Mathematics required to become a physicist + References ?

[Alg0r1thm]

Hi guys,
I'm passionately curious about physics and applying it to pure mathematics, but for some reason I'm learning medical field and I'm senior high school student,
What I want to know is :
1 - Which books should I cover to become good at mathematics ?
2 - How did Albert Einstein do that ? ( Learning mathematics )
3 - Which subjects should I cover ? ( Calculus, Geometry, Algebra , ... )
By third question I mean which of them are prerequisite for example : What should I learn in geometry to apply it to physics , how much calculus ...
and some topics like Number theory ~ is it required ?
What about combinatorics and statistics ? what about graph ? (graph theory)
I want to improve my mathematics also learn some fundamental of physics , please guide me through it ,
Please answer thoroughly and meticulously
Thanks in advance

 

[voko]

Physics is mathematics. Well, almost. Physics is less concerned with "mathematical rigor", and may be less abstract, but it still utilizes a sizable portion of the modern mathematical apparatus. If you are serious about it, attend undergrad courses in geometry, algebra, calculus and complex analysis, or study undergrad courses of the same subjectss. Everything you learn there will have applications to physics. Once you learn that, you will see for yourself what else you need to learn to be fluent in modern physics.

 

[Alg0r1thm]

I can't attend undergraduate physics courses because my major is not physics or Mathematics, also they don't provide courses for people whose major aren't physics so I need to be self-taught, I need some resources to learn, specially about math, and basic physics ... .
Thanks a lot

 

[voko]

I am surprised no one replied to this. Anyway, please follow these two threads:

https://www.physicsforums.com/showthread.php?t=240792

https://www.physicsforums.com/showthread.php?t=122924

The second is about becoming a mathematician, but most undergrad mathematics is about the same anyway. This thread has a lot of textbooks covered, so you will sure find something useful.

 

[Arsenic&Lace]

Other people can add to this, but the foundation is calculus, linear algebra, differential equations, maybe a little probability, complex analysis, etc; but beyond that, how much math you learn depends upon where you take physics.

A mathematical physicist will invariably learn a lot of math!

 

[demonelite123]

for physics, calculus (single, multi-variable, vector), linear algebra, and ordinary differential equations are must haves and these are usually covered in the first year of university.

beyond that there is usually a course called mathematical physics which covers topics like complex variables, partial differential equations, calculus of variations, Green's functions, Fourier series, etc. and these are important for obtaining a more advanced knowledge of physics.

the use of differential geometry is also becoming more prevalent in theoretical physics as it is used extensively in general relativity, electromagnetism, classical mechanics, etc.

the deeper and further you delve into physics, the more math you find you will need. more modern theoretical physics involves ideas from topology and algebra. in fact, string theory research just about uses almost every piece of math you will probably learn (a mathematical physics professor has told me this).

 

[michaelc187]

Hi guys,
I'm passionately curious about physics and applying it to pure mathematics, but for some reason I'm learning medical field and I'm senior high school student,
What I want to know is :
1 - Which books should I cover to become good at mathematics ?
2 - How did Albert Einstein do that ? ( Learning mathematics )
3 - Which subjects should I cover ? ( Calculus, Geometry, Algebra , ... )
By third question I mean which of them are prerequisite for example : What should I learn in geometry to apply it to physics , how much calculus ...
and some topics like Number theory ~ is it required ?
What about combinatorics and statistics ? what about graph ? (graph theory)
I want to improve my mathematics also learn some fundamental of physics , please guide me through it ,
Please answer thoroughly and meticulously
Thanks in advance

1. mathematics, physics is math... apply principles of superposition (ie breakdown into components, demensions/axis)

2. same

3. same

no books