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I am a 61 year retired guy who truly is captivated with understanding the questions in physics. My primary interest in EM, visible light and the rest of the spectrum. It's not a fad. I have always had this interest but never had the time. So what I'd like to know is if I took the time to learn the math would the insight I gain be great? And considering my age, is there a type of math I could focus on that would help me get the biggest insight for my time. Currently, I can do basic algebra. I took pre-calculus in college, but have forgotten most.

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    $\begingroup$ "So what I'd like to know is if I took the time to learn the math would the insight I gain be great?" It's subjective of course but I'd say YES. Study differential calculus and learn to solve equations like the wave equation and Maxwell's equations for a 'deeper' understanding of the subjects you seem interested in. A good online math educational resource: tutorial.math.lamar.edu $\endgroup$
    – Gert
    Sep 11 '16 at 1:19
  • $\begingroup$ I took a crack at exposing the limits of qualitative explanations in an earlier answer, only I left out the part where you need to take a still deeper mathematical look to understand why the permittivity and permeability vary as they do (a driven harmonic oscillator formalism will capture the basics). Without the math you have to "just accept what you are told" much sooner than otherwise. $\endgroup$ Sep 11 '16 at 1:28
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    $\begingroup$ Consider that Newton's laws are calculus statements, Maxwell's equations are calculus statements, Schrodinger's equation is a calculus statement, and that general relativity boils down to calculus. Aesthetically I like to say that anything that is self consistent will have a mathematical description. So if you want to do anything self consistent... you'll need some kind of math! $\endgroup$
    – user12029
    Sep 11 '16 at 1:35
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    $\begingroup$ You don't sound like the kind of person who should ever be defined by a label like "Retired". Look up the Walter Lewin lectures (on YouTube) - you will be captivated and if you find the math hard to follow, go learn it. It's an iterative process which you will enjoy. My advice: don't learn "math in case you need it". Learn it "just in time". $\endgroup$
    – Floris
    Sep 11 '16 at 1:57
  • $\begingroup$ My recommendation is to go to your local community college and take a few classes. You could take a calculus series (usually three courses) and two semesters of calculus-based physics, which is probably sufficient for your continued self-studies. Obviously, self-study is useful, but I think it is more powerful to be a part of a classroom discussion on physics and its relevance. $\endgroup$
    – zhutchens1
    Sep 11 '16 at 2:32
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I am in middle school, and I love physics and math. I have found science class disappointing. It doesn't talk about the interesting stuff, and it doesn't go in-depth enough, in my opinion. When I started learning about physics on my own, with my dad encouraging, it was so wonderful to finally get things. Like understanding about how gluons, the carriers of the strong force, hold quarks together to make up protons and neutrons, which are held together themselves by the strong force, to make up the nucleus. Like understanding about how the speed of light is always constant, and just how weird that is. Stuff like that.

Then, recently, I started getting interested in the math behind that physics. I never really understood it. I'm only taking geometry this year, so I don't know calculus, or some of the stuff needed to understand what is going on mathematically. I found it hard, however, to get myself to put the work in to get the math. Then, I found myself interested in quantum computing (besides liking physics and math, I also enjoy coding).

I found a nice looking introductory video series on YouTube, but it said that it had no requirements (yay!) except a basic understanding of linear algebra (oh). I didn't know what to do. So I just figured, aw, whatever, I'll try to take a crack at getting some of it. Khan Academy to the rescue! They have a nice, so-far understandable video series about linear algebra. It was when I watched the second video (the first was an overview, and I was just half-wincing, like, oh, the second one is where it's going to get hard...) about vector addition and multiplication, when I got so excited about it.

I got it, how to add vectors, and multiply them, and how this related to real life, and physics! Coincidentally, I was talking with my dad in the car, and looking back on it, it was basically a conversation about vectors, about how if they are going in the same direction you add, and if one is going in the opposite direction, it is negative with regards to the other, etc. This just brought it directly into the real world. So I found practice problems online, with solutions, for manipulating vectors, and I got them right, even with variables introduced. It is really hard to describe how excited I was, and am, after watching that video.

So I am continuing with that series of videos, and getting more and more excited about learning math, and learning the math behind the science.

I would say yes, definitely learn physics, and the math behind physics. It is interesting, it is wonderful to teach yourself (you have a feeling indescribable when you know you really just taught yourself something new and useful), and it is practical. It allows you to bring physics into the real world, and read more in-depth books so you can understand even more.

As for the type of math, from what I've read, I'd probably say calculus, as it describes and is the basis for so many things. But, I'm probably the wrong person to give an answer to that part of your question, as I'm learning myself.

I hope this helps!

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    $\begingroup$ Keep learning. And keep talking to your dad. $\endgroup$
    – Floris
    Sep 11 '16 at 1:52
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Getting the math will help you understand not only the topic you're interested in, but the entire world around you. It's worth the endeavor in and of itself, and I'm saying that as a guy who struggled with math, and who's not really that interested in it, but had to do it for an engineering degree. Calculus and differential equations literally changes your understanding of the world.

It's actually not that hard to get the basics down; calc 1-2/3 (depending on the school), diff. eq, and some minimal vector calculus (for EM). Getting this stuff under your belt would help you approach problems in other realms (circuits, for example) much easier as well.

If you're self-teaching EM, I recommend doing trig, the basic calc series, and vector calculus in a community college. The rigor of a classroom really is necessary for most people, in my opinion. Differential equations would help as well.

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