Focus on in-depth understanding of the Maths behind Physics

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In summary, a good understanding of mathematics is necessary for studying physics, but there are differences in the approach between the two fields. Physics involves learning a new language and coordinate systems, while mathematicians may focus more on theorems. While calculus is important in both fields, more abstract concepts may require further exploration. It is best to seek guidance on specific examples and over time, a balance between the two will naturally develop.
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Carolus_Rex
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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.
 
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Carolus_Rex said:
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 :welcome: !

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.
 
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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.
 
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"Physics is to math what sex is to masturbation"

-RF
 
  • #5
fresh_42 said:
Hello and :welcome: !

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.
 

FAQ: Focus on in-depth understanding of the Maths behind Physics

1. What is the importance of understanding the math behind physics?

Understanding the math behind physics is crucial because it allows us to accurately describe and predict the behavior of the physical world. Without a strong foundation in math, it would be impossible to fully comprehend the fundamental principles and laws of physics.

2. What are some key mathematical concepts that are essential for understanding physics?

Some key mathematical concepts that are essential for understanding physics include calculus, algebra, geometry, trigonometry, and vectors. These concepts are used to describe and solve problems related to motion, forces, energy, and other fundamental concepts in physics.

3. How can focusing on in-depth understanding of math improve my understanding of physics?

By focusing on in-depth understanding of math, you will develop a strong foundation in the fundamental concepts and principles that govern the physical world. This will allow you to approach physics problems with a more analytical and critical thinking mindset, leading to a deeper understanding of the subject.

4. Are there any resources available to help me improve my understanding of the math behind physics?

Yes, there are many resources available such as textbooks, online tutorials, and practice problems that can help you improve your understanding of the math behind physics. It is also beneficial to seek guidance from a teacher or tutor who can provide personalized instruction and support.

5. Can I still understand physics without a strong background in math?

While it is possible to have a basic understanding of physics without a strong background in math, it is highly recommended to have a solid understanding of mathematical concepts in order to fully grasp the complexities of physics. Without a strong foundation in math, it may be difficult to fully understand and apply the principles and laws of physics.

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