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Comment by kiyoto | Hacker News Reader

Yes. For example, to follow CS229's lecture notes, the following material should suffice.

- Linear Algebra Done Right by Sheldon Axler

- Linear Algebra by Steven Levandosky

- Linear Algebra and Multivariable Calculus, and Manifolds by Ted Shifrin (you probably do not need the manifolds part)

Also, as paradoxical as it may sound, CS229 lecture notes themselves. The key here is to verify the details painstakingly. In math, we joke that whenever a book says something is "trivial" or "easy to verify" or "clear to show", it is a substantial exercise in disguise.

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Yes, the whole "trivial exercise" thing is in itself a big problem with how mathematics is taught. Someone who's struggling just to understand the text could probably really use a worked-out example.

That's the wrong interpretation. In math, a 'trivial' or 'clearly' is supposed to indicate that a certain detail is important to understanding the subject. And if it isn't clear or trivial then the reader is expected to delve deeper before moving on.

The "big problem" is that math is taught in a restricted time scale - a semester, just like all other standard courses. In reality it might take someone many weeks or months to pick up a certain piece of measure theory or hilbert spaces. Math builds upon itself and when it is rushed there is a lack of connection and then ultimately failure to understand.

This is why MOOCs are a great boon for many, as they allow more freedom to self-dictate the pace.

If that's what it really means then a perfectly good way to say it is: "To test your understanding, make sure you can do this exercise before continuing."

I suspect many mathematicians like being intimidating.

"Left as an exercise to the reader," the bane of my existence as a college student. I especially remember the Sipser book doing this. He'd show a super-simple example, like proving 2+2=4, and then the next thing would be actually interesting and would be left as an exercise. Awesome.

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