The set of maths i would need to learn all of physics?

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Discussion Overview

The discussion centers around the mathematical prerequisites necessary for learning various branches of physics, including classical mechanics, electro/thermodynamics, quantum mechanics, relativity, and particle and nuclear physics. Participants explore the relationship between mathematics and physics, addressing the order in which to tackle these subjects and the specific mathematical concepts required.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses a desire to learn physics but acknowledges a lack of familiarity with the necessary mathematics, primarily knowing only integral and differential calculus.
  • Several participants emphasize the importance of differential equations (both ordinary and partial) as critical for understanding physics, suggesting that without this knowledge, progress may be hindered.
  • There is a discussion about the foundational nature of differential and integral calculus, with some participants noting that these topics are just the beginning of more complex mathematical concepts.
  • One participant argues that physics is fundamentally about concepts and ideas, suggesting that one can learn additional mathematics as needed rather than mastering all math beforehand.
  • Another participant recommends starting with popular science books on particle physics that require minimal mathematical knowledge, advocating for a more conceptual approach to learning physics.
  • Some participants debate the mathematical abilities of historical figures like Einstein and Faraday, with differing opinions on their proficiency and the role of mathematics in physics.
  • Linear algebra is mentioned as another important area of mathematics to learn in conjunction with physics.
  • One participant advises against learning math from physics books, suggesting a more structured approach to mathematics education.

Areas of Agreement / Disagreement

Participants express a mix of views regarding the relationship between mathematics and physics. While there is some consensus on the necessity of differential equations and linear algebra, opinions diverge on the approach to learning physics and the extent to which one should prioritize mathematics before engaging with physical concepts. The discussion remains unresolved regarding the best order and method for learning these subjects.

Contextual Notes

Participants highlight various assumptions about the prerequisites for learning physics, including the dependence on individual learning styles and the potential for learning mathematics concurrently with physics. There are also unresolved discussions about the depth of mathematical knowledge required for different areas of physics.

mpatryluk
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I decided this would be better in the physics forum than math.

Ultimately, I've set a goal for myself to commit to learning as much physics as i can.

I tried to skip forward to particle physics and see if i could pick up the math prerequisites as i went, but there was too much i was unfamiliar with, so my question is:

What are the maths i would need if i wanted to learn classical mechanics, elcectro/thermodynamics, quantum mechanics, relativity, and particle and nuclear physics?

The math i know right know really just consists of integral and differential calculus

Also I've come to realize that despite my ambitions, i just don't have the physics prerequisites to start at particle physics, given i only know classical mechanics/thermodynamics.

In which order should i be tackling these, and, am i missing anything?
 
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If you don't know differential equations (ordinary and partial, linear and nonlinear) you will be stopped in your tracks at some point.
 
SteamKing said:
If you don't know differential equations (ordinary and partial, linear and nonlinear) you will be stopped in your tracks at some point.

That's very true- although isn't that a fundamental component of integral/derivative calculus?- any of the equations that I've dealt with that involve solving for/dealing with derivatives/integrals? Or, i guess it gets a lot more complicated and specialized than that?

Edit: Yea, i whipped out my calc book and there are chapters on DEs that haven't even covered... Thanks!
 
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The differential and integral calculus is just the basic material, like what arithmetic is to algebra. ODEs and PDEs, especially harmonic functions (Laplace eqn., etc.) are found quite frequently in connection with describing various physical phenomena. In addition, while the theory of linear differential eqns. is fairly well developed, non-linear DEs are not as well understood, and a comprehensive theory (if one exists) has yet to be developed.
 
Physics is about what happens and how it happens...maths is part of the story...learn about physics...maths is just a tool.
Maths is not physicsFaraday...cannot ignore him!...was useless at maths...so was einstein
 
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technician said:
Physics is about what happens and how it happens...maths is part of the story...learn about physics...maths is just a tool.
Maths is not physicsFaraday...cannot ignore him!...was useless at maths...so was einstein

But how can i learn physics if i can't even understand the notation explaining the prerequisite concepts for what I am trying to learn?

I understand that i can learn the qualitative aspects and descriptions, but to be useful in any sense i feel like i would need to know the specific quantitative relationships, and by extension the maths that dictate how those quantitative relationships are represented.

Also, I've heard that Einstein was actually quite good at math, just that comparatively to the math of mathematicians he was utterly confused.
 
mpatryluk said:
I decided this would be better in the physics forum than math.

Ultimately, I've set a goal for myself to commit to learning as much physics as i can.

I tried to skip forward to particle physics and see if i could pick up the math prerequisites as i went, but there was too much i was unfamiliar with, so my question is:

What are the maths i would need if i wanted to learn classical mechanics, elcectro/thermodynamics, quantum mechanics, relativity, and particle and nuclear physics?

The math i know right know really just consists of integral and differential calculus

Also I've come to realize that despite my ambitions, i just don't have the physics prerequisites to start at particle physics, given i only know classical mechanics/thermodynamics.

In which order should i be tackling these, and, am i missing anything?

Very frankly, if you know differential and integral calculus you can get started on learning physics right away. Physics is more about concepts and ideas really and in general, you shouldn't let not knowing the math hold you back, you can learn the additional math as and when you require it (The only exception to this rule is basic differential and integral calculus, which is a must know.). I would really recommend Feynmann's Lectures in Physics as an excellent starting point. The great thing about this book is that he teaches you the additional math(for eg. vector calculus) as and when you require it. Also it is full of insights and anecdotes.
If you're thinking 'you should first learn all the math and then learn all the physics' its not going to work very well that way. Chances are good that you may never get to the physics that way.
Physics is really more about concepts and ideas, the math is just a means to the end.
As far as particle physics is concerned I would suggest that you just start out with one of the popular science books on particle physics written for the general public. You wouldn't need to know much more than algebra to read those.
 
  • #10
technician said:
Physics is about what happens and how it happens...maths is part of the story...learn about physics...maths is just a tool.
Maths is not physicsFaraday...cannot ignore him!...was useless at maths...so was einstein

Neither Einstein nor Faraday were useless at math. They may not have excelled at math the way some of their contemporaries did, but both were more than competent at math. The language of physics is math. You can find some good translations, but the more you understand math, the easier it will be to figure out the physics. This is especially true if you are trying to learn from books which often assume a certain level of math.

Edit:
to the original question, ODE and PDE for sure. Linear algebra is important. After that (IMO) learn physics and take detours when the math gets over your head.
 
  • #11
The only extra advice I can give you, that hasn't been said already, is: never learn math from a physics book.
 
  • #12
All math is based on addition, except when it's not.

Faraday may not have used a lot of math in his studies of fields, but he had men like Green and Stokes coming along to fill the gap. Soon, Maxwell would put the cherry on top, so to speak.

Then again, there have been mathematicians who were no slouches in the physics department. J. v. Neumann and S. Ulam were trained as mathematicians and made significant contributions to physics, particularly the nuclear type.
 

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