Is double majoring in physics and math worth it?

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I'm a high school senior this year, and next year i'll be going to university. My orientation is next week, and I need to declare my major(s) and choose classes at that time.

I've always planned on getting a degree in physics and going to grad school. However, I've really started liking math recently. Would it be worth it to double major? Would the math that I learn be useful for a career in physics?
 

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  • #2
Nabeshin
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Generally you'll have to be taking some introductory (calculus, diff EQ, linear algebra) classes anyways for a physics major, so you probably don't need to decide on the math until later. Once you're done with the intro classes, take a class in analysis or algebra and see if you like it.

In general, as far as the math in math classes being applicable to physics classes, it's generally not. The math you need for physics classes is usually introduced as you go, and in a way so that it's directly applicable to the problem at hand. Even if you've seen the mathematics in a math class, it might take some footwork to see how it applies. The situations in which this is false are probably a mathematical/theoretical physicist who might use some advanced mathematics, but generally this is not taught as an undergraduate anyways (and could easily be picked up as a grad student).
 
  • #3
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Generally you'll have to be taking some introductory (calculus, diff EQ, linear algebra) classes anyways for a physics major, so you probably don't need to decide on the math until later. Once you're done with the intro classes, take a class in analysis or algebra and see if you like it.

In general, as far as the math in math classes being applicable to physics classes, it's generally not. The math you need for physics classes is usually introduced as you go, and in a way so that it's directly applicable to the problem at hand. Even if you've seen the mathematics in a math class, it might take some footwork to see how it applies. The situations in which this is false are probably a mathematical/theoretical physicist who might use some advanced mathematics, but generally this is not taught as an undergraduate anyways (and could easily be picked up as a grad student).
That's the main problem I am having. My advisor said that I could normally wait a year to add a math degree, but I'll be entering freshman year already having calculus III complete. So I need to decide at the very latest end of the first semester.

If the degree was in applied mathematics rather than pure mathematics, would this make a difference? I enjoy math, and I don't expect every single thing I learn to be 100% applicable to physics, but if some of it did overlap, that would be useful.

Maybe I should rephrase my question a bit: Are there any benefits in double majoring rather than getting a single degree in physics?
 
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  • #4
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That's the main problem I am having. My advisor said that I could normally wait a year to add a math degree, but I'll be entering freshman year already having calculus III complete. So I need to decide at the very latest end of the first semester.

If the degree was in applied mathematics rather than pure mathematics, would this make a difference? I enjoy math, and I don't expect every single thing I learn to be 100% applicable to physics, but if some of it did overlap, that would be useful.

Maybe I should rephrase my question a bit: Are there any benefits in double majoring rather than getting a single degree in physics?
There are benefits of course. I am entering third year physics in a couple months, and I have a couple physics classes each semester with the mathematical physics students. They generally get higher marks, because physics becomes increasingly mathematical as you go on. Taking math courses will definitely help you later on in physics, it just depends on whether or not you think its worth the extra stress. As far as jobs go, pure mathematics probably wont help that much,but applied mathematics might.
 
  • #5
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There are benefits of course. I am entering third year physics in a couple months, and I have a couple physics classes each semester with the mathematical physics students. They generally get higher marks, because physics becomes increasingly mathematical as you go on. Taking math courses will definitely help you later on in physics, it just depends on whether or not you think its worth the extra stress. As far as jobs go, pure mathematics probably wont help that much,but applied mathematics might.
I'm by no means a genius at mathematics, but I'm sure I could handle the extra work. I study a lot and have a good handle on the math that I've learned so far. I think I'll go ahead and sign up for two majors, and if it turns out to be more than I can handle, I can always just switch to physics.
 
  • #6
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I have many friends who are math/physics double majors, IMO many of them are wasting their time and money with the math major; their excuse is they want to do either theoretical physics or mathematical physics however they never mention what kind of either they want to do. I suppose there are tracks where the extra math is helpful but it seems many physicists don't use that much math apart from calculus, differential equations, complex analysis, linear algebra, numerical analysis, and prob/stats. My school offers a course in theoretical physics which is essentially differential geometry, abstract algebra, and group theory applied to questions in theoretical physics such as black holes so I suppose those methods are useful depending on what type of physics you want to go into.
 
  • #7
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IMO Applied math is much more suitable for a Physics major who wants to build on his mathematical skills. Math majors soon diverge into areas that are pretty "out there" as far as what a physicist would consider useful.

Math is all about abstract relationships and really doesn't care if they have any physical meaning or application. Physics is really concerned about how nature works.
 
  • #8
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Thanks for all of the advice.

Obviously I don't know what area of physics I want to specialize in just yet. I'm probably more of an industry person, however, than a theoretical physicist. I also have the opportunity to work for a minor in mathematics, which sounds like what I'm going to do right now. I'll be able to change to a major later down the road if I wish.
 
  • #9
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I am glad I found this thread. I was also a double physics/math major but have been rethinking my choice this semester. I don't mind doing proofs and was looking forward to some of the upper level math. However I am about 3/4 through discrete math and can barely stand it. Maybe it is because it seems to be more CS based, but I absolutely hate it.

I think this thread has confirmed my thought to drop the double major. :)
 
  • #10
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I'm a double major in math and physics and I'll be graduating in the fall, so at this point I've thought about the choice quite a bit.

First some context. I started on a slightly different path - I started as a physics major and took 1 math class per semester out of interest. I had plans to go to grad school for physics. Eventually I took the first abstract algebra class, which was by far the most eye-opening and mind-blowing class I've ever taken. This convinced me to go to grad school for math instead, and since I only had one physics requirement left at that point I decided just to keep the physics major.

I actually feel like my math studies have benefited a lot from the physics classes and vice versa. It is probably true that I would be better at math now if I had only taken math classes, or better at physics if I had only taken physics classes, but having a reasonable amount of knowledge of both has given me more than one point of view to look at things. For example, I'm in my last physics class now, electrodynamics using Griffith's textbook, and since I've done graduate level coursework in topology, I have been thinking about the material in terms of differential forms, exterior derivatives, the generalized Stoke's theorem, etc. Because of this, most of the derivations in the textbook are very easy for me to read since I can see that it is just repeated applications of the very basics of the theory of differential forms as opposed to several different theorems that initially appear unrelated. On the other hand, I'm also currently taking a class on operator algebras, and since I've had a year of quantum mechanics, everything in the class already has a lot of motivation for me. Some other students in the class without any physics background have had a difficult time seeing the motivation for a lot of the concepts and it is always more difficult to learn math when you don't see the motivation.

There's a good chance that I won't study anything physics-related in grad school, but I do not feel that studying physics has been a waste of time at all. For the other way around, i.e. planning on going to grad school for physics instead, I cannot say as much since I know less about it. What I can say is that theory can involve some pretty hardcore mathematics if you want it to - I worked for a mathematical physicist last summer, and ended up doing a lot of algebraic topology, K-theory, functional analysis, etc, none of which you would typically learn as a physics undergrad, and if I hadn't had a strong interest in pure math before going into the project then I do not think I would have gotten the opportunity to begin with simply because most physics undergrads do not have the background to work on such topics.
 
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  • #11
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Interesting experience. I really have no clue what type of physics I'm going to be doing. I suppose majoring in math couldn't hurt, unless I can't keep up with the work.
 

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