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Is analysis beneficial for a physics major

  1. Oct 5, 2015 #1
    Hello all,

    I am a physics major in my 2nd year. My current math courses include vector calculus and differential equations. I have a bit of a desire to try my hand at analysis next semester. The first course I would take assumes no prior knowledge of proof writing and builds from the ground up (I have some experience from my linear methods class). I have electives to fill so it would not interfere with my degree.

    I am just curious to here from people more experienced than I if they found real, complex, and functional analysis to be beneficial to them during their physics degree in any way? I am unsure if analysis or abstract algebra find their way into physics at the undergrad or grad level.

    Thanks for any input in advance!
  2. jcsd
  3. Oct 5, 2015 #2


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    I did some analysis in my physics degree, but no abstract algebra. I don't think not doing it held me back much, but I did regret not doing more analysis and some algebra when I came to upper level theory classes - they certainly find their way into physics. If you can do it, and you're not missing out on physics courses, I'd definitely do the courses.
  4. Oct 5, 2015 #3

    Andy Resnick

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    With the benefit of hindsight, I wish I had taken a course in functional analysis; that approach is appearing more frequently in fluid mechanics research.
  5. Oct 6, 2015 #4
    I took both analysis and abstract algebra.

    I think analysis was very instructive from a methodological standpoint - for us, it was the main "proof-writing" class in addition to the subject itself and was generally the transition point into "real world" math- but if you have to only take one, for usefulness to a physics degree, then take abstract algebra, no question. But you definitely need real analysis also if you want to get into advanced calculus and functional analysis.

    Just...don't take them at the same time. You'll be scarred for life.
  6. Oct 7, 2015 #5
    Thanks for the replies everyone!

    I have yet to decide if I want to take the theory or experimental route (or if I want to continue with my plan to teach highschool math and physics for that matter), but I have always had an interest in the QFT/particle physics area and had always wondered how deep the math went. I have four electives to fill for the next two years, so I may take Analysis I next semester and Algebra I (not the highschool algebra!) next fall.
  7. Oct 7, 2015 #6


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    I could not resist adding that yes, analysis is more than beneficial for a physics major, particularly if he is interested in theory. Also, I would like to add that certain courses from physics, such as mechanics or electrodynamics, are more than beneficial for a mathematics major with an interest in analysis, particularly if he is curious about the origins of and motivations for his own field.
  8. Oct 7, 2015 #7
    You can't lose if you build towards functional analysis. (as posted before, I also regret not taking more than the obligated real and complex analysis courses)
    It's used in almost all branches of theoretical physics (e.g. condensed matter, nuclear, ...)

    It is incredible (in the sense of cool) though how much highly abstract maths penetrate the field of physics.
    For example you can handle phase transitions with a high level of rigour, measures are important here.
    Of course there is GR which could be used as a stereotypical example, differential geometry.
    However to introduce analytical mechanics and just why it works you can (and depending on your field I would argue should) use the same differential geometry as used in GR.

    Abstract algebra pops up everywhere, symmetry is closely related to groups and algebras.
    Vector spaces are the basis of for example quantum mechanics.
    A basic course introducing these structures would go a long way already.
  9. Oct 7, 2015 #8
    This all good to hear. In recent discussions with classmates, all have told me that analysis and abstract mathematics have no place in my degree and would be a waste of my time. I personally wanted to take them out of pure enjoyment of math. Its definitely encouraging to hear they are useful. Even if it's later down the road, I like to keep my options open.

    I'm thinking to take Pinters and maybe Spivaks book out of the library to work on in my free time to get a head start.

    Thanks for the feedback everyone.
  10. Oct 7, 2015 #9


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    There really is no such thing as too much math in physics, the more the merrier is the usual mantra. Physics undergrads often opt for a dual major in physics and math because you gotta choke down a clod of math anyways. You can earn a bachelor degree by taking an only what's necessary approach to the math curriculum, but, you will pay for that in spades in grad school.
  11. Oct 8, 2015 #10
    Well there can never be too much math in my life :) it's a hobby of mine that drives my family/friends up the walls sometimes. I took out Elementary Analysis by Ross and Spivaks calculus book, which I've read are good places to start.
  12. Oct 8, 2015 #11
    I share this opinion. I graduated on a topic related to finite element methods and functional analysis is really useful if you want to understand the mathematical details of this method. At this moment I am self-studying some abstract algebra topics, stuff like group theory is extremely useful if you want to dive into the details of solving differential equations (instead of using the tools, you can make your own).

    Do you need to pay extra if you follow 'too much' courses? If not, then just do it.
  13. Oct 8, 2015 #12


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    That's really the only reason you need. The attitude your classmates have is sad. You have this opportunity to learn a subject just for the sake of satisfying your curiosity, and they see it as a "waste of time."
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