acyclic graph so every edge points forward, which is exactly what dependency resolution requires.PageRankRanking nodes by the stationary distribution of a random walk that occasionally teleports, so importance flows from important neighbours.Graph Traversal BFS and DFS4 build on thisThe two canonical ways to explore a graph: breadth-first expands level by level, depth-first descends as far as possible before backtracking.Social Network AnalysisStudying social structure through the graph of relationships — centrality, communities, brokerage and diffusion across ties.Dijkstra Shortest PathFinding shortest paths from a source in a graph with non-negative edge weights by repeatedly expanding the closest unvisited node.
Information Theory8
Shannon Entropy3 build on thisThe average surprise in a distribution, measured in bits, and the theoretical floor on lossless compression of samples from it.Data Compression6 build on thisEncoding data in fewer bits, losslessly by exploiting statistical redundancy or lossily by discarding perceptually unimportant detail.Mutual InformationHow much knowing one variable reduces uncertainty about another, capturing any dependence rather than only linear correlation.Huffman CompressionBuilding an optimal prefix-free code by repeatedly merging the two least frequent symbols, giving short codes to common symbols.KL DivergenceThe extra cost, in bits, of coding data from one distribution using a code built for another.Cross-Entropy Loss4 build on thisThe negative log-likelihood of the correct class under the model's predicted distribution — the standard objective for classification and next-token prediction.KL Divergence AsymmetryWhich distribution you place first changes what minimising KL divergence actually does — one direction spreads mass to cover everything, the other concentrates on a single mode.ELBOThe evidence lower bound, the tractable objective variational inference maximises in place of an intractable marginal likelihood.
Recursion6
Recursive Thinking12 build on thisFraming a problem in terms of a smaller instance of itself, identifying the parameters, base cases and the relationship between them before writing code.Base Cases and RecurrenceThe terminating conditions of a recursion and the rule relating a case to smaller ones — together a complete definition of the computation.Stack Memory Behaviour3 build on thisEach recursive call consumes a stack frame holding its locals and return address, so recursion depth translates directly into memory.Depth-First Search with BacktrackingExploring choices recursively and undoing them when a branch fails, the standard pattern for constraint problems and puzzles.Tail RecursionA recursive call in final position, where nothing remains to do afterwards, allowing the frame to be reused instead of stacked.Tower of HanoiThe classic puzzle of moving a stack of disks between pegs, whose recursive solution is three lines and whose cost is exponential.
Statistical Inference12
Descriptive Statistics9 build on thisSummarising a dataset's central tendency, spread and shape before any inference — means, medians, quantiles, standard deviations and the distributional picture behind them.Null and Alternate Hypotheses4 build on thisThe two competing statements a test adjudicates: a null of no effect, and an alternative representing what you would conclude if the null is rejected.Scatterplots and RelationshipsPlotting two variables against each other to reveal association, nonlinearity, clustering and outliers before any correlation coefficient is computed.Significance LevelsThe pre-chosen probability of rejecting a true null hypothesis, conventionally 0.05, which sets the threshold a p-value is compared against.Sufficient StatisticsA statistic that captures everything in the data relevant to a parameter, so that conditioning on it leaves no further information about that parameter.Hypothesis TestingA formal procedure for deciding whether data provide enough evidence against a null hypothesis, controlling the rate of false rejections at a chosen level.Q-Q Plots and NormalityPlotting sample quantiles against theoretical ones so that agreement appears as a straight line, making departures from an assumed distribution visible.ANOVAAnalysis of variance partitions total variability into components attributable to group differences and to residual noise, testing whether group means differ.Cross-Validation PartitionsSplitting data into folds so every observation serves once as validation, giving a less variable performance estimate than a single holdout.Mixed-Effects ModelsModels combining fixed effects shared across all observations with random effects varying by group, appropriate when data is clustered or repeatedly measured.Gaussian Process RegressionA nonparametric Bayesian method placing a distribution over functions, returning both a prediction and a calibrated uncertainty at every point.Partial Least SquaresA regression method that constructs components maximising covariance with the response, rather than variance in the predictors alone as PCA does.
Numerical Methods2
Quantum ComputingComputation exploiting superposition and entanglement, promising asymptotic speedups on specific problem classes rather than general computing.Kalman FilterA recursive estimator combining a dynamic model with noisy measurements to track a system's state optimally under linear-Gaussian assumptions.
Optimization17
Linear Programming and SimplexOptimising a linear objective over linear constraints.Gradient Descent15 build on thisIteratively stepping parameters against the gradient of the loss.Stochastic Gradient Descent3 build on thisEstimating the gradient from a minibatch instead of the full dataset, trading exactness for far more updates per unit of computation.Hyperparameter TuningSearching over settings that are not learned from data — learning rate, depth, regularisation strength — using grid, random or model-based search.Lagrange Multipliers3 build on thisFolding equality constraints into the objective with multipliers, converting a constrained problem into a stationary-point problem on the Lagrangian.Line SearchChoosing how far to move along a chosen descent direction, either exactly or by accepting the first step that improves the objective sufficiently.Newton MethodUsing second-derivative information to jump toward the optimum, converging quadratically near the solution instead of linearly.Optimal ControlChoosing a control policy over time to optimise a cost functional subject to system dynamics — the continuous-time ancestor of reinforcement learning.Training DynamicsHow loss, gradients and representations evolve over the course of training, including warmup, plateaus, sharp drops and the effect of schedules.Double DescentThe observation that test error falls, rises around the interpolation threshold, then falls again as capacity keeps growing — contradicting the classical U-shaped curve.Duality Primal and DualEvery optimisation problem has a dual whose optimum bounds the original.Least Squares Regression5 build on thisFitting parameters by minimising the sum of squared residuals, the oldest and still most-used estimation criterion.KKT ConditionsThe first-order necessary conditions for optimality with inequality constraints — stationarity, feasibility, dual feasibility and complementary slackness.Convex Optimization3 build on thisProblems where any local minimum is global, giving strong guarantees and reliable algorithms.Inverse ProblemsRecovering unknown causes from observed effects, typically ill-posed because many causes explain the same observations.Nonsmooth OptimizationOptimising objectives with kinks or discontinuous gradients, where classical descent assumptions fail and subgradients or specialised operators are needed.Proximal Gradient MethodsSplitting an objective into a smooth part handled by a gradient step and a nonsmooth part handled by a proximal operator, which has a closed form for common penalties.
