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Ask HN: Is is possible to self study undergrad mathematics from books?

18 points by optbuild ↗ HN
Undergrad mathematics is still a wide range of topics. But the must include topics are calculus(analysis), linear algebra, algebra, combinatorics, probability and statistics, etc.

Is it possible to learn most of undergrad mathematics through self studying books and solving problems? Has anyone done it for whatever reason they decided to do so?

Which books are most suitable for self studying topic XYZ of undergrad math?

Often books listed in course webpages are good reference books but not good for self study. A book suitable for self study should invoke the curiosity and desire to dig deeper and learn more about it. Formalism with strict rigour comes after that.

14 comments

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wly_cdgr
Yes
082349872349872
Yes — do the exercises (both the explicit, and the implicit within the text)

(as for books: I would suggest anchoring with a good reference book, while using the internet to provide inspiration and motivation)

senkora
The main reason this is hard, is that learning to write proofs that are both rigorous and human-readable is extremely difficult without a teacher+grader.

This process is not taught in high school, most or all textbooks implicitly assume that you know how to do it, and if you don’t know how to do it then it isn’t obvious what’s wrong until you realize that you can’t do the exercises anymore.

Math is largely proof-writing. Proofs are an interactive process between writer and reader. Without a reader there is no feedback loop and you don’t learn to write understandable proofs. If you can’t explain math than you don’t truly understand it.

Once you know how to write proofs, it becomes possible to learn more through books. But you really need a class setting for that first part.

an_aparallel
why is that the case? in the many years since maths has existed - have educators...or just...people in general not thought that folks may want to learn this for themselves? it boggles my mind how much of this stuff is locked away and gate kept.
senkora
It isn’t that it’s locked away. It’s just that it’s much, much easier to learn some skills with a teacher than on your own.

Imagine, e.g. trying to learn to play piano without a teacher. You could technically maybe do it but it would be 100x harder and you’d end up with a bunch of bad habits. But once you have the basics down you can learn new music on your own.

Proof-based mathematics is similar. There’s just a lot of technical, non-obvious stuff that you have to learn before you go off on your own.

Atiscant
Learning to write proofs is really learning a new kind of thinking, and that is not easy to do alone. For sure you can learn from books or other resources alone, but as with everything, when you are stuck in some way, good guidance can be very beneficial. I’ve thought proofs and logic at multiple levels and even though people struggle with similar issues, there is almost never a one-size-fits-all way to help an individual progress. It all depends on your context, way of learning, temperament etc etc.
adyavanapalli
I've thought of this before, and it makes a lot of sense! Sometimes one can write a seemingly "correct" proof, but there may be gaps in the argument that isn't obvious until someone else looks at it. Heck, even professional mathematicians get it wrong sometimes.

Another thought I've had to help solve this issue is to supplement learning mathematics with formal methods. Using something like Lean, one may make a mathematical argument that is truly airtight and the student may feel at ease knowing their understanding of a proof is complete. This could be the feedback loop that you mentioned.

abudabi123
You can pair self study from books with an Emacs session to internet relay chat on the ##math channel for beehive mind feedback.
segmondy
Yes it's possible. If you're motivated enough and willing to put the time, you can do it. There are unlimited resources on the net, find what works for you. Key is to stick to it and work through it. Get the fundamentals out of the way, begin with Khan Academy for those.
akasakahakada
And you can see from the comments that Math is not self-learnable because someone decided this property and they intentionally make Math not self-learnable through books.

Just look at those excuses. "you need a mentor" "you need someone teach you how to prove" "you will do it wrong" blah blah blah. Are these just implying that Math is not a storable and transferable knowledge because you simply not smart enough to record the knowledge down into analogue or digital form whatsoever?

That is why I love Math, but hate mathematicians. Unlike programmers, programmers just write and teach every god damn thing they know without a hassle. But mathematicians? They keep everything as secret and bring them to their tomb.

AprilPhoenix
I think the issue isn’t resources, it’s having people around you to keep you going and help you when you get stuck. Especially if you are working full time as a grown up.

We ought to form a group here for people attempting to do this. Not just with math either.