Bridge to mathematical physics book?

AI Thread Summary
The discussion centers on a final year MSci Physics student expressing a strong interest in electromagnetism (EM), quantum mechanics (QM), and mathematics, despite lacking confidence in their mathematical abilities. The student reflects on their educational journey, noting a solid foundation in physics but a desire for deeper mathematical knowledge, particularly in areas relevant to theoretical physics. They seek recommendations for books that can help bridge the gap between the mathematical skills typically taught in undergraduate physics courses and those required for theoretical physics. The student also expresses an interest in pursuing a PhD but feels uncertain about their qualifications for a theoretical position, emphasizing the importance of mathematical proficiency in the sciences. A suggestion is made to check a specific resource on arXiv for further guidance.
Livethefire
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Background

Next year I am going to be a final year student - Msci Physics. I am fairly mathematically competent even though I don't "take" any theoretical/math options (my confidence in this area is another question). In first year we had a standard introduction to all the topics we were supposed to need. Any book with the title: "Mathematical methods for Sciencetists and engineers" would be a typical example of around about the same content for the full year course with some topics missing or not covered in depth etc.

I quite enjoy all fields I have been exposed to, if I had to choose favourites I would say EM and QM. Ironically these topics are the areas in which have a huge mathematical framework - I cannot say whether or not that is the reason I like them so much or not. In retrospect I would say I was in pretty good standing to actually change my "degree pathway" from just physics to Theoretical Physics- just so I could do more math. Although, I am still not sure if this would have been better because I would have been exposed to less physics.

Main point:
I am a student on a regular physics course with strong interest in EM, QM and mathematics in general. I wouldn't say I am confident in mathematics but I do have good grades. I would say I equally enjoy experiments and theory.

Question

Are there any books that bridge the gap between typical Physics undergrad math to that taught to Theoretical undergrad students?

I would have the interest in proceeding with a PhD after university, however I definatly feel that I am not of the calibur to apply for a theoretical position- and I am not sure I'd even want to. I think that being aware of/ and or being able to use as much maths as posible is advantageous for any person in science.


Additionally I would be happy to hear any advice.
 
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Livethefire said:
I am a student on a regular physics course with strong interest in EM, QM and mathematics in general. I wouldn't say I am confident in mathematics but I do have good grades. I would say I equally enjoy experiments and theory.

Question

Are there any books that bridge the gap between typical Physics undergrad math to that taught to Theoretical undergrad students?

Try http://de.arxiv.org/abs/0810.1019
 
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I've gone through the Standard turbulence textbooks such as Pope's Turbulent Flows and Wilcox' Turbulent modelling for CFD which mostly Covers RANS and the closure models. I want to jump more into DNS but most of the work i've been able to come across is too "practical" and not much explanation of the theory behind it. I wonder if there is a book that takes a theoretical approach to Turbulence starting from the full Navier Stokes Equations and developing from there, instead of jumping from...

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