Machine Learning
54Algorithms and Complexity7
Big-O Notation5 build on thisDescribing how resource use grows with input size, discarding constants and lower-order terms to expose scaling behaviour.Binary SearchLocating an element in a sorted sequence by repeatedly halving the search interval, achieving logarithmic time.Loop InvariantsA condition true before and after every iteration, used to prove a loop does what it claims.MemoizationCaching function results by their arguments so repeated calls return immediately, turning exponential recursion into polynomial work.Dynamic ProgrammingSolving problems by combining solutions to overlapping subproblems, storing each result once instead of recomputing it.Space-Time Tradeoffs3 build on thisSpending memory to save computation or vice versa — precompute and store, or recompute on demand.Merge Sort and QuicksortTwo divide-and-conquer sorts: merge sort splits evenly and merges, quicksort partitions around a pivot and recurses.
Causal Inference2
Data Structures5
Binary Tree Traversal4 build on thisVisiting every node in a defined order — pre-order, in-order or post-order — each suited to a different task.Bloom FiltersA probabilistic set membership structure that can say definitely-not-present or probably-present, using very little space.Hash FunctionsMapping arbitrary keys to fixed-size indexes, ideally spreading keys uniformly so collisions are rare.Balanced Trees and B-TreesSearch trees that maintain a height invariant so operations stay logarithmic, with B-trees widening nodes specifically to suit block storage.Heaps and Priority QueuesA partially ordered tree giving cheap access to the minimum or maximum element, used wherever you repeatedly need the next-best item.
Machine Learning Foundations18
Data Mining3 build on thisDiscovering patterns in large datasets at the intersection of machine learning, statistics and database systems.Decision Trees5 build on thisModels that recursively split the feature space on single-feature thresholds, producing rules readable end to end.Decision JunglesDecision forests whose trees are directed acyclic graphs rather than trees, letting paths merge and reducing memory.Random ForestsEnsembles of decorrelated decision trees, each trained on a bootstrap sample with a random feature subset, averaged for prediction.Gini and Information GainThe impurity criteria trees use to choose splits — Gini impurity and entropy-based information gain.Naive BayesA probabilistic classifier applying Bayes' rule under the assumption that features are conditionally independent given the class.Linear Regression8 build on thisFitting a linear relationship between predictors and a continuous outcome, the foundational model of applied statistics.Polynomial RegressionExtending linear models with powers of the predictors to fit curvature while remaining linear in parameters.Two-Class and Multiclass Classifiers8 build on thisBinary classification and its extensions to many classes, via one-vs-rest, one-vs-one or natively multiclass models.Logistic Regression4 build on thisModelling the log-odds of a binary outcome as a linear function of predictors, giving calibrated probabilities.Stock Price PredictionForecasting price movement from historical and alternative data — the canonical example of a low signal-to-noise problem.Support Vector MachinesClassifiers finding the hyperplane with maximum margin between classes, extended to nonlinear boundaries through kernels.Titanic and Iris Case StudiesThe canonical teaching datasets, small and clean enough to make a full modelling workflow visible end to end.Crop Disease DetectionIdentifying plant disease from leaf and field imagery, a widely studied agricultural computer vision application.K-Nearest NeighboursClassifying or predicting by looking at the k closest training examples — a method with no training phase and all the cost at prediction.Rare Event PredictionPredicting outcomes that occur very infrequently, where extreme class imbalance breaks default assumptions across the board.Rule-Based ClassifiersClassifiers expressed as explicit if-then rules, either handcrafted or induced from data.Churn PredictionEstimating which customers will stop using a product, so retention effort can be targeted before they leave.
Machine Unlearning7
Right to Be ForgottenThe legal right to have personal data erased, which extends to models trained on that data and not merely to databases.Utility Preservation3 build on thisKeeping a model useful after unlearning — the central tension between forgetting a record and degrading everything else.Approximate UnlearningEfficiently reducing a record's influence without full retraining, accepting bounded rather than absolute guarantees.Deletion RequestsThe operational process of receiving, validating, executing and evidencing a data removal request end to end.Exact UnlearningRemoving a record's influence so completely that the result is indistinguishable from having never trained on it.Federated UnlearningRemoving a participant's data influence from a federated model, without ever having had the raw data centrally.SISA Sharded TrainingSharded, isolated, sliced and aggregated training — partitioning data so each record touches only one shard's model.
Model Evaluation2
Regularization1
Reinforcement Learning3
Q-LearningLearning the value of taking an action in a state by bootstrapping from observed rewards, without needing a model of the environment.Bellman EquationsRecursive relations expressing a state's value in terms of immediate reward and the discounted value of successors.AlphaGo and MCTSMonte Carlo tree search guided by learned policy and value networks — the combination that beat top human Go players.
Unsupervised Learning5
DBSCAN and OPTICSDensity-based clustering that finds arbitrarily shaped clusters and labels sparse points as noise.Apriori Frequent ItemsetsFinding item combinations that co-occur above a support threshold, then deriving association rules from them.Hierarchical ClusteringBuilding a tree of nested clusters by successively merging or splitting, visualised as a dendrogram.Dimensionality Reduction and PCAProjecting data onto the directions of greatest variance, compressing many correlated features into a few components.K-Means ClusteringPartitioning data into k groups by alternately assigning points to the nearest centroid and recomputing centroids.
Feature Engineering4
Imbalanced DataThe general problem of skewed distributions in training data, across classes, slices or time periods.Feature StoresShared infrastructure computing, storing and serving features consistently for both training and inference.Feature SelectionChoosing which features to keep — by filtering, wrapping around a model, or embedding the choice in training.Class ImbalanceWhen one class vastly outnumbers others, so a model can score well by ignoring the minority entirely.
