# Signals to learning: curriculum and implementation specification

Research and planning review: 3 October 2026. This is a bounded, substantial first masterclass, not a claim to replace a DSP degree or cover every branch of ML. It connects signal processing, mathematics, statistical learning, sequence representations and computational practice. The existing nine essays and nine labs remain available as deeper reading and are incorporated rather than replaced.

## Audience and learning contract

Start with basic arithmetic and reading a graph; introduce algebra, trigonometry, vectors, complex numbers, derivatives and probability when needed. No installation or programming is necessary for the browser lessons. Optional implementation tasks use a notebook or editor; their reference solutions do not constitute a browser code runner. Advanced modules assume earlier objectives, with explicit prerequisite links and open navigation rather than locked gates.

Each of the 40 lessons must include: a motivating question; two observable objectives; plain-language explanation with defined symbols; a worked example; a misconception; an interactive experiment with a prediction and a specific task; two retrieval checks with corrective explanations; a practical transfer task and a disclosed solution/rubric; sources; previous/next links. Capstones combine earlier skills and use richer rubrics. Estimated lesson times are guidance, not measured learning rates. Completion records successful checks and self-confirmed practical work, not certified mastery.

## Course map

| Module | Lessons in prerequisite order | Demonstrable outcome |
| --- | --- | --- |
| 1. Read the signal | What is a signal?; Frequency, amplitude and phase; Vectors and similarity; Complex numbers and rotation | Interpret axes and units, synthesise a sinusoid, compute a dot product and rotate a vector. |
| 2. Maths for experiments | Slopes and gradients; Probability and uncertainty; Noise and signal-to-noise ratio; Data splits and leakage | Differentiate a simple loss, normalise probabilities, calculate power ratios and design a leakage-safe split. |
| 3. From time to samples | Sampling and time; Aliasing and Nyquist; Quantisation and clipping; Resampling safely | Convert indices into seconds, explain indistinguishable samples, distinguish amplitude/time discretisation and filter before downsampling. |
| 4. Change coordinates | Projection onto waves; The discrete Fourier transform; Windows and leakage; Time-frequency analysis | Calculate Fourier coefficients, map bins to Hz, distinguish resolution from grid density and select an STFT window/hop. |
| 5. Build systems | Linearity and time invariance; Convolution step by step; Frequency response and filter trade-offs; Recurrence and stability | Check superposition/shift behaviour, calculate boundary terms, read response curves and reason about poles. |
| 6. Learn from data | Features and linear regression; Gradient descent; Classification and cross-entropy; Evaluation and generalisation | Define a supervised objective, follow updates, calculate probabilities/loss and choose appropriate held-out metrics. |
| 7. Neural building blocks | Nonlinear features and neural networks; The chain rule and backpropagation; Convolutions in neural networks; Regularisation and model selection | Explain why activations matter, verify a gradient, calculate CNN shapes and select models without test leakage. |
| 8. Learn sequences | Position and representation; Attention as weighted retrieval; Rotary position; State-space memory | Separate content from position, calculate attention, demonstrate relative rotation and unroll a fixed recurrence. |
| 9. Make it reliable and fast | Nonlinear aliasing; FFTs and memory traffic; Numerical stability; Benchmarking and reproducibility | Recognise newly generated harmonics, separate operation and byte costs, stabilise softmax and design a fair benchmark. |
| 10. Integrate and investigate | A denoising pipeline; A leakage-safe classifier; A sequence-model investigation; Read and reproduce a research claim | Produce an evidence-based design, compute held-out classification metrics, compare model assumptions and write a reproducibility/limitations report. |

Core order is 1→10. Short routes: signal processing (1–5, 9, denoising project); ML (1–2, 6–8, 9, classifier and sequence projects); computational practice (all core concepts then 9–10). Skipping is allowed, not represented as prerequisite completion. Retrieval questions revisit earlier concepts (units, train/test boundaries, linearity, numerical error).

## Pedagogical and accuracy review

Coverage deliberately includes commonly omitted bridges: complex phase, power rather than amplitude SNR, finite-record leakage, anti-aliasing before decimation, initial states, convolution versus correlation, chain rule, class imbalance, grouped/time splits, numerical stability, and honest benchmark methodology. Noise assumptions and toy data are labelled. Nyquist is strictly above the highest retained frequency for the lesson's band-limited real-baseband model; equality can lose phase information. DFT grid spacing is not universal spectral resolution. A fixed linear state-space model is not the whole of Mamba. RoPE demonstrations hold content vectors fixed. Traffic is analytical, not runtime. No toy experiment is described as a trained production model.

