How can you build a good understanding of math for machine...
Santiago@svpino
96 views
Nov 08, 2025
~2 min read
Advertisement
1
How can you build a good understanding of math for machine learning?
Here is a complete roadmap for you.
In essence, three fields make this up:
• Calculus
• Linear algebra
• Probability theory
Let's take a quick look at them!
Here is a complete roadmap for you.
In essence, three fields make this up:
• Calculus
• Linear algebra
• Probability theory
Let's take a quick look at them!
2
This thread is courtesy of @TivadarDanka.
3 years ago, he started writing a book about the mathematics of Machine Learning.
It's the best book you'll ever read:
tivadardanka.com/books/mathemat…
Nobody explains complex ideas like he does.
3 years ago, he started writing a book about the mathematics of Machine Learning.
It's the best book you'll ever read:
tivadardanka.com/books/mathemat…
Nobody explains complex ideas like he does.
3
1. Linear algebra.
In machine learning, data is represented by vectors. Essentially, training a learning algorithm is finding more descriptive representations of data through a series of transformations.
Linear algebra is the study of vector spaces and their transformations.
In machine learning, data is represented by vectors. Essentially, training a learning algorithm is finding more descriptive representations of data through a series of transformations.
Linear algebra is the study of vector spaces and their transformations.
4
Simply put, a neural network is just a function that maps the data to a high-level representation.
Linear transformations are the fundamental building blocks of these. Developing a good understanding of them will go a long way, as they are everywhere in machine learning.
Linear transformations are the fundamental building blocks of these. Developing a good understanding of them will go a long way, as they are everywhere in machine learning.
5
2. Calculus.
While linear algebra shows how to describe predictive models, calculus has the tools to fit them to the data.
If you train a neural network, you are almost certainly using gradient descent, which is rooted in calculus and the study of differentiation.
While linear algebra shows how to describe predictive models, calculus has the tools to fit them to the data.
If you train a neural network, you are almost certainly using gradient descent, which is rooted in calculus and the study of differentiation.
6
Besides differentiation, its "inverse" is also a central part of calculus: integration.
Integrals express essential quantities such as expected value, entropy, mean squared error, and more. They provide the foundations for probability and statistics.
Integrals express essential quantities such as expected value, entropy, mean squared error, and more. They provide the foundations for probability and statistics.
7
When doing machine learning, we are dealing with functions with millions of variables.
Functions work differently in higher dimensions. This is where multivariable calculus comes in, where differentiation and integration are adapted to these spaces.
Functions work differently in higher dimensions. This is where multivariable calculus comes in, where differentiation and integration are adapted to these spaces.
8
3. Probability theory.
How do we draw conclusions from experiments and observations? How do we describe and discover patterns in them?
Probability theory and statistics, the logic of scientific thinking, answer these questions.
How do we draw conclusions from experiments and observations? How do we describe and discover patterns in them?
Probability theory and statistics, the logic of scientific thinking, answer these questions.
9
@TivadarDanka's book explains every one of these concepts.
It's 100% focused on the math required in machine learning, and you won't find better explanations anywhere else.
tivadardanka.com/books/mathemat…
Trust me on this one.
It's 100% focused on the math required in machine learning, and you won't find better explanations anywhere else.
tivadardanka.com/books/mathemat…
Trust me on this one.