26 thoughts on “What Kind Of Math Do You Need For Physics?”

  1. Linear algebra and probability.

    Master those and the rest (of the math – not the physics) becomes corollaries.

  2. Don’t go into physics. It’s the english major of the tech world. Employers say, “Oh, we love phyics grads!” But they’re lying. Physics grads have no technical experience and will not get hired.

    1. Getting hired is a fairly diverse affair — too many things go into that to make generalizations.

      You might better phrase your point as “Don’t go into physics and then try to get a job as an engineer, programmer, or master chef”.

      Go into physics if you want to learn to think clearly and mathematically about lots of problems.

      Elon Musk (Physics degree) doesn’t care about who might not hire him.

      1. You can usually get hired with a masters or PhD, but not with a bachelors. I wouldn’t say it’s generalizing. Yes, physics helps you think clearly and mathematically about problems, but it doesn’t get you a job. That is why I call it the equivalent of an English degree–employers love people who can communicate clearly, but that doesn’t get one hired.

  4. The truth is that if you are a Physicist or Engineer or Mathematician you do math all the time. In your head. For fun. If you don’t already do that, then learn a trade.

  5. If you think you want to study physics, study engineering instead. You will have a much better chance of finding a job. I had to invent my own job that I could live with.

      1. Designing and manufacturing instruments for gliders (sailplanes). Got stuff in 33 countries at last count from Israel to Iceland to Indonesia. Also do some things for agricultural electronics for grain harvesting machinery and temperature controllers for wineries for the fermentation tanks and whatever else interesting comes along.
        Best thing I ever did was marry my lovely wife who runs the business stuff while I do the tech stuff.

        See the website. The pic is me in my glider.

          2. We don’t patent. Too expensive and just a license to sue and be sued. Don’t want to spend time mixing with lawyers. Just get something new out there and sell it and be quiet about certain key things that aren’t obvious to reverse engineering attempts.
            For latest glider instrument, about to be released, I’ve managed to write the installation and operations manual without saying anything about how it works. It completely solves a 50 year problem with glider instruments by using techniques never used before for them.

  6. Physics major here… My school was on the trimester schedule, so I had all 3 trimesters of calc 1, 2 trimesters of calc 2, 1 trimester of linear algebra, 1 trimester of diff equations, 1 trimester of a class called Mathematical Methods for Physics (all kinds of math you won’t get in the other classes but still need to know, like spherical harmonics). I still didn’t know as much math as I should have. Everybody should take a real statistics/probability class as well; I had to teach myself everything about statistical tests and such, not much fun.

  7. Hmm.
    I majored in Physics at Cal in 1974. I eventually dropped out in my 3rd year – Calculus of Variations and Classical Mechanics did me in.
    (Diff Eq and Quantum were easy by comparison, for me anyway.) I tell people that I concluded I was not a good enough mathematician to get a PhD. I worked in Silicon Valley for 3 years and then went back to get a EE/CS. I even took more math – Abstract Algebra was my last course.
    The amusing thing was this: At Berkeley, which one might suppose to be a Physics Mecca (oops, can I say that?) there were so few declared Physics majors that, as a Freshman, I got a key to the Physics Grad Students Lounge. We were so few that we weren’t even on the list that the Daily Cal published of 1st and 2nd year student declared majors.

    1. You quit when you got to the best part:

      Everyone knows eff-equals-em-ay (F = ma), but what separates men from boys is Eye-omega-dot plus omega-cross-Eye-omega.

      (That gives the torque applied to a rotating body, and it works the same in both the inertial frame as well as a body-local frame. When you buy a set of automobile tires, the guy who mounts them on your wheel rims and balances them uses this equation all the time, although most can’t recite it to you in this form. Amazing.)

      By the way, Berkeley is Physics Medina. Pasadena, CA is Physics Mecca.

  9. All I can say is that I never met math I didn’t like. There was a long stretch after graduation where I took an insane amount of graduate level math classes while attempting to get (and finally getting) a PhD in mathematical physics.

    Agent J has it mostly covered. But there some other things to consider. If you’re looking at some sort of programming or computer science in addition, then discrete math, combinatorics, and number theory are good add ons (they might be good anyway, even if you’re not into writing programs, with a good teacher they can be a lot of fun). Numerical methods and scientific computing are big ones (there are two broad areas to consider, solving of differential equations and solving of linear algebra systems).

    If you’re adding in some philosophy, then logic or higher level proof-based classes might be useful (I wouldn’t recommend such classes unless you’re keen on that sort of math since it tends to be almost completely detached from reality, but they are great ways to think outside the box).

    Group theory can be useful for those in high energy physics or chemistry-side physics. If you’re thinking about finance or similar field, stochastic differential equations, if offered, would be a good thing to take.

    When I was an undergrad majoring in physics, I ended up taking calculus, differential equations, numerical differential equations, discrete math, foundations of math, and vector analysis. I too missed out on statistics.

  10. Physics here. I agree that the fields recommended in the article will take you a long way — fifty years later, I still find myself using then now and then on a variety of problems.

    One other thing that has struck me is that math is a rich source of metaphor and can provide useful ways of thinking about things even in non-mathematical areas.

  11. The math used for most computing, on the other hand, is things like logic, combinatorics, and even category theory (which is closely related to the theory of parameterized data types and is used extensively in the programming language Haskell.)

    I heard at one point that a significant number of physics bachelor’s degree recipients were going to work for Schlumberger, but that was some time ago so I don’t know if it’s still true.

  12. Looking back at my own education (BS & PhD in physics) and career thus far, I find it odd that I was required to spend a whole semester on diff eqs, but linear algebra was pretty much optional and numerical methods were not even mentioned. In retrospect, I’d say that it’s important to know how to solve a 2nd-order diff eq with constant coefficients, including a few choice such partial differential equations. Many, many things either boil down to that or are well approximated by it. After that, linear algebra and numerical methods are more useful.

  13. But even if you’re a physicist, try to learn your math from mathematicians rather than from physicists or engineers. Mathematicians do it better: clearer definitions and better notation, even in areas that were originally invented by physicists (e.g., calculus [Newton’s formulation, at least] and Dirac delta functions). It’s a crime that physicists and engineers are still taught Gibbs’ vector calculus (gradient, curl, divergence, and all that) a century after the simpler, more intuitive, more elegant and more general tools of differential forms were developed by the mathematician Cartan.

    1. It’s a crime that physicists and engineers are still taught Gibbs’ vector calculus (gradient, curl, divergence, and all that) a century after the simpler, more intuitive, more elegant and more general tools of differential forms were developed by the mathematician Cartan.

      I have to strongly agree. For example, my favorite book along these lines is Harley Flander’s Differential Forms with Applications to the Physical Sciences (originally published in 1963) which has since been picked up by Dover Books. It describes differential forms as oriented towards physicists.

      Multi-variable integration and a variety of identities like Stokes Theorem (which equates an integral over a volume with a particular integral over the boundary of the volume) are much easier to describe and do with differential forms.

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