Mathemathics or physics? I can't decide

[Nanovector]

Hey. I Will Be attending University in approx. 1 year, and I am having a hard time deciding for either mathematics or physics. Thing is, I've always preferred mathematics. This may be due to the rather trivial physics I am presented with here in HS, but so far mathematics seems more interesting to me - not that I don't like physics, it's definitely still awesome :)

But to get back on topic - the issue at hand is, that while I am very good deriving different formulas, Correlations and more "visuel" proofs mathematically, i seem to Be having a hard time grasping the art of deriving proofs in some of the more abstract maths such as real analysis, set theory and number theory, which is essentially what higher level mathematics is all about I guess. Doing proofs in that area of mathematics is quite difficult to me, and I can only proof the simplest traits hehe.

So what I want to know is whethe you mathematicians out there also had a hard time doing proofs in real analysis and number theory in the middle of high school, if so, I might be able to improve. If not, my understanding of physics/math is that there a less proofs of that distinction in physics, and more deriving correlations such as I'm doing now, in a very simplified manner of course! :) so maybe I am more of a physics kind of person? I think the whole real analysis scheme is very interesting, and I would love to study it, but it seems that my mastery of the subject is kind of lacking. I haven't spent that much time with it yet though, but that is mostly due to it being rather discouraging to be stuck in a trivial proof-assignment .. :)

If I was not to choose mathematics I would definitely love to go into theoretical physics, maybe particle or astrophysics.

Which would you say were the most difficult? Astro, particle physics or pure math? Aiming for research in all of them:) which would you say is right for me given my preference and my traits?

 

[Highway]

i know a few people who get degrees in math and physics, so i assume if you're capable of the material, the math degree is totally possible. and the other thing is, you could probably take both programs at the same time, and eventually decide which you would like to pursue once you get a few terms in at school. . . seeing as most math degrees start with calc 1-3, real analysis / intro to proofs, LA proofs based, differential equation proofs based, etc. -- since all of these classes will be required for your physics degree.

 

[Mépris]

Okay, since you've used the term "visuel" instead of "visual", I'm going to go out on a limb and assume you're from a country where French (or perhaps, German?) is the main language? If that's the case, do consider attending a classes preparatoires aux grandes ecoles, where if you choose the MPSI track, you do *both* Maths and Physics and choose to specialise in either field as from your 3rd year!

If you're in the US, it's even easier. Don't even worry about which to choose now. Do what Highway said!

 

[homeomorphic]

If you have looked at real analysis books, maybe the ones you have tried are too formal (which is what you want the end result to be like, maybe, but they leave out too much of the inspiration that gets you there). So, you might look around for better books. In real analysis, the inspiration for proofs, at least for me, is often visual, but the trick is to be able to translate that into a formal proof, which can be difficult at first. It takes some practice, and it also requires that you should have a very good understanding of the concepts.

 

[Mmm_Pasta]

You have one more year until university; I wouldn't worry about not being able to prove things in real analysis books. A lot of people don't take real analysis until second or third year of university. You will have gained a lot more maturity in math by then. Also, what is your math background anyway?

 

[Nanovector]

Im afraid that the at the universities i can attend, i have to choose whether i want to focus on math or physics once i start. I guess i can change it later on, but let's say i choose mathematics as my focal point, then i would study 5 years of mathematics, but only approx. 1 year of physics (roughly).

@Highway and @mmm_pasta
The stuff i can prove, invent and mess around with are different kind of riemann integrals, 3d vector formulas and so on - basic High school end-tier stuff hehe. I've invented quite a few sum-integrals (sry, not good with their official names) for the volume of a graph spun around either y or x axis, the trapezoid integral, i once found my own arc length formula, a weird version of, which i later stumbled on, herons formula the list goes on.. So it's nothing spectacular, rather mainstream :) I just enjoy giving a shot at deriving the stuff on my own, before i look at other peoples work. The only thing extraordinary 'bout me is the drive hehe. You can prob. say, that my mathematical knowledge and proficiency spans the 3-year Advanced HS curriculum + quite a bit of differential equations in one variable ( i love modelling and solving problems with these, and i especially enjoy solving them using series My math knowledge is a mixed bag you could say :)

@homeomorphic
I've been reading a bit in the "An Introduction to Analysis" Third Edition by William R. Wade, but i find most of it rather difficult, and the progress is very slow and cumbersome hehe. Lol I've been searching for a "real analysis for dummies" to get me started, but no such book exists i think :)

 

[nucl34rgg]

Almost everyone in my math class struggled with real analysis at some point. Math just gets hard. Don't let it discourage you, and don't feel ashamed if you spend many hours on some proofs. That's just how it is. If you like math, stick with it.

 

[homeomorphic]

@homeomorphic
I've been reading a bit in the "An Introduction to Analysis" Third Edition by William R. Wade, but i find most of it rather difficult, and the progress is very slow and cumbersome hehe. Lol I've been searching for a "real analysis for dummies" to get me started, but no such book exists i think :)

I always hate recommending books that I haven't read, but from what I have heard, Understanding Analysis is pretty good. Also, a Radical Approach to Real Analysis is good at providing motivation (also might be too formal in places, but each book has its strengths and weaknesses).

I actually used Wade in my second semester of Analysis. I think the prof explained things better than the book did. Plus, you can get help in office hours. So, taking a class might help.