Machine Learning and Neural Networks

Welcome! I'm really excited to dive into the world of machine learning and neural networks with you. Before we get ahead of ourselves, I'd love to know a bit more about your background so we can make this journey as fun and tailored as possible.

To get us started on the right foot, could you tell me a little bit about your background with programming or mathematics? Knowing this will help me tailor our examples and explanations.

I'm comfortable with math, but new to programming.

It is great to have you here! Since you are comfortable with math, you already possess the perfect foundation for understanding how these systems actually calculate and learn. We will skip the programming syntax for now and focus entirely on the beautiful logic and mathematical concepts that make these systems tick.

Your path

The Neuron: The Building Block

Neural Network Architecture

How Neural Networks Learn

The Grand Hierarchy

To kick off our journey, let's clear up some common terminology. People often throw around "Artificial Intelligence," "Machine Learning," and "Neural Networks" as if they are the exact same thing, but they actually fit inside one another like Russian nesting dolls. At the very outside, we have (AI). This is the broadest umbrella, representing any technique that enables computers to mimic human behavior or decision-making. If you write a massive, complex list of "if-then" rules to make a computer play chess, that is AI, even though the computer is just following rigid, pre-written instructions. Inside AI lies (ML). Instead of us writing the explicit rules, we give the computer data and a mathematical goal, and the computer "learns" the rules itself by finding statistical patterns. Finally, nestled deep inside Machine Learning, we find (NN). This is a highly specific, powerful class of mathematical models inspired by the structure of biological brains, built to master incredibly complex, non-linear relationships.

Three concentric nested circles showing the hierarchy of Artificial Intelligence, Machine Learning, and Neural Networks.

I've started generating an interactive diagram above to help you visualize how these three terms nest together.

To make this concrete: if you wanted to build a system to predict housing prices, a traditional statistical formula where you manually select the variables is Machine Learning. But if you feed raw satellite images of the houses into a web of simulated neurons to let it calculate the prices, that is a Neural Network.

Would you like to explore some everyday real-world examples of how these technologies are used, or should we continue on to find out what makes neural networks so special?

i want the full course

I love that attitude! Let's build the ultimate foundation. Before we dive into the math of individual neural network equations, let's look at how these three tiers of technology actually show up in your daily life.

Everyday Technologies in the AI Hierarchy

To make this hierarchy feel concrete, let's trace some common digital tools you probably interact with every week to see exactly which category they fall under.

1. Classical Artificial Intelligence (The Rules-Based Outer Shell)

Think of the navigation system on your phone calculating the fastest route home. It uses classical, deterministic mathematical algorithms (like ) to step-by-step calculate the shortest path through a network of roads. No "learning" is happening here; the system does not look at millions of trips to figure out how roads work. Human programmers wrote the strict mathematical rules of the grid, and the computer executes them flawlessly to find the optimal path. It is incredibly smart, but it is pure, rules-based AI.

2. Machine Learning (The Pattern-Finding Middle Layer)

Now think of your email's spam filter. If engineers tried to write manual rules for this, spammers would bypass them in five minutes by changing "free" to "fr33." Instead, developers use Machine Learning. They feed a statistical model millions of emails already flagged as "spam" or "not spam." The algorithm analyzes the frequency and co-occurrence of words, automatically calculating a mathematical probability that a new email is junk. The system continuously refines its internal variables based on user feedback (like when you click "mark as spam").

3. Neural Networks (The Brain-Inspired Core)

Finally, think of facial recognition on your phone, or speech-to-text systems like Siri and Alexa. If you try to use basic statistical machine learning on a raw picture, it fails because a face is just a grid of millions of individual color pixels. A shadow, a tilted head, or a new pair of glasses completely changes the pixel values. To solve this, we use a Neural Network. This architecture passes the raw pixel math through layers of simulated, interconnected , where each layer learns to calculate increasingly complex features—detecting simple edges in the first layer, geometric shapes in the middle layers, and full facial structures at the end.

Now that we have mapped out where these technologies live in the real world, we are ready to open up the hood of the inner doll. Let's look at the actual mathematical building block of a Neural Network: the single artificial neuron.