The complete journey

Your route

Work down the list, or open any lesson. Progress is shared across paths: a lesson you have completed elsewhere counts here too. Completing checks is a useful milestone, not proof of mastery.

Progress loads from this browser when JavaScript is available.

1. What is a signal?What does a waveform actually tell you?15 min · Progress unavailable without JavaScript
2. Frequency, amplitude and phaseHow can three numbers describe an oscillation?20 min · Progress unavailable without JavaScript
3. Vectors and similarityHow does a list of numbers become a geometric object?20 min · Progress unavailable without JavaScript
4. Complex numbers and rotationWhy do transforms use an imaginary coordinate?20 min · Progress unavailable without JavaScript
5. Slopes and gradientsHow do you decide which way to change a parameter?25 min · Progress unavailable without JavaScript
6. Probability and uncertaintyHow should several plausible outcomes share one unit of probability?20 min · Progress unavailable without JavaScript
7. Noise and signal-to-noise ratioHow much unwanted variation is in a measurement?25 min · Progress unavailable without JavaScript
8. Data splits and leakageWhen is a good test score too good to be true?20 min · Progress unavailable without JavaScript
9. Sampling and timeHow do equally spaced measurements encode motion?20 min · Progress unavailable without JavaScript
10. Aliasing and NyquistCan different waves produce exactly the same samples?25 min · Progress unavailable without JavaScript
11. Quantisation and clippingWhat changes when sample values have a finite alphabet?20 min · Progress unavailable without JavaScript
12. Resampling safelyWhy is keeping every other sample sometimes wrong?25 min · Progress unavailable without JavaScript
13. Projection onto wavesHow can a dot product detect a frequency?25 min · Progress unavailable without JavaScript
14. The discrete Fourier transformWhat exactly is in an FFT output array?30 min · Progress unavailable without JavaScript
15. Windows and leakageWhy does one tone make many spectral bars?30 min · Progress unavailable without JavaScript
16. Time-frequency analysisWhat if the signal’s frequency changes over time?30 min · Progress unavailable without JavaScript
17. Linearity and time invarianceWhen can one impulse response describe a whole system?25 min · Progress unavailable without JavaScript
18. Convolution step by stepWhich input samples contribute to one output?30 min · Progress unavailable without JavaScript
19. Frequency response and filter trade-offsWhy does averaging suppress some frequencies more than others?30 min · Progress unavailable without JavaScript
20. Recurrence and stabilityWhen does yesterday’s state fade, persist or explode?30 min · Progress unavailable without JavaScript
21. Features and linear regressionWhat exactly does a model learn from examples?30 min · Progress unavailable without JavaScript
22. Gradient descentHow can a repeated local update find better parameters?30 min · Progress unavailable without JavaScript
23. Classification and cross-entropyWhy penalise a confidently wrong prediction so strongly?30 min · Progress unavailable without JavaScript
24. Evaluation and generalisationWhich mistakes does a single accuracy score hide?30 min · Progress unavailable without JavaScript
25. Nonlinear features and neural networksWhat does adding a hidden layer actually add?30 min · Progress unavailable without JavaScript
26. The chain rule and backpropagationHow does one weight receive credit for a distant error?35 min · Progress unavailable without JavaScript
27. Convolutions in neural networksHow does one learned filter scan an entire representation?30 min · Progress unavailable without JavaScript
28. Regularisation and model selectionHow can a better training fit make a worse model?30 min · Progress unavailable without JavaScript
29. Position and representationHow can a model distinguish the same content in different places?30 min · Progress unavailable without JavaScript
30. Attention as weighted retrievalHow can a query choose which information to combine?35 min · Progress unavailable without JavaScript
31. Rotary positionWhy does a shared position shift disappear from a rotary score?35 min · Progress unavailable without JavaScript
32. State-space memoryWhen is a recurrence also a convolution?35 min · Progress unavailable without JavaScript
33. Nonlinear aliasingCan a cleanly sampled signal create aliases later?35 min · Progress unavailable without JavaScript
34. FFTs and memory trafficWhy can fewer arithmetic operations still run slower?35 min · Progress unavailable without JavaScript
35. Numerical stabilityCan the same exact formula behave differently on a machine?35 min · Progress unavailable without JavaScript
36. Benchmarking and reproducibilityWhat evidence supports a claim that an implementation is faster?30 min · Progress unavailable without JavaScript
37. Project: a denoising pipelineCan you reduce interference without hiding signal distortion?75 min · Progress unavailable without JavaScript
38. Project: a leakage-safe classifierCan your feature choice survive a truly held-out evaluation?90 min · Progress unavailable without JavaScript
39. Project: a sequence-model investigationWhich sequence mechanism suits the dependency you need?90 min · Progress unavailable without JavaScript
40. Project: read and reproduce a research claimWhat would convince you that a result is both correct and useful?90 min · Progress unavailable without JavaScript

After a lesson, return here to pick the next step in this path. With JavaScript enabled, lesson next/previous links stay in this route. Without JavaScript, they follow the complete course; return here to choose your next route lesson. Export or import your shared notebook on the course page.