About Maths and Statistics for AI
Every AI model, from a simple line of best fit to a large language model, is built on
a small set of mathematical ideas. This course teaches exactly those ideas, with a
focus on why they matter and how they show up in real code. It starts
with Why Maths Matters for AI, a map of where each topic is used,
then builds your toolkit in Vectors & Matrices and
Eigenvalues & Decompositions, the language of data and the basis of
techniques like PCA.
Next comes calculus, the engine of learning. Calculus Essentials
and Gradients & the Chain Rule show how a model measures its own
error and works out which way to improve, and Optimization turns that
into gradient descent and its modern variants.
The second half covers the mathematics of uncertainty. You'll learn
Probability Fundamentals and
Random Variables & Distributions, then move into statistics with
Descriptive Statistics & Correlation and
Inference & Hypothesis Testing, so you can tell a real effect from
noise.
Finally, Bayesian Thinking shows how to update beliefs as evidence
arrives, and Information Theory & Loss Functions ties everything
together by explaining entropy, cross-entropy, and the loss functions used to train
modern models.
No advanced maths background is required. Comfort with school-level algebra and basic
Python will help. Each module builds directly on the last, with worked examples and
hands-on coding using NumPy, SciPy, and Matplotlib.
Content
12 modules
01
Why Maths Matters for AI
A roadmap of the maths behind AI: where linear algebra, calculus, probability, and statistics appear in real models, plus a quick refresher on notation and functions.
Roadmap
Notation
Functions
02
Vectors & Matrices
Representing data as vectors and matrices: dot products, norms, distances, matrix multiplication, and why they power every neural network layer.
Vectors
Matrices
NumPy
03
Eigenvalues & Decompositions
Eigenvectors, eigenvalues, and singular value decomposition: the maths behind PCA, recommender systems, and data compression.
Eigenvalues
SVD
PCA
04
Calculus Essentials
Limits, derivatives, and integrals explained through rates of change, with the rules you actually need for machine learning.
Derivatives
Integrals
Rates of Change
05
Gradients & the Chain Rule
Partial derivatives, gradient vectors, and the chain rule: the foundation of backpropagation and automatic differentiation.
Partial Derivatives
Gradients
Backpropagation
06
Optimization
Gradient descent from scratch, learning rates, momentum, Adam, and the difference between convex and non-convex loss landscapes.
Gradient Descent
Learning Rate
Adam
07
Probability Fundamentals
Events, conditional probability, independence, and Bayes' theorem, plus expectation and variance for reasoning about uncertainty.
Probability
Conditional Probability
Expectation
08
Random Variables & Distributions
Discrete and continuous random variables, and the distributions that appear constantly in AI: Bernoulli, binomial, Gaussian, and more.
Distributions
Gaussian
Sampling
09
Descriptive Statistics & Correlation
Summarizing data with mean, median, variance, and quantiles, spotting outliers, and measuring relationships with covariance and correlation.
Mean & Variance
Correlation
Outliers
10
Inference & Hypothesis Testing
The central limit theorem, confidence intervals, p-values, and A/B testing: how to tell a genuine result from random noise.
Confidence Intervals
p-values
A/B Testing
11
Bayesian Thinking
Priors, likelihoods, and posteriors: updating beliefs with evidence, maximum likelihood estimation, and how Bayesian ideas appear in machine learning.
Bayes' Theorem
MLE
Posterior
12
Information Theory & Loss Functions
Entropy, KL divergence, and cross-entropy, and how they lead to the loss functions that train classifiers and generative models.
Entropy
KL Divergence
Cross-Entropy
What You Can Do After This Course
By the end of the curriculum you'll have built five hands-on projects and gained the
mathematical foundation needed to understand how AI models work. Concretely, you'll
be able to:
Think in vectors and matrices — represent data and model operations the way machine learning libraries do.
Understand dimensionality reduction — use eigenvalues and SVD to see how PCA and compression really work.
Explain how models learn — compute gradients, apply the chain rule, and follow backpropagation step by step.
Write optimizers from scratch — implement gradient descent and understand momentum, learning rates, and Adam.
Reason about uncertainty — use probability and common distributions to model randomness and noise.
Analyze data with statistics — summarize datasets, measure relationships, and test hypotheses with confidence.
Apply Bayesian and information-theoretic ideas — update beliefs with evidence and understand cross-entropy and other loss functions.
Show proof of skill — a linear algebra toolkit, a gradient descent optimizer, a Monte Carlo simulation, an A/B test analysis, and a Bayesian spam filter.