Focus on in-depth understanding of the Maths behind Physics

[Carolus_Rex]

As a Junior year physics undergrad, how much should i focus on understanding the maths behind the physics i use. One one hand i believe that understanding maths behind the physics i use is necessary but sometimes specially in calc i feel that i am going in too much.
Simply speaking from your experience is it worth to go deep into the maths?

P.S. this is my first writing on physics forum, actually first time writing on a forum so i am sorry if the title seems off.

P.P.S. I have forgotten to give an example, For example Frenet-Serret Eqn, they haven't been taught in my class, though the principal normal is used heavily in my electrodynamics class.

 

[fresh_42]

As a Junior year physics undergrad, how much should i focus on understanding the maths behind the physics i use. One one hand i believe that understanding maths behind the physics i use is necessary but sometimes specially in calc i feel that i am going in too much.
Simply speaking from your experience is it worth to go deep into the maths?

P.S. this is my first writing on physics forum, actually first time writing on a forum so i am sorry if the title seems off.

P.P.S. I have forgotten to give an example, For example Frenet-Serret Eqn, they haven't been taught in my class, though the principal normal is used heavily in my electrodynamics class.

Hello and !

I am sure that good physicists also have a good understanding of mathematics. But there are differences. The most different and least obvious thing is, that studying - probably any field, but here, too - is far more learning a new language than it is learning theorems. The same things can be expressed very differently, hence your question could be rephrased as: Will I have to learn both new languages?

Well, yes, in a way, but certainly not at the beginning. E.g., physics is all about frames. You need a coordinate system to measure something! Hence there will be coordinates of all kinds all over the place. Mathematicians normally hate coordinates. They distract from looking at the essentials.

You mentioned calculus. A subject which wouldn't come to mind first. It is pretty much the same in both fields; at least if it isn't taught the most possible abstract way in mathematics, which it usually isn't. I.e. knowing the mathematical principles in calculus is equally essential for physics and mathematics. Things change if we talk about abstract algebra or topology. Maybe it is better to ask this question on specific examples rather than in general. PF is a good place to do so.

You will automatically develop a balance between the two over the years.

 

[Zexuo]

I consider a mathematical method understood once I've followed the proof for it step by step, noting the techniques involved. I find it helpful in holding the method in mind or, failing that, deriving it from more basic principles when needed.

 

[onatirec]

"Physics is to math what sex is to masturbation"

-RF

 

[Carolus_Rex]

Hello and !

I am sure that good physicists also have a good understanding of mathematics. But there are differences. The most different and least obvious thing is, that studying - probably any field, but here, too - is far more learning a new language than it is learning theorems. The same things can be expressed very differently, hence your question could be rephrased as: Will I have to learn both new languages?

Well, yes, in a way, but certainly not at the beginning. E.g., physics is all about frames. You need a coordinate system to measure something! Hence there will be coordinates of all kinds all over the place. Mathematicians normally hate coordinates. They distract from looking at the essentials.

You mentioned calculus. A subject which wouldn't come to mind first. It is pretty much the same in both fields; at least if it isn't taught the most possible abstract way in mathematics, which it usually isn't. I.e. knowing the mathematical principles in calculus is equally essential for physics and mathematics. Things change if we talk about abstract algebra or topology. Maybe it is better to ask this question on specific examples rather than in general. PF is a good place to do so.

You will automatically develop a balance between the two over the years.

Thank you. I will try to develop better understanding of the maths behind the physics. Though it will be both hard and time consuming. I hope in the end,it will be all worth it.