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Comment by chobytes | Hacker News Reader

Ive never read this book in particular, but had a similar experience with another book (Serge Lang, Basic Mathematics) that changed my life trajectory. If you find this stuff remotely interesting please give it a go! Math is really wonderful!

Learning math in some prescribed way (book or sequence of books) is the mathematics equivalent of "what programming language should I learn first". The most important thing is simply doing anything at all! Don't get planning paralysis!

If you think you'll actually do or read anything, then give it a try. Definitely push yourself some, but if it becomes a slog don't be afraid to move on to something that looks more interesting. Youll find your way back to anything that was actually important anyway. :)

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I always recommend anybody wanting to learn a language should just start using it. Find a project and learn the language and libraries as you need them.

What's the equivalent for learning mathematics? A lot of mathematics seems only useful for learning more advanced mathematics.

Projects in pure math are basically just research. I would say just follow your curiosity and try to figure things out. You might not be scratching novel work for awhile, but its still enjoyable.

I don't know exactly what you like to work on, but perhaps theres some related mathematical area youre curious to know more about?

To me, projects in math usually meant trying to apply it to model something or understand something/answer some question by finding a solution.

But that may be because my education always put the pure math and applications in close proximity.

Yeah I think that's basically the idea. Just solve whatever problems you find interesting via whatever means you can.

Eg Galois theory kind of looks like this: Applying an abstract model of symmetry to a model of polynomials to answer a question about solvability.

Write an optimizer or route finder.

There's a 74 episode set of videos for this from Real Physics

https://www.youtube.com/playlist?list=PLMcpDl1Pr-viA25VUkHNm...

Just found it. So no clue as to the quality

Any other recommendations? I'll find that book but you sound like you might have others

I dont know what level youre at, but if you don't already know how to write proofs then something on that. Its an extremely important foundation for everything else.

I learned in a class and we didnt use a book so I cant recommend one. I dont think it should matter too much though.

Aside from that, what kind of things are you curious about?

I got a master's in engineering, so a lot of the foundations stuff is missing. Basically the math there is all very applied stuff, not a lot of elegance and overview.

No tbh I think that's fantastic. Engineering and physics are a great way to get the right intuition. Having a firm grasp of the basics and having lots of possible examples in mind is very useful! Basically I would try to round out the basic pure math stuff for sure, but I think youre better equipped than most.

Another intro book I thought of was Peter Eccle's introduction to mathematical reasoning. Might be worth looking at.

If you want a nice leisurely introduction to groups Nathan Carter's Visual group theory is nice.

I got a lot of use out of the princeton encyclopedias of math. Dont expect for them to really teach you anything, but the articles are nice for seeing whats out there.

Definitely try to learn basic analysis and algebra. I dont think any book I know is amazing, but basically any will do the job.

Importantly, dont be afraid to try to learn something out of your depth. In fact I think its important to try! If something really grabs you, try to read more and backfill what you don't know.

lang is a wizard. all his books are absolutely excellent

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