Should I learn mathematical proofs or focus on current coursework during college break?

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Carolus_Rex
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My country has been hard hit by second wave of covid, so bad that the colleges that were conducting classes online had to be paused for two weeks. So since i have time, i am thinking of using it properly.
I was wondering should i pursue how to proof in maths since i have linear algebra in my course and the book that we are using, Stephen Andrilli's Elementary linear algebra, has a little bit of proofing in it. So should i pursue the basics of proofing or should i study something else which is more related to my syllabus.
For background, I am currently an undergrad(first year) in physics. Currently in my second semester. My core for this semester are Electrodynamics and Waves&optics(Only wave optics).

P.S. i know it normally takes a while to get answers on the forum, so me posting an time urgent(atleast in my opinion) thread seems like foolish but i sure i will try.

P.P.S I could rush ahead in the syllabus, but the fact is that my entire second semester is most likely online again. So i normally find plenty of time to easily cover and stay a little ahead of the class.
 

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Being a physics major, you will likely benefit more with applied mathematics study and less with proofs.

You could investigate Vector Analysis as it combines the techniques Calculus and Linear Algebra together into a more powerful tool allowing one to understand Maxwell's EM theory.

As an example, vector curl is usually a mystery to students more so than vector divergence. Understanding them will go a long way in understanding the physics of Maxwell's equations.

https://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/

Alternatively, you could look into Differential Equations since the four math pillars for physics are Calculus, Linear Algebra, Differential Equations and Statistics.

@PeterDonis or @Vanadium 50 could chime in here with better suggestions for physics. @fresh_42 could add better commentary on the value of proofs.
 
jedishrfu said:
Being a physics major, you will likely benefit more with applied mathematics study and less with proofs.

You could investigate Vector Analysis as it combines the techniques Calculus and Linear Algebra together into a more powerful tool allowing one to understand Maxwell's EM theory.

As an example, vector curl is usually a mystery to students more so than vector divergence. Understanding them will go a long way in understanding the physics of Maxwell's equations.

https://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/

Alternatively, you could look into Differential Equations since the four math pillars for physics are Calculus, Linear Algebra, Differential Equations and Statistics.

@PeterDonis or @Vanadium 50 could chime in here with better suggestions for physics. @fresh_42 could add better commentary on the value of proofs.
Yeah it might be better for me to pursue better understanding of applied mathematics. however i find that when i tried to study vector calculus from my books. most of them gave a formulae based approach to the entire concept of divergence,curl etc. Can you recommend some book or lectures that goes into the depth of the reasoning behind these mathematical methods. the closest thing i found to an understanding of these mathematical methods were in my physics book, namely Electricity and magnetism By Edward Purcell.

P.S. I can easily borrow Mathematical Methods For Physics And Engineering by K.F. Riley from one my neighbors. I currently own mathematical physics by H.K Dass (a native writer), though i have found that his books are more focused on doing questions to pass the exam rather than teaching the subject.

P.P.S i also asked my prof. about this issue however i have yet to receive an answer.
 
There’s a book called Div Grad Curl and All That by Schey that gives an applied approach using EM theory as the applied field sandbox.
 
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Carolus_Rex said:
My country has been hard hit by second wave of covid, so bad that the colleges that were conducting classes online had to be paused for two weeks. So since i have time, i am thinking of using it properly.
I was wondering should i pursue how to proof in maths since i have linear algebra in my course and the book that we are using, Stephen Andrilli's Elementary linear algebra, has a little bit of proofing in it. So should i pursue the basics of proofing or should i study something else which is more related to my syllabus.
For background, I am currently an undergrad(first year) in physics. Currently in my second semester. My core for this semester are Electrodynamics and Waves&optics(Only wave optics).

P.S. i know it normally takes a while to get answers on the forum, so me posting an time urgent(atleast in my opinion) thread seems like foolish but i sure i will try.

P.P.S I could rush ahead in the syllabus, but the fact is that my entire second semester is most likely online again. So i normally find plenty of time to easily cover and stay a little ahead of the class.
You listed good options for yourself. If you are doing well in your courses, TRY STUDYING AHEAD. When the sections or topics are delivered to you in normal instruction, you will then be reviewing them.
 
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jedishrfu said:
There’s a book called Div Grad Curl and All That by Schey that gives an applied approach using EM theory as the applied field sandbox.
I believe that Edward Purcell has used the similar approach in his book, i will try to download its pdf and check for myself. thanks for the suggestion