Deep Learning
55Backpropagation2
Deep Learning19
Keras and TensorFlowA high-level model-building API over a production-oriented deep learning runtime, emphasising concise layer composition and a managed training loop.Loss Function SelectionChoosing the objective that encodes what counts as a good prediction — squared error, absolute error, cross-entropy or a task-specific alternative.Perceptron and Decision BoundariesThe single-unit linear classifier and the hyperplane it induces — the historical starting point and the clearest illustration of linear separability's limits.Multi-Layer Perceptrons4 build on thisFully connected feedforward networks — the baseline architecture where every unit connects to every unit in the next layer.Forward Propagation19 build on thisComputing a network's output by passing inputs layer by layer through weights, biases and activations.Activation Functions5 build on thisThe nonlinearity applied after each layer's linear transformation.Softmax and LogitsLogits are the raw unnormalised scores a network produces; softmax exponentiates and normalises them into a probability distribution.AutoencodersNetworks trained to reconstruct their input through a narrow bottleneck, forcing a compressed representation that captures the essential structure.DropoutRandomly zeroing units during training so the network cannot rely on any single pathway, then using the full network at inference.Neural Tangent KernelIn the infinite-width limit, gradient descent on a network behaves like kernel regression with a fixed kernel determined at initialisation.Universal Approximation TheoremsResults showing that sufficiently wide networks can approximate any continuous function on a compact set to arbitrary accuracy.Vanishing GradientsGradients shrinking multiplicatively as they propagate backwards, so early layers receive almost no learning signal.Width vs DepthWhether to add units per layer or add layers — a tradeoff between representational efficiency and optimisation difficulty.ReLU and Dead NeuronsReLU passes positives unchanged and zeroes negatives.Sigmoid and TanhThe classic saturating activations, squashing inputs into a bounded range.Xavier InitializationSetting initial weight scale from layer fan-in and fan-out so activation and gradient variance stay roughly constant across layers.Barron SpacesA function class whose approximation by shallow networks escapes the curse of dimensionality, characterised by a Fourier-based smoothness condition.Kolmogorov-Arnold NetworksNetworks placing learnable activation functions on edges rather than fixed activations on nodes, inspired by the Kolmogorov-Arnold representation theorem.GELUA smooth activation that weights an input by the probability a standard normal falls below it, giving a soft rather than hard gate.
Natural Language Processing6
Speech Emotion RecognitionInferring emotional state from vocal characteristics — prosody, energy and spectral features — rather than words.Fake News DetectionIdentifying misleading or fabricated content from linguistic signals, source characteristics and propagation patterns.Sentiment Analysis4 build on thisClassifying the polarity or attitude expressed in text, the most widely deployed text classification task.Emotional Intelligence in NLPSystems that recognise and respond appropriately to affect, going beyond polarity to intent and emotional context.NLP for Mobility and TransportationApplying language processing in transport contexts — incident reports, passenger communication and operational text.Bi-Encoders and Cross-EncodersBi-encoders embed query and document separately for fast retrieval; cross-encoders score them jointly for accuracy.
Convolutional Networks8
Stride and PaddingStride is the step between filter applications; padding adds border values so filters can cover the edges.Pooling as a StatisticSummarising a local region with a single value — max or average — reducing resolution while retaining the presence of a feature.Convolution Arithmetic3 build on thisThe relationship between input size, kernel size, stride, padding and dilation that determines an output's spatial dimensions.Scattering TransformsA convolutional architecture with fixed wavelet filters rather than learned ones, whose stability and invariance properties can be proven in advance.Convolutional Layers4 build on thisLayers applying learned filters across a signal with shared weights, detecting the same local pattern wherever it appears.Receptive FieldsThe region of the input that influences a particular unit's activation, growing with each successive layer.CNN Visualization for InterpretationInspecting what a convolutional network has learned by visualising filters, activation maps and the input regions driving a prediction.Fourier Analysis of NetworksAnalysing what frequencies a network represents and learns, revealing systematic preferences in what it fits first.
Neural Network Architectures6
Encoder-DecoderAn architecture that compresses input into a representation and then generates output from it, separating understanding from production.LSTM Networks3 build on thisRecurrent networks with gated cells designed to carry information across long sequences without the gradient decay that plain RNNs suffer.LSTM Cell StateThe carried vector running through an LSTM across time steps, modified only by gentle gated operations.Layer NormalizationNormalising activations across features within a single example, independent of batch composition.CNN-LSTM HybridsStacking convolutional feature extraction under a recurrent layer, so spatial structure is captured first and temporal structure second.Stateful and Bidirectional LSTMsStateful variants carry state across batches for continuous sequences; bidirectional ones run two passes so each position sees both past and future.
Computer Vision1
Transformers8
Self-Attention from Scratch4 build on thisComputing queries, keys and values from the same sequence, scoring every position against every other, and mixing values by those scores.Causal Attention MaskingPreventing a position from attending to later positions by masking future scores before the softmax.Multi-Head AttentionRunning several attention operations in parallel on projected subspaces, then concatenating, so different heads can specialise.Positional Encoding4 build on thisInjecting order information into attention, which is otherwise permutation-invariant, through sinusoidal patterns, learned vectors or rotations.Cross-AttentionAttention where queries come from one sequence and keys and values from another, conditioning generation on separate content.RoPE Rotary EmbeddingsEncoding position by rotating query and key vectors by an angle proportional to position, so attention scores depend on relative distance.Feed-Forward Blocks3 build on thisThe position-wise multilayer perceptron applied after attention in each transformer layer, typically expanding then contracting the dimension.GPT ArchitectureA decoder-only transformer trained autoregressively — stacked masked self-attention and feed-forward blocks with normalisation and residuals.
