Physics advice for math phd student

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Discussion Overview

The discussion centers around the transition from a mathematics PhD, specifically in number theory, to potential opportunities in physics and industry. The participant seeks recommendations for advanced physics textbooks and inquiries about the level of physics knowledge required for industry roles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • The original poster expresses a desire to read about classical mechanics and other physics topics, seeking mathematically mature textbooks that balance intuition with advanced content.
  • Suggestions for physics textbooks include "QM for Mathematicians" for quantum mechanics and Arnold's "Mathematical Methods of Classical Mechanics" for classical mechanics.
  • One participant notes a lack of textbooks specifically for mathematics students in electromagnetism, mentioning Jackson's "Classical Electrodynamics" as a common reference.
  • The original poster asks about the level of physics knowledge needed for industry roles, questioning whether undergraduate knowledge suffices or if graduate courses are preferred.
  • Another participant suggests that knowledge in optimization, particularly integer programming, may be beneficial for industry, linking it to the original poster's background in number theory.

Areas of Agreement / Disagreement

Participants provide various textbook recommendations and insights into industry requirements, but there is no consensus on the specific level of physics knowledge necessary for industry roles or the best resources for learning.

Contextual Notes

Participants express differing views on the applicability of number theory in industry and the relevance of physics knowledge, indicating a range of perspectives on the transition from academia to industry.

Who May Find This Useful

Mathematics PhD students considering a shift to physics or industry, as well as those interested in advanced physics textbooks suitable for mathematically inclined readers.

evoluciona2
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Hi,

I'm completing my phd in mathematics (number theory) within a year or so. I'm not sure I want to pursue academia and would like to work in the industry first. I'm interested in pursuing physics, electronics, and building things :) and was curious about working in a physics related job before deciding about academia. I haven't taken any physics courses, but have done functional analysis but no PDEs. I have two sets of questions and I apologize in advance for any overlap with other postings :)

(1) I would like to start reading about classical mechanics (followed by EM, QM, Relativity, and so on). I'm looking for a good book that is mathematically more mature but would still cover what a first course would cover (perhaps more quickly). I'm finding that the books I pick off the library shelf are either "Second courses" which don't provide the intuition or enough basic examples, or are "First courses" which are too introductory. Currently I'm reading Marion's Classical Dynamics and it's an okay compromise, but I was curious if there was something better. The same question applies for EM, QM, etc.

(2) This one may have been posted, but how much physics would I need to start in the industry and be useful. I'd be able to learn on my own additionally. Would one be able to get by with an undergrad level knowledge or would graduate courses be highly desired? Which courses?

Thanks!

-evoluciona
 
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There are a few textbooks of physics which are addressed to maths graduate students.

In QM, I have seen just one such textbook which is called QM for mathematicians.
In classical mechanics there's Arnold's classic textbook mathematical methods of classical mechanics, there are also some new notes from Darryl Holm which you can find in his website.
In EM, I am not aware of a textbook which is for maths students, I guess everyone thinks Jackson's textbook (classical electromagnetism) is THE reference to be used.
 
Thanks for all the suggestions!

-evo
 
For industry I think physics is probably just as useful as number theory (out of the frying pan into...). Number theory in it self is a large field but for the type of person who was interested in that field I would suggest learning stuff on optimization in particular "integer programming" that has good prospects industry wise and leaves the door open to comeback to academia (but you will go to an operations research/ industrial engineering group). good luck with whatever you decide
 

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