The maths behind machine learning, worked out in full.Free guides for absolute beginners.
183Free guides
40Interactive calculators
6Subject tracks

Learn the Maths Behind Machine Learning from the Ground Up

Every algorithm explained in plain English, with the linear algebra, calculus and statistics it actually rests on. Written for people who never did a maths degree.

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y = Xβ + ε β = (XᵀX)⁻¹Xᵀy least squares 31 02
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Vectors & MatricesDerivatives & GradientsProbabilityRegressionNeural NetworksTransformers
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The learning path orders every guide on the site, from vectors and derivatives through to transformers.

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Index

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Every guide on the site, alphabetically — 183 topics across linear algebra, calculus, statistics and machine learning.

Featured Calculators
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How alike two vectors are — the distance metric behind search and recommendations.

Builds the covariance matrix step by step, the object at the heart of PCA.

Eigenvalues and eigenvectors, with the characteristic polynomial in full.

Inverts a matrix and shows every row operation on the way.

Population and sample standard deviation with each term laid out.

Fits a line to your data and shows the slope, intercept and R² working.

The mlforbeginners Promise
Our Process

Every formula is derived, not asserted. If a result is stated, the working that produces it is on the page.

Every diagram is generated from the real numbers it describes, so the picture and the maths always agree.

Guides are corrected and updated when an error is found — including ones already published.

Written for people who never did a maths degree. School algebra is the only assumed prerequisite.

Who Writes This
About
JH

Jamal Hussein

Founder & Editor

I write every guide on this site. The goal is the explanation I wanted when I was learning this material myself: the actual mathematics, worked through in full, without the notation standing in for understanding. Found a mistake? Tell me — corrections get made and noted.

Learning Tracks
See the Full Path

Track 01

Linear Algebra

  1. Vectors and vector operations
  2. Matrix multiplication
  3. The determinant and the inverse
  4. Eigenvalues and eigenvectors
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Track 02

Calculus

  1. Derivatives from first principles
  2. The chain rule
  3. Partial derivatives and gradients
  4. Gradient descent
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Track 03

Machine Learning

  1. Linear and logistic regression
  2. Decision trees and k-NN
  3. Clustering and dimensionality reduction
  4. Attention and transformers
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