Multimodal AI5
Cross-Modal FusionCombining representations from different modalities into a joint one the model can reason over.Diffusion Image GenerationProducing images by iteratively denoising from random noise, conditioned on a text prompt.Vision Encoders3 build on thisComponents turning images into embeddings a language model can consume, usually a pretrained vision transformer plus a projection.Modality-Specific PipelinesSeparate ingestion and processing paths per modality before any fusion, because video, text and sensor data need different handling.TrOCR and OCRConverting images of text into machine-readable characters, now commonly with transformer-based encoder-decoder models.
LLMs and Generative AI
83Large Language Models11
Tokenization10 build on thisSplitting text into the discrete units a model actually processes.Temperature and Sampling3 build on thisDecoding controls that shape how the next token is drawn from the predicted distribution — temperature, top-k and top-p.Byte-Pair EncodingBuilding a vocabulary by repeatedly merging the most frequent adjacent pair, yielding subword units that cover any input without unknown tokens.Token IDs and Special TokensTokens map to integer IDs, alongside reserved markers for padding, sequence boundaries, roles and other control functions.Context WindowThe maximum number of tokens a model can attend to at once — its entire working memory for a given call.Multi-Token DecodingGenerating more than one token per forward pass — speculative decoding and related methods — to reduce the sequential bottleneck.Sliding Window SamplingGenerating training examples by moving a fixed-size window across a corpus, with stride controlling overlap between consecutive samples.Quality-Cost-Latency TradeoffThe three-way tension in model selection, where improving one dimension typically costs another.LLM NondeterminismThe same prompt can yield different outputs, because sampling is stochastic and even greedy decoding is affected by batching and hardware nondeterminism.Foundation Models7 build on thisLarge models pretrained broadly enough to adapt to many downstream tasks, serving as a shared base rather than a task-specific artifact.Reasoning ModelsModels trained to produce extended intermediate reasoning before answering, trading latency and tokens for accuracy on hard problems.
Fine-Tuning12
Cross-Lingual TransferCapability learned in one language carrying over to another, exploiting shared multilingual representations.LoRA and QLoRATraining small low-rank matrices alongside frozen base weights, with QLoRA additionally quantising the base to fit larger models on modest hardware.Pre-Trained Model Adaptation13 build on thisThe general practice of taking an existing trained model and adjusting it for a new task or domain rather than training from scratch.Classification Fine-TuningAdapting a language model for label prediction by attaching a classification head and training on labelled examples.Catastrophic ForgettingLosing previously acquired general capability while training on new narrow data — the central risk of domain adaptation.Continued Pre-TrainingExtending pretraining on domain-specific corpora before any task tuning, to inject vocabulary and knowledge a base model lacks.Instruction Tuning7 build on thisFine-tuning on instruction-response pairs so a model follows directions rather than merely continuing text.Multi-Tenant Adapter ServingServing many customers from one base model by loading their individual adapters on demand.PEFTParameter-efficient fine-tuning: the family of methods that adapt a model by training a small number of added or selected parameters.QLoRA for FinanceApplying quantised low-rank adaptation to financial models, where domain vocabulary matters and data cannot leave controlled environments.Chat Format TemplatesThe role-tagged structure — system, user, assistant — that conversational models were trained to expect.The Steering TestA decision heuristic: if you can get the behaviour you need by steering with prompts, context or retrieval, you do not need to fine-tune.
Inference Optimization6
Test-Time ComputeSpending more computation during inference — sampling multiple answers, searching, or extended reasoning — to improve output quality.QuantizationRepresenting weights and activations at lower numerical precision to cut memory and often latency, with modest and measurable quality loss.Latency and SpeedupsReducing perceived and actual response time through caching, batching, streaming and decoding strategy.Knowledge DistillationTraining a small student model to reproduce a large teacher's outputs, transferring capability into a cheaper package.Local Model DeploymentRunning models on your own hardware rather than calling an API, for privacy, cost predictability or offline operation.Edge and Air-Gapped InferenceServing models on devices or in isolated networks with no external connectivity, under strict compute and update constraints.
LLM Evaluation21
Answer Relevancy and CorrectnessDistinguishing whether an answer addresses the question from whether what it says is true — two separate failures.Evaluation Datasets18 build on thisCurated sets of inputs with expected properties or outputs, forming the fixed reference against which changes are compared.Benchmarking4 build on thisComparing models on standardised task suites to get a common frame of reference.BLEU and Reference MetricsAutomatic metrics comparing generated text to reference answers by n-gram overlap.Deterministic ValidatorsProgrammatic checks — schema validity, format, forbidden content, numerical bounds — that give unambiguous pass or fail signals.Gold and Adversarial SetsGold sets capture correct expected behaviour; adversarial sets deliberately probe for failure.Minimum Evaluable ProductBuilding the smallest version that can be measured, rather than the smallest that can be demonstrated.Offline vs Online EvaluationOffline evaluation runs against fixed datasets before release; online evaluation measures real traffic after it.Promptfoo and LightEvalOpen-source harnesses for running structured evaluations over prompts and models with reproducible configuration.Regression GatesAutomated thresholds in the release pipeline that block a deployment when evaluation metrics degrade.Repeatability Under StochasticityGetting stable measurements from a system that returns different outputs each run, through repetition and variance control.Synthetic Eval DataGenerating test cases with models to reach coverage that manual authoring cannot, with careful validation.LLM as Judge3 build on thisUsing a model to score another model's output against a rubric, making open-ended evaluation scalable.LLM Safety BenchmarksStandardised suites probing harmful, unsafe or policy-violating behaviour, often paired with guard models that classify inputs and outputs.ROUGE and Human EvalRecall-oriented overlap metrics for summarisation, paired with human review as the ground truth they approximate.Training-Time vs Inference-Time EvaluationEvaluating during training to guide model development, versus evaluating live behaviour on real traffic.Skill Testing and EvalsApplying evaluation discipline to reusable agent skills, checking they behave correctly across intended cases.Evals GapThe widespread pattern of shipping LLM applications with no real measurement discipline, so quality regressions go unnoticed.Evaluator DriftThe evaluation apparatus itself changing over time — judge model updates, rubric edits, annotator turnover — invalidating comparisons.Four-Axis Quality, Safety, Cost and ReliabilityDefining what working means in production across four dimensions rather than a single quality score.Slice-Based CoverageEvaluating on meaningful subsets — language, customer type, query category — rather than only on the aggregate.
