Every prerequisites list is wrong, in both directions at once

Before you can take this course you will need: linear algebra, multivariable calculus, probability theory, and familiarity with Python.

You have some of that, from a long time ago. You cannot tell how much of it is still there, or how much you actually need. So you either bounce off and go study something else for a month, or you ignore the list and start anyway.

Ignoring it is usually the right call, because the list is almost certainly wrong. Not slightly wrong — wrong in two directions simultaneously.

Wrong direction one: it demands far too much

Prerequisite lists are typically written as subject names, and a subject name covers an enormous amount of ground. “Linear algebra” is a semester. What a practical machine learning course actually requires from linear algebra is usually a handful of ideas: that a matrix multiplication is a linear transformation, that dimensions have to line up, roughly what a dot product is measuring, and enough comfort with the notation not to freeze when it appears.

That is an afternoon, not a semester. But nobody writes “you will need about an afternoon on matrix notation”, because naming the subject is faster and sounds more responsible.

The same applies to almost every list you will meet. “Familiarity with Python” means you should not be learning what a for loop is at the same time — it does not mean decorators and metaclasses. “Probability theory” usually means you should not be startled by a conditional probability.

So the list systematically over-specifies, and the effect is to turn people away who could have done the course perfectly well. Prerequisites gate out far more capable people than they protect.

Wrong direction two: it omits the thing that will actually stop you

This is the more interesting failure, and it comes from the curse of knowledge.

There is a well-known demonstration of this. In a study at Stanford, people were asked to tap out the rhythm of a famous song with their fingers while a listener tried to name it. Tappers estimated that around half their listeners would get it. In fact about one in forty did. Once the tune is playing in your head, it is nearly impossible to imagine hearing only the taps.

Everyone who writes a prerequisites list is a tapper. They know the material so well that large parts of what they use have become invisible to them, and the invisible parts are precisely the ones that never make the list.

In practice, what actually stops people is rarely the named subjects. It is:

• Notation fluency. Not the mathematics — the ability to read a summation with three indices without your working memory emptying. This is a separate, trainable skill that is never listed because to the author it is not a skill, it is just reading.
• Tooling and environment. The course assumes you can get the thing running. Half the abandonment happens in the first hour, at an installation step that appears in no syllabus.
• A tacit workflow. How you are supposed to work when stuck: what to look up, what to try, when to read the source. Experts do this automatically and have forgotten they learned it.
• One specific prior concept, buried, unnamed, that the whole thing rests on — and which the author would name instantly if you asked them directly, but which did not occur to them while writing a list of subjects.

So the list warns you about things that will not stop you and stays silent about the things that will.

Why lists are long

There is an incentive here worth naming. A prerequisites list is partly a teaching artefact and partly a defensive one.

If a learner struggles, a long list means the author warned them. Nobody is ever criticised for listing too many prerequisites; plenty of people are criticised for a course being harder than advertised. The pressure runs one way, and lists grow accordingly.

What to do instead

Start the thing and let it tell you what you need. This sounds reckless and is usually optimal, for a specific reason: when you hit a wall, the wall is precise. It is not “you need linear algebra”, it is “I do not know what this notation means on this line.” That is a fifteen-minute question with a findable answer, and you will remember it, because you needed it for something.

Learning a prerequisite on demand is faster and stickier than learning it speculatively, and it is the only method that tells you which parts you needed.

Two honest caveats.

Some subjects genuinely are sequential. You cannot pick up measure theory on demand while reading a probability text that assumes it; the dependency is real and deep, and no amount of just-in-time looking things up will substitute. The just-in-time approach works well where dependencies are shallow and wide — most of engineering, most applied work — and badly where they are narrow and deep, which is most of pure mathematics and parts of physics.

And it costs some comfort. You will spend time not fully understanding things, which is unpleasant, and you have to be willing to carry a few unknowns for a while rather than resolving every one before continuing.

The list nobody can write

The deeper issue is that a prerequisite is a relation between a course and a person, and a list is written knowing only one of those.

The right prerequisites for you are the difference between what this course assumes and what you actually have. That difference is different for every reader, so the honest version of the list would have to be computed per person after finding out what they know.

What gets published instead is the difference between what the course assumes and what its author imagines a typical newcomer has. Which is a guess about a person who does not exist, made by somebody who cannot remember not knowing.