Mathematics for AI

Mean, Median and Mode

Measures of the centre, and when each misleads

Code: compare the measures on skewed data

x̄ = Σxᵢ / n

Variance and Standard Deviation

How spread out values are

Code: compare two classes with the same mean

σ² = Σ(xᵢ − x̄)² / n

Percentiles, Quartiles and Outliers

Box plots and the 1.5 × IQR rule

Code: find outliers in salaries

IQR = Q3 − Q1

Correlation

Measuring how two variables move together, and why correlation is not causation

Code: correlation heatmap

r = cov(X,Y) / (σₓσᵧ)

Probability Basics

Events, outcomes and simple probability

Code: simulate dice rolls

P(A) = favourable / total

Conditional Probability

Probability when we already know something

Code: spam given a word

P(A|B) = P(A∩B) / P(B)

Bayes' Theorem

Updating a belief with new evidence, using a medical test example

Code: the rare-disease test

P(A|B) = P(B|A)P(A) / P(B)

Probability Distributions and the Normal Curve

Uniform, binomial and normal distributions, and z-scores

Code: simulate heights

z = (x − μ) / σ

Vectors and Matrices

How data becomes rows and columns of numbers

Code: represent students as vectors

Vector Operations and the Dot Product

Adding, scaling and comparing vectors

Code: similarity between two users

a·b = Σ aᵢbᵢ

Distance and Similarity

Euclidean distance and cosine similarity

Code: find the most similar document

d = √Σ(aᵢ − bᵢ)²

Matrix Multiplication

Combining tables, as every neural network layer does

Code: a bill for many customers at once

(AB)ᵢⱼ = Σ AᵢₖBₖⱼ

Functions and Graphs

Inputs, outputs and the shape of a function

Code: plot common functions

Slope and the Derivative

How fast a value changes, in pictures first

Code: estimate a slope numerically

f′(x) ≈ (f(x+h) − f(x)) / h

Gradients and Gradient Descent

Walking downhill to make an error smaller

Interactive: roll a ball to the bottom of a curve

θ ← θ − η∇L

Module Review and Assessment

Worked problems and a scored quiz

Graded problem set