This course does not attempt full proofs of continuous transforms, comprehensive analogue filter synthesis, advanced stochastic estimation, control theory, reinforcement learning, generative modelling or distributed training. These are further-study directions, not silently missing lessons in the advertised path. A real coding sandbox, server sync, teacher administration and certificates are out of scope. The course must still be useful without JavaScript: explanations, worked answers and project rubrics render statically; interactive checks/progress require JavaScript and say so.

## Research-informed design decisions

- [MIT Signals and Systems](https://ocw.mit.edu/courses/res-6-007-signals-and-systems-spring-2011/): coverage cross-check for systems, transforms, filtering and sampling; our order prioritises visual sampling intuition before formal transforms.
- [Dive into Deep Learning: preliminaries](https://d2l.ai/chapter_preliminaries/index.html) and [regression](https://d2l.ai/chapter_linear-regression/index.html): a bridge from mathematical/data prerequisites into trainable models. We teach smaller deterministic examples rather than reproduce the book.
- [CMU retrieval practice](https://www.cmu.edu/teaching/resources/instructionalstrategies/activelearningstrategies/retrievalpractice/index.html): motivates recall with feedback and later review. The browser implementation is a design inference, not a claim that this course has measured efficacy.
- [CMU learning principles](https://www.cmu.edu/student-success/other-resources/need-advice/learning-principles.html): informs goals, practice, component skills and integration projects.
- [Seeing Theory, Brown University](https://seeing-theory.brown.edu/): inspiration for direct manipulation of probability; no code or assets copied.
- [scikit-learn common pitfalls](https://scikit-learn.org/stable/common_pitfalls.html): practical reference for preprocessing and leakage.
- [SciPy signal processing guide](https://docs.scipy.org/doc/scipy/tutorial/signal.html) and [polyphase resampling](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.resample_poly.html): implementation-oriented DSP references.
- [Attention Is All You Need](https://arxiv.org/abs/1706.03762), [RoFormer](https://arxiv.org/abs/2104.09864), [Mamba](https://arxiv.org/abs/2312.00752): primary sources for advanced sequence lessons, with architectural claims separated from the small browser models.

All lesson prose, questions and examples are original. Sources are linked per lesson, with existing research essays providing supplementary context. Source review does not imply source-author endorsement.

## Architecture and privacy

Typed, declarative lesson data supplies static Astro routes under `/learn/`. Pure numerical functions live in `src/lib`; SVG rendering and UI state in `src/scripts`; reusable lesson/lab components in `src/components`. Reuse existing figures wherever they teach the right concept. New small SVG experiments cover prerequisite maths, noise, quantisation, windows, frequency response, regression, optimisation, classification, activation, gradients, attention and numeric precision. All plots label axes/units, disclose assumptions and have textual readouts and reset.

Progress and optional notes are local browser storage with a versioned schema, validated reads, graceful unavailable-storage behaviour, and user-controlled export and clearing. Completion requires correct answers to both checks plus acknowledgement of the practical task. The catalogue offers filters, resume and a review list; review is practice, not automated spaced-repetition claims. No course telemetry or new cookies. Existing web-server request logs still operate independently. No notes or answers are sent to the server.

## Implementation order and acceptance gates

1. Record and review curriculum (this document), sources and exclusions.
2. Implement mathematical primitives with analytical/edge-case tests; existing lab reuse must remain intact.
3. Implement typed lesson content module by module; validate IDs, prerequisite order, question answers, sources and lab configurations.
4. Build catalogue, static lesson pages, glossary/reference, checks, hints, notes, progress, export/clear, review and mobile navigation.
5. Review every lesson against the contract; verify worked arithmetic, units and assumptions; run interaction regressions for every control/check mode.
6. Run lint, tests, type checks, production build and browser end-to-end checks (desktop/mobile, keyboard, reload, blocked/corrupt storage, no-JavaScript text and links). Do not claim browser verification without executing it.
7. Deploy only the validated build to `/var/www/sinusoidal.space/`; verify public routes, lesson discovery and assets. Record results in `docs/masterclass-review.md` and update the backlog.

No placeholder lesson should be presented as finished. Content and implementation status must be recorded honestly after review.