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Comment by sabas123 | Hacker News Reader

I would advice against resources like KA and 3B1brown.

I'm a firm believer that you don't truly understand material unless you also understand a proof for it. Ane while those resources are AMAZING for simple intuition building, they aren't sufficient.

Go pick up a book about proofs to develop mathematical maturity and then delve into some undergrad books for analysis (Abbott) or linear algera (Axler)

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I would advise the opposite, especially 3 blue 1 brown. I think getting the intuition first before diving into the deep proofs gives you a north star so you know where proofs will be taking you. I believe that for most people, getting the intuition first is going to make learning a lot easier.

Absolutely you should not use 3B1B as a replacement for reading a textbook and doing problems.

However, I don’t think you that means you should skip watching 3B1B videos at all. In fact, Grant repeats quite often in his videos that they’re not a substitute for doing problems.

I’d highly recommend watching the videos side by side with reading through Axler. They will help develop the right geometric intuition (which Axler does a decent job of, but books can only do so much as a medium). I believe the 3B1B videos can also be quite motivating, which in my experience is the most important factor when self studying.

Perhaps another facet to this is that both KA and 3B1B are primarily video lectures, and it's common knowledge that simply listening to someone explain something performs poorly for learning relative to actually getting hands-on with the topic. KA is even trying to fill this gap. They've added interactive visualizations for some topics.

I'd say the same is true for proofs. Simply reading a proof isn't the best if you want to understand/retain it. If you can "re-invent" the proof step by step (or in some contexts you might be able to translate steps between geometric and algebraic representations), then you have probably internalized it sufficiently.

The more engagement with the topic, the better.

You're right, but a) those are effectively (small) lectures, b) practice does not preclude watching lectures.

Yep. I love watching 3B1brown, but those seem to be in-depth videos on a particular topic.

I was wondering how you feel about Professor Leonard? He's pushing recordings of his college classes online on YouTube. It's a veritable trove of useful lectures. [1]

[1] https://www.youtube.com/user/professorleonard57

Axler is too abstract for most people who want applications (I have worked through it). Unfortunately, I don't know of a good linear algebra text that is focused on actual calculations and isn't boring. Linear algebra has so many interesting applications, but I found learning it tedious.

There is a good one by A.O. Morris (but largely out of print)

While I agree they are not enough to build a strong basis, they are a wonderful aid.

I would advise following a more traditional path, with a good book, but I cannot think of any good reason to not take a break from the book to watch some related 3B1b video from time to time.

Do you have any recommendation on a book about proofs? Every time I delve into algorithms most CS books seem to make large jumps in logic when demonstrating proofs.

The best book about proof I've read is "How to prove it" by Daniel J. Velleman. A lot of set theory. But to understand it, you must do the exercises in the book. And for the solution, checkout this blog: https://www.inchmeal.io/htpi/index.html

Thanks for the recommendation and solutions. It's the second one in this thread. I'll definitely be purchasing it.

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