Prompt Engineering5
Structured Output ConstraintsForcing generation to conform to a schema through grammar-constrained decoding or validated function calls.Context PacksCurated bundles of the context an agent or prompt needs for a task — specifications, examples, conventions — assembled deliberately.Prompt Iteration3 build on thisRefining a prompt through cycles of change and measurement rather than intuition.Prompt OptimizationAutomatically improving a prompt against measurable criteria, using data rather than manual editing.Prompt Registry and VersioningStoring prompts as versioned artifacts with aliases, history and controlled promotion, the same way code is managed.
Retrieval-Augmented Generation13
Retrieval QualityMeasuring the retrieval stage independently of generation, so you know which half of a RAG system is failing.ChunkingSplitting documents into retrievable units.Context Precision and RecallRetrieval metrics for RAG: precision measures how much retrieved context was relevant, recall whether the needed context was retrieved at all.Vector Native StorageStorage designed around embeddings as a first-class type, with indexes, filters and hybrid scoring built in rather than bolted on.GraphRAGRetrieval over a knowledge graph of entities and relationships, so answers can follow connections rather than only match text.Multi-Document Retrieval3 build on thisAssembling evidence from several sources for a single answer, including deduplication and ordering of the retrieved set.Vector SearchFinding the nearest embeddings to a query vector, using approximate algorithms to keep the search fast at scale.Citations and EvidenceRequiring generated claims to point at the retrieved passages supporting them, making answers checkable.Hybrid and Semantic SearchCombining lexical keyword matching with dense vector similarity so exact terms and semantic meaning both contribute to ranking.Admissible Evidence SpansRestricting answers to specific verified passages that may legitimately be cited, common in regulated and legal settings.Enterprise Knowledge AssistantsAssistants grounded in an organisation's own documents, requiring permission-aware retrieval and honest handling of gaps.RerankingRe-scoring an initial candidate set with a more expensive, more accurate model before passing results to the generator.Agentic RetrievalLetting the model decide what to retrieve, evaluate whether it sufficed, and search again — retrieval as a loop rather than a single step.
Hallucination Mitigation4
Content Moderation GuardrailsLayered checks on inputs and outputs that block, filter or redirect unsafe content before it reaches a user or an action.Object HallucinationDescribing entities that are not present in a provided image — the most studied multimodal grounding failure.Multimodal Grounding FailuresThe general class of outputs making claims the supplied non-text evidence does not support.Cross-Modal DriftProducing output plausible for the training distribution generally, but not for this particular input.
Post-Training Alignment11
Supervised Fine-TuningTraining on curated demonstrations of desired behaviour — the first and most important stage of post-training.Synthetic Data Generation3 build on thisUsing models to produce training data — instructions, preferences, self-play trajectories — where human annotation is too slow or costly.On-Policy vs Off-PolicyWhether training data comes from the current policy's own outputs or from a different, earlier or external source.Preference Data Collection4 build on thisGathering human comparisons between model outputs — the annotation process that determines everything downstream in alignment.Bradley-Terry ModelA statistical model turning pairwise comparisons into latent scalar scores, the standard bridge from preferences to a reward function.Reward Modeling4 build on thisTraining a model to predict human preference, producing a scalar signal that stands in for human judgement during optimisation.Alignment Case StudyA worked end-to-end alignment example — collect preferences, train a reward model, optimise the policy, then evaluate the result honestly.Direct Preference OptimizationOptimising directly on preference pairs without training a separate reward model, using a loss derived from the RLHF objective.GRPOGroup relative policy optimisation, which scores a group of sampled responses against each other rather than against a learned value function.Reward HackingA policy maximising the reward signal in ways that do not reflect genuine quality — exploiting the proxy rather than satisfying the intent.ORPO and Preference OptimizationThe family of methods aligning models directly from preferences, with ORPO folding preference optimisation into a single supervised stage.
AI Agents
18AI Agents11
Agent Loop7 build on thisThe cycle at the heart of every agent: receive context, decide an action, execute it, observe the result, repeat until done.SubagentsDelegating a scoped task to a separate agent with its own context, returning only the result to the parent.Agent ExecutorsThe runtime that drives the agent loop — dispatching tool calls, managing state, enforcing limits and handling errors.Agent Communication Protocols3 build on thisStandards for agents to exchange messages, delegate tasks and share results across systems and vendors.Agent Memory SystemsThe stores an agent reads and writes across turns — working context, episodic history, semantic facts and procedural skills.Agent CardsMachine-readable descriptions of an agent's identity, capabilities and interfaces, so other agents can discover and invoke it.Escalation WorkflowsDefined paths for handing a case to a human or a higher-authority process when confidence, risk or policy demands it.Conversation StateWhat the system remembers and re-sends across turns — history, summaries, extracted facts and pending actions.Analyst AgentsAgents built for research and analysis workflows — gathering sources, extracting evidence, synthesising and citing.Routing and Expert SpecializationDirecting each request to the most appropriate model, tool or specialised agent rather than sending everything to one endpoint.Conversational AgentsDialogue systems maintaining coherent multi-turn interaction, tracking state and intent across a conversation.
Model Context Protocol1
AI Coding Assistants6
Skill Design and ScopingDeciding what a skill covers and where it stops, which is the main craft in making one useful.Agentic Test AuthoringUsing agents to generate, maintain and repair test suites, driven from the application under test.No-Code Model BuildingBuilding and deploying models through visual interfaces without writing code, lowering the barrier to first results.Claude SkillsPackaged, reusable instructions that turn repeatable work into something invokable rather than re-explained each time.Agent Instruction FilesPersistent repository files giving a coding agent standing context — conventions, architecture, commands, constraints.Business Workflow IntegrationConnecting agents and skills into real business systems — CRM, ticketing, calendars, finance — where the work actually lives.
