Math for AI: From Zero to Model Intuition

What's inside

1. Level 1: What is a Variable?Free
   Understand variables as placeholders for numbers, the building blocks of all math in AI.
2. Level 2: Functions: Inputs & OutputsFree
   Learn that a function maps an input to an output, just like an AI model does.
3. Level 3: Linear Functions & Slope
   Explore straight-line functions and how slope measures rate of change.
4. Level 4: Graphing Basics
   Learn to plot points and lines on a coordinate plane, visualizing relationships.
5. Level 5: Systems of Equations
   Solve two linear equations together to find where they intersect.
6. Level 6: Exponents & Powers
   Understand exponent notation and how repeated multiplication works.
7. Level 7: Polynomials: Adding & Multiplying
   Work with expressions that have multiple terms, like x^2 + 3x + 2.
8. Level 8: Quadratic Functions & Parabolas
   Explore functions with x^2 and their U-shaped graphs.
9. Level 9: Solving Quadratic Equations
   Learn to find x-values where a quadratic equals zero.
10. Level 10: Introduction to Logarithms
    Understand logarithms as the inverse of exponentiation, key for scale in AI.
11. Level 11: What is a Derivative?
    Learn that a derivative measures instantaneous rate of change, like speed at a moment.
12. Level 12: Derivatives of Simple Functions
    Apply basic rules to find derivatives of polynomials and powers.
13. Level 13: Slope & Tangent Lines
    Connect derivative values to slopes of tangent lines on graphs.
14. Level 14: Maxima & Minima
    Use derivatives to find where functions peak or bottom out.
15. Level 15: Gradient: The Multi-Variable Derivative
    Extend derivatives to functions with many inputs, like a model with many weights.
16. Level 16: Gradient Descent Intuition
    Understand the iterative algorithm that moves downhill to find a minimum.
17. Level 17: Learning Rate & Convergence
    Explore how step size affects whether gradient descent finds the minimum.
18. Level 18: Chain Rule: Composing Changes
    Learn how to differentiate nested functions, essential for backpropagation.
19. Level 19: Error Functions & Loss
    Define a loss function that quantifies model error, the target of minimization.
20. Level 20: From Derivative to Weight Update
    Combine gradient descent and loss to update a single weight in a model.
21. Level 21: What Is Probability?
    Learn the fundamental language of probability: sample spaces, events, and the three axioms that govern all random phenomena.
22. Level 22: Conditional Probability & Independence
    Understand how the probability of one event changes when we know another has occurred, and when events are independent.
23. Level 23: Bayes' Theorem: Updating Beliefs
    Discover Bayes' theorem, the mathematical core of how AI revises predictions based on new evidence.
24. Level 24: Random Variables
    Move from events to numbers: define random variables, distinguish discrete and continuous, and use probability functions.
25. Level 25: Expected Value & Variance
    Learn the two key numbers that summarize a random variable: the center (mean) and the spread (variance).
26. Level 26: Common Probability Distributions
    Meet the most important distributions in AI: Bernoulli, Binomial, Normal, and Uniform.
27. Level 27: Law of Large Numbers & Central Limit Theorem
    Understand why averages become stable and why the normal distribution appears everywhere.
28. Level 28: Introduction to Statistics
    Bridge from probability to statistics: sampling, estimation, and the difference between a population and a sample.
29. Level 29: Hypothesis Testing
    Learn the framework of hypothesis tests: null hypothesis, p-value, and significance level.
30. Level 30: Confidence Intervals & Margin of Error
    Quantify the uncertainty of an estimate using confidence intervals and understand the margin of error.
31. Level 31: Vectors: The Building Blocks
    Define vectors and their fundamental operations: addition, subtraction, scalar multiplication, and dot product.
32. Level 32: Vector Spaces & Linear Combinations
    Explore the structure of vector spaces, linear combinations, span, and the concept of a basis.
33. Level 33: Matrices: The Data Tables
    Introduce matrices, their operations (addition, multiplication, transpose), and how they represent data.
34. Level 34: Solving Systems of Linear Equations
    Use matrices to solve systems of linear equations via Gaussian elimination and row reduction.
35. Level 35: Determinants & Inverses
    Learn determinants for 2x2 and 3x3 matrices and how they relate to invertibility.
36. Level 36: Eigenvalues & Eigenvectors
    Discover the special vectors that only scale under a matrix transformation, and why they matter for AI.
37. Level 37: Linear Transformations
    See how matrices represent linear transformations like rotation, scaling, and shearing.
38. Level 38: Orthogonality & Projections
    Understand orthogonal vectors, orthonormal bases, and how to project a vector onto a subspace.
39. Level 39: Singular Value Decomposition (SVD)
    Learn the powerful matrix factorization SVD and its intuitive meaning: rotate, scale, rotate.
40. Level 40: Principal Component Analysis (PCA)
    Apply SVD to perform PCA, the go‑to method for dimensionality reduction in AI.
41. Level 41: Neural Network as Math Function
    See a simple neural network as a composition of linear transformations and activation functions.
42. Level 42: Forward Pass: Input to Output
    Calculate the output of a tiny neural network given specific inputs and weights.
43. Level 43: Loss Functions and Error Measurement
    Learn how squared error and cross-entropy quantify prediction mistakes.
44. Level 44: Gradient Descent Intuition
    Use derivatives to understand how adjusting weights reduces loss.
45. Level 45: Chain Rule for Backpropagation
    Apply the chain rule to propagate error gradients through a network.
46. Level 46: Backpropagation Through One Layer
    Manually compute gradients for a single hidden layer network.
47. Level 47: Matrix Calculus for Neural Nets
    Extend derivatives to matrices and vectors for efficient gradient computation.
48. Level 48: Putting It Together: Forward and Backward
    Perform a complete forward pass and backpropagation for one training example.
49. Level 49: Debugging a Simple Network
    Identify and fix common errors in neural network math.
50. Level 50: Final Challenge: Full Model Analysis Exam
    Synthesize all course math to explain, calculate, and debug a complete AI model's learning process.

Access

The first 2 levels are free with a free account. Every level, the podcast edition and the AI tutor come with All Access at £4.99/month or any Creator plan — see pricing.

Start free →