The maths behind recommendations
Take this if you want to know what a recommendation engine is doing, and would accept a little geometry as the price of finding out.
What you’ll be able to do
You can explain how a thing becomes a list of numbers, why closeness in that space means similarity, and what it means for a direction in the space to carry meaning.
What it assumes
You can plot a point in two dimensions and understand what an average is. No prior linear algebra.
- Price
- Free
- Length
- 1 week
- Sessions
- 4
- Effort
- ~2 h/week · 2 h total
- For
- Anyone
Adds it to My courses on your dashboard. No card, nothing to cancel.
What’s taught, in order
- 01
A thing as a list of numbers
Scoring five films yourself on two invented axes, then plotting them. You have built an embedding by hand before the word appears, and you know exactly where the numbers came from.
- 02
Distance means similarity
Measuring which of your films sit closest together and checking it against your own taste. Where the geometry disagrees with you is the interesting part, and it is where the axes turn out to be wrong.
- 03
Directions carry meaning
In a real word-embedding space, subtracting one word from another and adding a third lands you somewhere meaningful. Doing this yourself is the moment vectors stop being arrows and start being ideas.
- 04
Why your feed does this
Nearest-neighbour lookup in an embedding space is most of what a recommendation system is. Knowing that also tells you why feeds narrow over time, which is worth understanding as a user.
What you build
In the word-embeddings visualiser, find the vector arithmetic that turns king into queen, then find two more analogies that work and one that fails badly. Write down the failure and a guess at why the space got it wrong.
Check it yourself against this
- You reproduced a working analogy of the king-to-queen kind.
- You found two further analogies that land on a sensible word.
- You found one analogy that fails, and can describe how it fails.
- You can explain what closeness between two vectors is claiming about the two things.
Then answer this
Nobody told the embedding space what royalty or gender mean, so how did a direction in it end up encoding them?
Two or three sentences, in your own words. If you cannot, the course is not finished — go back to the module it came from.
What this course does not do
This course gives you the geometry, not the machinery: how embeddings are actually trained, how vector databases index them at scale, and how real recommenders handle cold starts and feedback loops are all outside it. It also uses two and three dimensions throughout, where real embeddings have hundreds.
Where this leads
The embedding explorer is free on its own page, and the king-to-queen analogy takes about two minutes to reproduce — it is the fastest way to check whether this kind of thinking appeals to you before you commit an hour.
FAQ
- Is this a maths course or an AI course?
- Both, and that is the point. Vectors are taught here entirely through the thing they are for, so the geometry arrives with a reason attached. If you want the formal treatment afterwards, the Linear Algebra for AI sprint picks it up properly.
- Do embeddings really encode bias like the analogies suggest?
- Yes, and the course shows it rather than mentioning it. Because directions in the space are learned from human text, stereotypes in that text become geometry, and you will find at least one analogy that returns something uncomfortable. That is a real property of these systems, not a flaw in the demo.
- What comes after this?
- The Linear Algebra for AI sprint if you liked the geometry, or the RAG sprint if you want to use embeddings to build something that answers questions from your own notes.
Other courses
This is a standalone course. It does not add weeks to the 78-week curriculum or change your roadmap. If you want the whole path instead, the full programme is ₹399/month · ₹2,000/year — see what it covers.