Deciding between a math and physics major

[Essence]

Okay. So I’m a rising Junior and in a bit of a dilemma. I have to pick a major and right now I’m trying to decide between math and physics (hard to do both because I’m taking a fair number of computer science, economics, mechanical engineering courses et cetera). There are things that I like and dislike about both and I’m hoping I might get better data from people that have already gone through undergrad.

I like physics because I’m interested in the fundamental ways in which the universe works, but on the other hand I don’t really care about calculating a bunch of specific examples that relate to laws that we already have derived. For example in an upcoming class for a physics major (intermediate electromagnetism 1) after sifting through the textbook I’m realizing it’s just more convoluted problems that use Ampere’s law and what not. I did really enjoy reading a book that derived Maxwell’s equation from Coulomb’s law and special relativity however. I also generally despise doing experimental physics.

In reference to a math major I like the fact that we span a lot of new ideas quickly rather than spending a ton of time on examples related to one idea, but on the other hand I don’t like proving things that seem to me to be relatively obscure. For example, I don’t really enjoy doing random graph theory proofs that I am not looking to use for some specific application. I did enjoy how my partial differential equations class covered the wave equation in about a week where I spent an entire physics class on it though (math class did it better too).

Getting a major in one of these areas is important to me because I enjoy them a fair amount and have also enough credits in both that I could get a major in either while also pursuing my interest in robotics and things like that. I was hoping I might get some guidance though in regards to what area seems to be more suited to a “general and applicable” mindset. Thanks for reading :).

Made a mistake in putting this in courses - should have done programs... sorry about that.

 

[deskswirl]

I like physics because I’m interested in the fundamental ways in which the universe works, but on the other hand I don’t really care about calculating a bunch of specific examples that relate to laws that we already have derived.

You are not going to like the rest of undergrad physics.

we span a lot of new ideas quickly rather than spending a ton of time on examples related to one idea

I've always thought pure mathematicians move very slowly.

on the other hand I don’t like proving things that seem to me to be relatively obscure

cross out pure mathematican

I did enjoy how my partial differential equations class covered the wave equation in about a week

How exactly did they "cover it"? One could easily spend a whole semester on hyperbolic PDEs alone. Did you solve specific examples and that interested you?

Although you were very specific it sounds as though you are interested in Applied Math. Do they offer this at your university?

 

[Student100]

I like physics because I’m interested in the fundamental ways in which the universe works, but on the other hand I don’t really care about calculating a bunch of specific examples that relate to laws that we already have derived.

Physics is an approximation on how the universe operates given a set of initial conditions, constraints, or assumptions. Fundamental wouldn't be the correct word to use. What're you experiencing as far the examples go is quite common in lower division physics work, since they're primary aimed at both engineering and physical science students. Later the derivations and conceptual understanding will carry more weight- specific examples and applications never go away, generally. They're there to primarily reinforce the former.

For example in an upcoming class for a physics major (intermediate electromagnetism 1) after sifting through the textbook I’m realizing it’s just more convoluted problems that use Ampere’s law and what not. I did really enjoy reading a book that derived Maxwell’s equation from Coulomb’s law and special relativity however. I also generally despise doing experimental physics.

It's doubtful you even have a sliver of an idea of what experimental physics actually entails yet. Lower division labs are not accurate representations.

In reference to a math major I like the fact that we span a lot of new ideas quickly rather than spending a ton of time on examples related to one idea, but on the other hand I don’t like proving things that seem to me to be relatively obscure. For example, I don’t really enjoy doing random graph theory proofs that I am not looking to use for some specific application. I did enjoy how my partial differential equations class covered the wave equation in about a week where I spent an entire physics class on it though (math class did it better too).

Some of your statements seem contradictory. For example, in the physics courses you dislike specific applications (examples) of concepts, but you dislike abstract mathematics without readily apparent applications. Further, obscure isn't merely the realm of mathematics, much physics you would learn doesn't have readily apparent applications. Or are applicable to given real world problems, but needlessly so under current design paradigms.

Getting a major in one of these areas is important to me because I enjoy them a fair amount and have also enough credits in both that I could get a major in either while also pursuing my interest in robotics and things like that. I was hoping I might get some guidance though in regards to what area seems to be more suited to a “general and applicable” mindset. Thanks for reading :).

Made a mistake in putting this in courses - should have done programs... sorry about that.

Why are you limited to these two major areas? What makes these fields important to you? Don't throw good time after bad if you feel committed to one of these areas due to previous course work.

 

[Essence]

Ok. Just for the sake of completion I think I should respond, but I think I might have some sense as to what I'm going to do (you were definitely helpful though).

I do realize that there was some contradiction related to the fact that I had stressed applicability and yet showed interest in physics; I allowed this contradiction in my first post because I was describing a general trend line in my interest - there is a bit of a caveat that I am interested in physically descriptive fields such as general relativity that don't seem to have much applicability outside of for example GPS. I also realize that I don't have much exposure to real experimental physics; that was a misstatement due to lab work for courses and having to study different ways in which physicists managed to prove the existence of muons and neutrinos, which is far removed from anything comprehensive.

UPenn doesn't actually have an undergrad program in applied math as far as I can tell, but I do think that that is what I would be most interested in now that I've heard of it. I'm actually only about four classes away from getting a physics major, and five for a math major so from a purely pragmatic perspective I think it's best I stay on the horse that I started with; it's also not like there aren't times when I'm excited about what I'm being taught in these areas (I found the Fourier Transform and the Schrödinger equation both pretty exciting). After considering it, I will be more cautious with math (since I haven't done too much with proofs yet, and already don't love it), and will act as if I'm getting a major in physics while taking complex analysis to see if I want to bolt for a math major senior year.
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For the record my PDE class built d'Alembert's solution through some complicated guess work and then at the end of the class derived the solution methodically using a Fourier transform. We did do some plug-into-the-equation examples, but it often (especially towards the end) felt more conceptual rather than an activity of being extremely careful with one's algebra and integration. Contrastingly in a Physics homework we would spend a long time going line by line through our calculations to see where one of us made a rather anti-climatic accident in manipulations (especially in the case of Lagrangian mechanics for example).
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I do want to thank you both for your responses.

 

[amys299]

Have you thought about engineering? It sounds like you would enjoy mechanical a lot, possibly electrical too, or something in the middle. Also, what are your actual career goals?