Data Engineering and Analytics
27Data Visualization2
Data Governance2
Regulatory Compliance ControlsTechnical and procedural controls implementing regulatory obligations — retention, access, audit trails, approvals and evidence.Unity Catalog GovernanceA governance layer over a lakehouse providing centralised access control, lineage and discovery across data and models.
Data Engineering9
Point-in-Time DataReconstructing exactly what was known at a given moment, so models are never trained on information from the future.Streaming IngestionContinuously accepting events as they arrive, with buffering, ordering and backpressure handling.Text Mining at ScaleExtracting structure from large document collections, where scalability rather than accuracy is the binding constraint.Entity ResolutionDetermining when different records refer to the same real-world entity, across systems with no shared identifier.Semantic LayerA shared definition layer giving business meaning to raw data, so metrics mean the same thing everywhere.Data ContractsExplicit agreements between data producers and consumers covering schema, semantics, quality and change process.Data Fabric and MeshTwo architectural responses to scale: fabric unifies access through metadata and automation, mesh decentralises ownership to domain teams.Parquet and Flat-File HygienePractices for durable file-based data — columnar formats, schema evolution, partitioning and predictable naming.Continuous Learning LoopsPipelines feeding production outcomes back into retraining, so models improve from their own deployment.
Data Quality14
Handling Missing DataDeciding what to do about absent values — drop, impute, or model the missingness itself.Outlier HandlingIdentifying extreme values and deciding whether they are errors to remove or genuine observations to keep.Data Cleaning7 build on thisCorrecting or removing inaccurate, malformed and inconsistent records so downstream analysis rests on sound data.Data Literacy3 build on thisThe ability to read, interpret, question and communicate with data accurately and responsibly.Data TransformationReshaping data into the form analysis requires — type conversion, normalisation, encoding, aggregation and pivoting.Unstructured DataText, image, audio and video content lacking a predefined schema, which now dominates data volume.Null and Duplicate HandlingManaging absent values and repeated records, the two most common structural defects in real datasets.Found DataData generated for another purpose and repurposed for analysis, as opposed to data collected by design.Data DictionariesDocumentation defining each field's meaning, type, units, valid values and provenance.Unicode and Encoding PitfallsText failures caused by encoding mismatches, normalisation differences and the gap between bytes, code points and graphemes.Data Validation ConstraintsExplicit rules a dataset must satisfy — types, ranges, uniqueness, referential integrity — enforced automatically.Regular Expression ConstraintsValidating that string fields conform to expected patterns — identifiers, codes, dates, formatted values.Constraint GenerationAutomatically discovering constraints from existing data, then enforcing them on future data.Roll-Up ConstraintsRules asserting that aggregates reconcile — that details sum to totals across hierarchies.
MLOps and Platform
23Self-Hosting9
Portainer ManagementA web interface for managing Docker environments — containers, images, volumes, networks and logs.Docker ComposeDeclaring a multi-container application in one file — services, networks, volumes and dependencies — and running it with a single command.Container Orchestration BasicsManaging container lifecycle across restarts and hosts — scheduling, health checks, restart policies and service discovery.Backup and Hardware FailurePlanning for disks and machines failing — backup strategy, offsite copies and tested restoration.Data Ownership and PrivacyKeeping data under your own control rather than a third party's, the primary motivation for self-hosting.LTS Distribution ChoiceChoosing a long-term-support Linux release so security updates continue for years without forced upgrades.Reverse Proxy and TLSFronting internal services with a proxy that terminates TLS, routes by hostname and issues certificates automatically.WSL and VM SetupRunning Linux inside Windows or macOS through a subsystem or virtual machine, to get a Linux host without dedicated hardware.Tailscale Mesh NetworkingA peer-to-peer VPN creating a private network across devices without exposing services publicly or configuring firewalls.
MLOps13
Model Serving APIsThe HTTP or RPC surface exposing a model, including schema validation, health checks and versioned endpoints.Model Registry and VersioningA catalogue of trained models with versions, stages, aliases and lineage, making promotion an explicit auditable act.Tall Array ComputationApplying familiar array operations to data larger than memory, with execution deferred and performed in chunks.Canary ReleasesRouting a small traffic share to a new version, comparing metrics, and expanding only if it holds up.MLflow TracingRecording the full execution of a generative request — prompts, retrievals, tool calls, outputs and timings — as an inspectable trace.Azure ML StudioA cloud workspace for building, training and deploying models with both visual and code-based authoring.Code Generation for DeploymentCompiling models or analytical code into standalone artifacts — C, ONNX or similar — for embedded or restricted environments.Drift DetectionMonitoring for changes in input distribution, prediction distribution or the input-output relationship over time.Training-Serving SkewDivergence between the transformations applied during training and those applied in production, producing silent quality loss.Trace-First DevelopmentInstrumenting before optimising, so every iteration is guided by observed behaviour rather than assumption.Production Feedback LoopsChannelling real usage signals — corrections, ratings, downstream outcomes — back into evaluation sets and training data.Release and Rollback SafetyMaking deployments reversible — versioned artifacts, staged rollout and a rehearsed path back to the previous state.Human-in-the-Loop FeedbackDesigned points where a person reviews, corrects or approves system output, feeding judgement back into the system.
