Understanding math will make you a better engineer.

Imagine a translating device that allows you to engage in fluent conversations with any person in the world, regardless of the language. This is what mathematics can do for you in science and engineering.

So, I am working to create the best book to study the mathematics of machine learning.

Join the early access!

What the readers say

  • With great pleasure I can recommend this wonderful book the creation of which I experience every week. You can explore it in pdf, html and jupyter notebooks.
    Ryszard Zygała
    Ryszard Zygała
    Data scientist, PhD
    from Poland
  • This book is a fantastic resource for those who want to understand the foundations of ML algorithms and are no longer satisfied with considering them as 'black boxes'. BTW with the 'early access' scheme, waiting for the next chapter to be published feels like waiting for your favourite weekly TV show. Nice.
    Adam Hulman
    Adam Hulman
    Senior Data Scientist
    from Denmark
  • Very impressed with what you’ve done with the book. As someone who’s not an expert in math I found your material super helpful. Thank you!
    Parviz D.
    Parviz D.
    Lead Solutions Architect
    from the US
  • Being part of early access gives the reader the pleasure to travel with the author. I'm enjoying it thoroughly. Even more excited about what awaits 2 years from now as per your roadmap. I'm sure this will be a gold mine for data science enthusiasts and practitioners.
    Raj Arun
    Raj Arun
    Lead - Analytics & Data Science
    from India
4.9 from 57 reviews

Math explained, as simple as possible.

Every concept is explained step by step, from elementary to advanced. No fancy tricks and mathematical magic. Intuition and motivation first, technical explanations second.

MSE figure
MSE figure

Open up the black boxes.

Machine learning is full of mysterious black boxes. Looking inside them allows you to be a master of your field and always understand what is going on.

Black boxes figure
Black boxes figure

Be a part of the process.

This book is being written in public. With early access, you’ll get each chapter as I finish, with a personal hotline to me. Is something not appropriately explained? Is a concept not motivated with applications? Let me know, and I’ll get right on it!

Mathematics of machine learning timeline
Mathematics of machine learning timeline

Check out the free preview!

Not convinced yet? Check out the first two chapters for free. No catch, you don’t even have to give me your email address. Just click on the button below, and it’ll take you to the book!

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Mathematics of machine learning logo

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If you don’t like the book, contact me within 60 days, and I’ll give you a full refund. No questions asked.

Any questions? I am here to help!

If you have any questions, shoot me a message on Twitter @TivadarDanka! I am happy to help!

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The roadmap

Mathematics of machine learning book roadmap

This is what will be covered in detail

Linear algebra

  • Vector spaces

  • Structure of vector spaces: norms and inner products

  • Linear transformations and their matrices

  • Eigenvectors and eigenvalues

  • Solving linear equation systems

  • Special matrices and their decomposition


  • Function limits and continuity

  • Differentiation

  • Minima, maxima, and the derivative

  • Basics of gradient descent

  • Integration

Multivariable calculus

  • Partial derivatives and gradients

  • Minima and maxima in multiple dimensions

  • Gradient descent in its full form

  • Constrained optimization

  • Integration in multiple dimensions

Probability theory

  • The mathematical concept of probability

  • Distributions and densities

  • Random variables

  • Conditional probability

  • Expected value

  • Information theory and entropy

  • Multidimensional distributions


  • Fundamentals of parameter estimation

  • Maximum likelihood estimation

  • The Bayesian viewpoint of statistics

  • Bias and variance

  • Measuring predictive performance of statistical models

  • Multivariate methods

Machine learning

  • The taxonomy of machine learning tasks

  • Linear and logistic regression

  • Fundamentals of clustering

  • Principal Component Analysis

  • Most common loss functions and what’s behind them

  • Regularization of machine learning models

  • t-distributed stochastic neighbor embedding

Neural networks

  • Logistic regression, revisited

  • Activation functions

  • Computational graphs

  • Backpropagation

  • Loss functions, from a neural network perspective

  • Weight initialization

Advanced optimization

  • Stochastic gradient descent

  • Adaptive methods

  • Accelerated schemes

  • The Lookahead optimizer

  • Ranger

Convolutional networks

  • The convolutional layer, in-depth

  • Dropout and BatchNorm

  • Fundamental tasks of computer vision

  • Alexnet and Resnet

  • Autoencoders

  • Generative Adversarial Networks

Want to find out more?

Listen to Practical AI’s interview with Tivadar about the book!

Practical AI 152: The mathematics of machine learning – Listen on Changelog.com

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