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The goal E University

The mathematics behind the models

Partial derivatives, gradients, integrals, linear maps, convexity and graphs — what is actually used when a model is trained.

Knowledge nodes
39
From zero
about 27 h
Labs
6
See what you already know — no account

The diagnostic removes what you already know, so your path is usually much shorter.

What you can do afterwards

Labs along the way

You write the code. Tests you cannot see decide whether it holds up.

Lab: dot product, norm and cosine similarityDin the browser · about 40 minLab: matrix multiplication and one layer of a neural networkDin the browser · about 45 minLab: lists, loops and dictionariesCin the browser · about 40 minLab: mean, median and standard deviation by handCin the browser · about 40 minLab: simulate dice and compare with the theoryCin the browser · about 40 minLab: your first Python functionsCin the browser · about 30 min

The whole path

Everything the goal builds on, grouped by level and in the order it builds on itself. Show on the map

AExplorer3 knowledge nodes
  1. Patterns and categories
  2. Sequences and precise instructions
  3. Integer arithmetic and order of operations
BInvestigator4 knowledge nodes
  1. Data in everyday life
  2. Algorithmic thinking
  3. Fractions, decimals, and percentages
  4. Negative numbers in everyday life and AI
CBuilder9 knowledge nodes
  1. Functions and coordinate systems
  2. Distance calculation and Pythagoras' theorem
  3. Programming logic — variables, conditions, loops
  4. Python — the basics
  5. Python — lists, loops and dictionaries
  6. Statistics — mean, median and spread
  7. Probability — the basics
  8. Variables and algebraic expressions
  9. Powers and roots
DAI developer11 knowledge nodes
  1. Discrete mathematics: graphs and relations
  2. Derivatives and optimisation
  3. Functions: domain, composition, inverse
  4. Integrals — the basics
  5. Python — functions, scope and exceptions
  6. Recursion
  7. Sets and logic
  8. Logarithms
  9. Vectors
  10. Matrices and matrix multiplication
  11. Partial derivatives and the gradient
EUniversity12 knowledge nodes
  1. Convexity and the optimisation landscape
  2. Integrals in probability: the expectation
  3. Proofs and induction
  4. Information theory: entropy and KL divergence
  5. Numerical stability and floating point
  6. Linear maps
  7. Eigenvalues and eigenvectors
  8. Matrix factorisation and low-rank approximation
  9. The chain rule in several variables
  10. Jacobians and Hessians
  11. Singular value decomposition (SVD)
  12. PCA — principal component analysis