The interactive masterclass
Signals to learning.
Understand the wave. Choose a representation. Build a model. Know what the result can—and cannot—tell you.
40 lessons · 10 modules · 4 integration projects. Start with arithmetic and curiosity; finish with the tools to investigate modern sequence models and computational claims. No account or installation needed for the browser lessons.
Your path
Each lesson follows understand → predict → experiment → check → apply. Short numerical checks have explanatory feedback; practical tasks have solutions or review rubrics. You can skip ahead using prerequisites, or follow the complete sequence.
Signal processing →
From waves and sampling to spectra, filters and a denoising investigation.
20 lessons · prerequisites included
Machine learning →
From vectors and gradients to neural networks and an honestly evaluated signal classifier.
23 lessons · prerequisites included
Sequence models & research →
Build the foundations for attention, rotary position, state-space memory and reproducible research claims.
32 lessons · prerequisites included
The complete journey →
All ten modules, including four integration projects, in prerequisite-first order.
40 lessons · prerequisites included
Most lessons suggest 15–35 minutes; projects suggest 75–90 minutes. Budget additional time for experimentation and implementation. Estimates are guidance, not measured completion times.
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Module 1 · Beginner
Read the signal
Begin with quantities you can draw and measure. Build the language that later becomes spectra, features and model scores.
Module 2 · Beginner
Maths for experiments
Learn the small amount of calculus, probability and experimental discipline needed to make reliable claims.
- Slopes and gradientsHow do you decide which way to change a parameter?
- Probability and uncertaintyHow should several plausible outcomes share one unit of probability?
- Noise and signal-to-noise ratioHow much unwanted variation is in a measurement?
- Data splits and leakageWhen is a good test score too good to be true?
Module 3 · Beginner
From time to samples
See what survives—and what becomes ambiguous—when time and amplitude become discrete.
Module 4 · Intermediate
Change coordinates
Turn samples into interpretable frequency coordinates while keeping finite-record limitations in view.
Module 5 · Intermediate
Build systems
Understand the operators that transform signals—and the boundary, phase and stability choices that make them work.
- Linearity and time invarianceWhen can one impulse response describe a whole system?
- Convolution step by stepWhich input samples contribute to one output?
- Frequency response and filter trade-offsWhy does averaging suppress some frequencies more than others?
- Recurrence and stabilityWhen does yesterday’s state fade, persist or explode?
Module 6 · Intermediate
Learn from data
Turn representations into predictions. Follow the objective, the update and the evidence—not just a fitted curve.
- Features and linear regressionWhat exactly does a model learn from examples?
- Gradient descentHow can a repeated local update find better parameters?
- Classification and cross-entropyWhy penalise a confidently wrong prediction so strongly?
- Evaluation and generalisationWhich mistakes does a single accuracy score hide?
Module 7 · Intermediate
Neural building blocks
Connect nonlinear representations to gradients, shared filters and responsible model selection.
- Nonlinear features and neural networksWhat does adding a hidden layer actually add?
- The chain rule and backpropagationHow does one weight receive credit for a distant error?
- Convolutions in neural networksHow does one learned filter scan an entire representation?
- Regularisation and model selectionHow can a better training fit make a worse model?
Module 8 · Advanced
Learn sequences
Follow content, position, weighted retrieval and recurrent state into modern sequence models, without mistaking a toy illustration for a trained architecture.
- Position and representationHow can a model distinguish the same content in different places?
- Attention as weighted retrievalHow can a query choose which information to combine?
- Rotary positionWhy does a shared position shift disappear from a rotary score?
- State-space memoryWhen is a recurrence also a convolution?
Module 9 · Advanced
Make it reliable and fast
Connect model mathematics to bandwidth, arithmetic, memory traffic and reproducible measurements.
- Nonlinear aliasingCan a cleanly sampled signal create aliases later?
- FFTs and memory trafficWhy can fewer arithmetic operations still run slower?
- Numerical stabilityCan the same exact formula behave differently on a machine?
- Benchmarking and reproducibilityWhat evidence supports a claim that an implementation is faster?
Module 10 · Project
Integrate and investigate
Combine representations, computation and evidence. Each project has a runnable starting point or a concrete investigation protocol and an honest assessment rubric.
- Project: a denoising pipelineCan you reduce interference without hiding signal distortion?
- Project: a leakage-safe classifierCan your feature choice survive a truly held-out evaluation?
- Project: a sequence-model investigationWhich sequence mechanism suits the dependency you need?
- Project: read and reproduce a research claimWhat would convince you that a result is both correct and useful?
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