Software Engineering
35Software Testing16
Accessibility TestingVerifying software works with assistive technology and meets standards for contrast, structure and keyboard operation.Equivalence Partitioning3 build on thisDividing inputs into classes expected to behave identically, then testing one representative from each.Playwright and SeleniumBrowser automation frameworks that drive a real browser to exercise an application as a user would.Boundary Value AnalysisTesting at the edges of input ranges, where off-by-one and comparison errors concentrate.Errors of Process vs InterpretationTwo distinct failure classes: the analysis did not do what you intended, or it did and you drew the wrong conclusion.Reference TestingPinning an entire output against a stored reference so any unintended change fails loudly.Visual Regression TestingComparing rendered screenshots against approved baselines to catch unintended visual change.Test Planning7 build on thisDeciding what to test, at which level and to what depth, given risk and available effort.API TestingTesting service interfaces directly — contracts, status codes, payloads, error handling and authorisation.Exploratory Testing FrameworksStructured approaches to unscripted testing — charters, tours and heuristics — that make exploration systematic rather than random.Pairwise TestingCovering all pairs of parameter values rather than all combinations, on the evidence that most defects involve at most two factors.Security TestingActively probing an application for vulnerabilities — injection, broken authorisation, exposed secrets and vulnerable dependencies.Shift-Left TestingMoving testing earlier in the lifecycle so defects are found when they are cheap to fix.Property-Based TestingAsserting properties that must hold for all inputs and letting the framework generate cases, including shrinking failures to minimal examples.Contract TestingVerifying that a provider and consumer agree on their interface, without running both together end to end.Frontend Performance TestingMeasuring what users actually experience — load, interactivity and visual stability — rather than server response time.
Software Architecture11
Layered ArchitectureOrganising a system into presentation, application, domain and infrastructure layers with a strict dependency direction.Ports and AdaptersPorts are interfaces the core defines for what it needs; adapters are the outside implementations that satisfy them.Single ResponsibilityA module should have one reason to change, keeping its purpose narrow enough to state in a sentence.The IlitiesThe non-functional qualities architecture actually trades between — maintainability, testability, scalability, reliability, observability.Database as Architectural PillarTreating the data store as a first-class architectural decision — its model, guarantees and access patterns shape everything above it.Dependency InversionDepending on abstractions rather than concrete implementations, so high-level policy does not depend on low-level detail.Microservice Cost TradeoffsWeighing independent deployability and scaling against the distributed-system complexity that services introduce.Separation of ConcernsKeeping distinct responsibilities in distinct places, so a change to one concern touches one region of code.Cohesion and CouplingCohesion is how related a module's contents are; coupling is how dependent modules are on each other.Hexagonal ArchitecturePlacing domain logic at the centre with all external interaction through ports implemented by adapters, so the core depends on nothing outside itself.REST and GraphQLTwo API styles: REST exposes resources over HTTP verbs, GraphQL exposes a schema clients query for exactly what they need.
Spec-Driven Development8
Product Requirements Documents5 build on thisA structured statement of what a product must do and for whom, from which technical design and tasks derive.Acceptance CriteriaTestable conditions defining when a requirement is satisfied, written before implementation begins.Engineering Intent DocumentsA short artifact capturing the build direction between a raw idea and a formal specification — problem, users, goals, constraints.Task CardsSmall self-contained work items derived from a specification, each carrying enough context for an agent or person to execute independently.Requirements TraceabilityMaintaining links from each requirement through design, tasks, tests and code, so coverage and impact are visible.Spec-to-Code PipelineThe controlled path from specification through tasks and tests to implementation, with agents doing generation and humans gating transitions.Review GatesExplicit checkpoints where work must be approved before advancing, with defined criteria and an accountable reviewer.Spec DriftImplementation gradually diverging from the specification, so the document stops describing the system.
Security and Privacy
15Privacy Engineering1
AI Security13
Adversarial ExamplesInputs perturbed almost imperceptibly to a human that cause confident misclassification.Data PoisoningCorrupting training data to implant a backdoor or degrade a model, attacking the pipeline rather than the deployed system.Intrusion DetectionIdentifying malicious activity in networks or hosts through signatures, anomalies or learned models of normal behaviour.MITRE ATLASA knowledge base of adversary tactics and techniques specific to AI systems, structured like ATT&CK.Adversarial PatchesPhysical or localised patterns that reliably fool a vision system regardless of where they appear in the scene.Liveness DetectionVerifying that biometric input comes from a live person rather than a photo, replay or synthetic generation.Membership InferenceDetermining whether a specific record was in a model's training set, from the model's behaviour alone.Gradient ObfuscationDefences that hide or break gradients, appearing to stop attacks while leaving the model fundamentally exploitable.Red and Purple TeamingAdversarial testing by a red team, and collaborative testing where red and blue teams work openly together.Carlini-Wagner AttackA strong optimisation-based attack that finds minimal perturbations causing misclassification, used as a benchmark for defences.Model ExtractionReconstructing a proprietary model's behaviour by querying it systematically and training a substitute on the responses.Prompt InjectionUntrusted content instructing a model to ignore its original directions, treating data in the context as if it were commands.OWASP LLM Top 10A consensus list of the most critical security risks in LLM applications, from prompt injection to excessive agency.
Applied Domains
9Biomedical Data Science1
AI in Finance8
Cash Flow Management3 build on thisManaging the timing of money in and out, which determines survival independently of reported profit.Balance SheetsThe statement of assets, liabilities and equity at a point in time — the structural snapshot of financial position.Financial Numerical ReasoningPerforming calculation and quantitative reasoning over financial documents, where language models are notably weak.Backtesting LLM StrategiesEvaluating model-driven financial strategies against historical data, under strict controls against lookahead.Market RiskThe risk of loss from movements in prices, rates, spreads, currencies or volatility.Financial SentimentClassifying sentiment in financial text, where domain conventions differ sharply from general sentiment.Earnings Call AnalysisExtracting signal from earnings call transcripts — guidance, tone, evasion and deviation from prepared remarks.FinBERT and BloombergGPTDomain-specific financial language models, trained or adapted on financial text where general models mishandle the vocabulary.
Trust, Governance and Ethics
7Fairness and Bias5
Black-Box vs White-Box AssessmentAssessing from outputs alone versus with full access to weights, data and training process.Perturbation RobustnessMeasuring how much a system's output changes when inputs are varied in ways that should not matter.Trust Rating ScalesExpressing an assessment of a system's trustworthiness as a comparable graded score.Protected AttributesCharacteristics such as race, gender, age or disability that law and ethics restrict from driving decisions.Sentiment and Emotion BiasSystematic differences in how sentiment and emotion models score text associated with different groups.
