Studying Do I need to learn more math as a physics autodidact?

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The discussion centers on the approach to studying mathematics in relation to physics after mastering foundational topics such as calculus, linear algebra, and differential equations. The consensus suggests that for someone primarily interested in physics, it is beneficial to learn mathematics as a tool through physics textbooks, supplemented by resources specifically designed for physicists, rather than delving into specialized math textbooks. This approach is applicable at both undergraduate and graduate levels. It emphasizes the importance of contextual learning, where mathematical concepts are integrated within the framework of physical applications, making it easier to grasp their relevance and utility.
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I managed to master the single variable, multivariable, and vector calculus, linear algebra, and some ordinary differential equations. After that, I studied advanced advanced introductions to classical mechanics and electrodynamics. I'm currently studying waves and oscillations and don't intend to stop somewhere. My question then is whether from now I should only study the physics textbooks and learn the math I need through physics, or learn math from specialized math textbooks.
Is the answer the same for both undergraduate and graduate level books?
 
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Ahmed1029 said:
My question then is whether from now I should only study the physics textbooks and learn the math I need through physics,
In general, now you have all the basics, this is probably the better approach.
Ahmed1029 said:
or learn math from specialized math textbooks.
Only now and again if it's something you need to nail down thoroughly. Note, however, that it's often difficult to relate the material in specialized maths books (e.g. Lie Groups and Lie Algebras) to the application of that mathematics to physics.
 
Ahmed1029 said:
I managed to master the single variable, multivariable, and vector calculus, linear algebra, and some ordinary differential equations. After that, I studied advanced advanced introductions to classical mechanics and electrodynamics. I'm currently studying waves and oscillations and don't intend to stop somewhere. My question then is whether from now I should only study the physics textbooks and learn the math I need through physics, or learn math from specialized math textbooks.
Is the answer the same for both undergraduate and graduate level books?
If your primary interest is physics, then you should view math as a tool for physics. Learn the math you need from physics books, supplemented by books geared towards "math for physicists (scientists, engineers)" rather than books geared towards math for mathematicians. This holds for undergrad and grad.
 
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