Tivadar Danka Profile picture
Jul 5, 2025 6 tweets 2 min read Read on X
If I had to learn Math for Machine Learning from scratch, this is the roadmap I would follow: Image
1. Linear Algebra

These are non-negotiables:

• Vectors
• Matrices
• Equations
• Factorizations
• Matrices and graphs
• Linear transformations
• Eigenvalues and eigenvectors

Now you've learned how to represent and transform data. Image
2. Calculus

Don't skip any of these:

• Series
• Functions
• Sequences
• Integration
• Optimization
• Differentiation
• Limits and continuity

Now you understand the math behind algorithms like gradient descent and get a better feeling of what optimization is. Image
3. Multivariable Calculus

Here's how you start:

• Multivariable functions
• Derivatives and gradients
• Optimization in multiple variables

In real life, neural networks involve functions with thousands of parameters, and you need to know how they change together. Image
4. Probability Theory

Learn this:

• Distributions
• Expected values
• Random variables

Now you know how to model uncertainty, learn from data, and make predictions. Image
If you are looking for a single resource containing all these topics, I have good news for you.

I have packed 20 years of math studies into 700 pages full of intuitive and application-oriented lessons, the ultimate learning resource for you.

Get it now: amazon.com/Mathematics-Ma…

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More from @TivadarDanka

Jan 20
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices.

Encoding matrices as graphs is a cheat code, making complex behavior simple to study.

Let me show you how! Image
If you looked at the example above, you probably figured out the rule.

Each row is a node, and each element represents a directed and weighted edge. Edges of zero elements are omitted.

The element in the 𝑖-th row and 𝑗-th column corresponds to an edge going from 𝑖 to 𝑗.
To unwrap the definition a bit, let's check the first row, which corresponds to the edges outgoing from the first node. Image
Read 18 tweets
Jan 14
Matrix multiplication is not easy to understand.

Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.

Let's pull back the curtain! Image
First, the raw definition.

This is how the product of A and B is given. Not the easiest (or most pleasant) to look at.

We are going to unwrap this. Image
Here is a quick visualization before the technical details.

The element in the i-th row and j-th column of AB is the dot product of A's i-th row and B's j-th column. Image
Read 17 tweets
Jan 8
Behold one of the mightiest tools in mathematics: the camel principle.

I am dead serious. Deep down, this tiny rule is the cog in many methods. Ones that you use every day.

Here is what it is, how it works, and why it is essential: Image
First, the story:

The old Arab passes away, leaving half of his fortune to his eldest son, third to his middle son, and ninth to his smallest.

Upon opening the stable, they realize that the old man had 17 camels. Image
This is a problem, as they cannot split 17 camels into 1/2, 1/3, and 1/9 without cutting some in half.

So, they turn to the wise neighbor for advice. Image
Read 18 tweets
Jan 1
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices.

Encoding matrices as graphs is a cheat code, making complex behavior simple to study.

Let me show you how! Image
If you looked at the example above, you probably figured out the rule.

Each row is a node, and each element represents a directed and weighted edge. Edges of zero elements are omitted.

The element in the 𝑖-th row and 𝑗-th column corresponds to an edge going from 𝑖 to 𝑗.
To unwrap the definition a bit, let's check the first row, which corresponds to the edges outgoing from the first node. Image
Read 18 tweets
Dec 11, 2025
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices.

Encoding matrices as graphs is a cheat code, making complex behavior simple to study.

Let me show you how! Image
If you looked at the example above, you probably figured out the rule.

Each row is a node, and each element represents a directed and weighted edge. Edges of zero elements are omitted.

The element in the 𝑖-th row and 𝑗-th column corresponds to an edge going from 𝑖 to 𝑗.
To unwrap the definition a bit, let's check the first row, which corresponds to the edges outgoing from the first node. Image
Read 18 tweets
Dec 9, 2025
Matrix multiplication is not easy to understand.

Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.

Let's pull back the curtain! Image
First, the raw definition.

This is how the product of A and B is given. Not the easiest (or most pleasant) to look at.

We are going to unwrap this. Image
Here is a quick visualization before the technical details.

The element in the i-th row and j-th column of AB is the dot product of A's i-th row and B's j-th column. Image
Read 17 tweets

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