Business, Career and Human Factors
22Entrepreneurship9
SWOT AnalysisA diagnostic framework listing strengths, weaknesses, opportunities and threats to structure strategic assessment.Business Plan WritingDocumenting the opportunity, model, market, operations and financials — as much a thinking discipline as a document.Business Model Design4 build on thisDefining how a venture creates, delivers and captures value — customers, offer, channels, cost structure and revenue.Exit and SellingTransferring ownership through sale, succession or closure, and preparing the business so it is transferable at all.FranchisingLicensing a proven business format to operators who invest their own capital and run local units under the brand.Startup FinancingFunding a venture through bootstrapping, debt, equity or grants, each with different control and risk implications.Business AcquisitionBuying an existing business rather than starting one, acquiring its customers, cash flow and operations directly.CrowdfundingRaising capital from many small contributors, whether as pre-orders, donations or equity.Family Business SuccessionTransferring leadership and ownership across generations, balancing family relationships against business needs.
Talent Management12
Behaviourally Anchored Rating ScalesRating scales where each point is defined by a concrete behavioural example rather than an abstract label.Organizational AmbidexterityRunning exploitation of the current business and exploration of new ones simultaneously without either starving.Talent AssessmentMeasuring capability and potential through psychometrics, competency evaluation and structured judgement.Competency FrameworksStructured definitions of the observable capabilities a role requires, used for assessment and development.Dynamic CapabilitiesAn organisation's ability to sense change, seize opportunity and reconfigure its resources accordingly.Psychometrics and TraitsStandardised measurement of stable individual differences, commonly along five broad personality dimensions.VRIO ModelA framework assessing whether a resource is valuable, rare, inimitable and organisationally exploited — the test for sustained advantage.Learning AgilityThe willingness and ability to learn from experience and apply the lessons in unfamiliar situations.Succession PlanningIdentifying and preparing candidates for critical roles before those roles become vacant.Adaptive ExpertiseThe capacity to apply deep knowledge flexibly to novel situations, as distinct from efficient routine performance.Career AdaptabilityThe resources that let people navigate transitions — concern for the future, control, curiosity and confidence.Workplace CoachingA collaborative, reflective, goal-focused relationship intended to unlock performance rather than instruct.
Sign in — the practice questions and tutor are mine, not the reader’s. Everything above is free to read.
The map
How far in I am
The pages above are written; this is the part that is learned. One square per concept, and it fills in only when something is answered and marked — reading moves nothing, so most of this stays dim until the work is done. It is my record, not a score you need.
1 in progress424 written
How this was made
Machines wrote this. I am the one learning it.
I have not read my way through this material.A language model worked through my reading list and produced the notes behind this map — 12 domains, 60 modules, 425concepts — organised by what rests on what.
DeepSeek wrote the 425 concept pages, one at a time, each with the relevant notes in front of it. So the explanations follow the framing of my own reading rather than a generic account, but the sentences are the model’s, not mine, and not any author’s. It also writes the practice questions and answers when I ask the tutor something.
A model on my own hardware rewrote the explanations. The first drafts were written for someone who already had the mathematics. They were not — that is the whole premise — so a second model, running on a machine under my desk, went back over them against a plainer brief: no computer science, no mathematics past school arithmetic, every term explained where it is first used. It rewrote the prose on 358 pages. The mathematics and code sections are still as DeepSeek first wrote them.
The order came last.Nothing knew what rested on what until a model read every page and worked out the dependencies — 552 of them. That is what arranges the index now, and what fills the “Rests on” list beside each concept.
Claude built the system— the database, the scoring, this page — and wrote a handful of question banks DeepSeek could not manage.
None of it has been fact-checked by an expert. Generated text is confidently wrong sometimes, and I am not yet able to catch every instance — that is rather the point of the exercise. Read it as one person’s study notes, not as a textbook. Where a page matters to you, check it against a source that had a human editor.
If you are reading this
How you can use it
You are welcome to all of it. Nothing below asks you for anything.
All of it is free to read
Every one of the 425 concept pages, the index, and the prerequisite graph. No account, no sign-up, no paywall — there is nothing here to join. Reading costs you nothing and costs me nothing, which is why it can stay open.
Follow the order, not the alphabet
Inside a module, concepts are listed so that each one comes after whatever it depends on. Where several concepts build on the same idea it is marked — those are the ones worth slowing down for, because getting one wrong makes every page after it harder. If a page still assumes something you do not have, its “Rests on” list at the side is where to go first.
Start where nothing is owed
Forty-three concepts rest on nothing at all, and the filter above the index will show you only those. Any of them can be read today without preparation, and everything else is reachable from them.
Take it as study notes, not a textbook
No expert has checked any of it. If a page matters to your work, verify it against something that had a human editor before you rely on it.
The practice side is mine
You can read everything; answering, marking and the tutor are not open. That is not a paywall — it is one person’s learning record, and someone else’s score would mean nothing in it.
The method
How I work through it
Rules the system enforces on me, not intentions. Each one is a constraint in the code rather than a promise.
Reading never counts
Opening a page moves nothing. A score changes only when I answer something and it is marked. Time spent is not progress, and the number on this page will not flatter me for scrolling.
Four kinds of evidence
Explain it, calculate it, code it, apply it. Each is scored separately and all four have to hold. Being fluent in the mathematics and unable to say what it is for is not knowing the thing.
Hints cost credit
Every question carries three: a nudge, then the method, then the full solution. Taking them is encouraged and it lowers what the answer is worth — 90%, then 75%, then 40%. A score that ignored help received would be measuring my patience, not my understanding.
Nothing is locked, yet
Every concept now knows what it rests on — 552 dependencies, worked out from the notes themselves. For now that only orders the index: no page is shut. Gating one behind a score would need scores to exist, and I have barely started answering. The graph says where to begin; it does not yet stand in the way.
It comes back
Anything I do not revisit decays and returns on a schedule — one day, three, a week, a fortnight, a month, a quarter — and sooner if I keep getting it wrong. Forgetting is the default; the schedule is the only thing that argues with it.
