What math topics should I study to prepare for physics or pure mathematics?

[MrMarvel]

Hello,

I've endeavored to self-teach math so I can eventually go on to study Physics or Pure Mathematics.

I was hoping someone may be able to give me a list of areas I should study and in what order and an equation or problem to work out throughout each section so I can monitor my progress and ability in said field.

I've tried to Google the lists and equations for that sort of thing but I've either fallen short or read a variety of differing opinions.

Thanks!

 

[micromass]

What's your current level in mathematics??

an equation or problem to work out throughout each section so I can monitor my progress and ability in said field.

No idea what you mean with this.

 

[MrMarvel]

I'm starting from scratch with Algebra.

As for what did I mean by the equations or problems - Aren't there any equations or problems I wouldn't be able to figure out unless I had a solid understanding of the corresponding area of mathematics?

 

[micromass]

Aren't there any equations or problems I wouldn't be able to figure out unless I had a solid understanding of the corresponding area of mathematics?

For sure, but if you get a good textbook, then this will already contain many such problems.

Did you ever do algebra before in HS?? If you didn't, then I recommend the books by Gelfand. This: https://www.amazon.com/dp/0817636773/?tag=pfamazon01-20 is a very good and basic introduction to algebra.

If you already know some algebra from HS (but somehow want to start over again or forgot everything), then you might want to go for Lang: https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20

Another book that I've heard good things about is Euler. I have never looked into it though. It is freely available: http://archive.org/details/elementsofalgebr00euleuoft Some people call the book "outdated" though. Not because the contents isn't good, but because the writing style is strange and old. If you don't mind that, then Euler is fine.