9

I am in high school and I find myself enjoying math a lot more than physics, probably because of the more focused teaching approach found in physics, which looks at specific cases and experiments and then goes on to explain these mathematically, where as in maths it seems to me a broader stance is taken; only after a foundation is laid one goes into specific examples. Still I would rather like to study physics or engineering at university, as I am more interested in the subject of physics itself than that of theoretical mathematics.

So how does university teaching compare to that found in high school in physics and mathematics, and where do I place engineering in this comparison?

PS: I am from Austria and plan to go to uni in Germany, in case that helps with answering the question.

PPS: I know this question is open ended and opinion based so feel free to flag.

Edit: I`m thinking of this, this or that.

1
  • Comments are not for extended discussion; this conversation has been moved to chat.
    – cag51
    Commented Feb 11, 2021 at 21:34

3 Answers 3

25

When studying physics at a German university, you will take three kinds of core modules:

  1. Experimental Physics
  2. Theoretical Physics
  3. Math

Of these, experimental physics is somewhat similar to physics in school. You have a discussion of concrete phenomena, how you can measure them, probably quite a bit of lab time, too.

Theoretical physics is similar to math in school. You learn some more overarching theories about how to model things mathematically (like Newtonian gravity, electromagnetism, thermodynamics, and so on). A lot of what you do is calculations (compute an integral, solve a differential equation). If you want to learn how to do complex calculations with pen and paper, theoretical physics is where you do it.

Math at university level is a very different beast from anything most pupils encounter at school (at least in Germany). You'll encounter some familiar concepts (differentation, vectors), but in a far more rigorous way. You will not just be told that stuff is true, but you'll see the proofs (and be asked to prove simple statements yourself [at least if your math courses are shared with mathematicians, if you have dedicated "math for physicists" courses this might not be the case]).

14
  • 1
    @AnonymousPhysicist I've clarified that I am talking about German universities here.
    – Arno
    Commented Feb 10, 2021 at 20:16
  • 7
    It should be added that the Math you learn as a physicists might be real university math, but it might also not - this really depends where you are studying. (If Math is taught jointly with the mathematicians - which I believe is getting less common - then it for sure is.)
    – user151413
    Commented Feb 10, 2021 at 20:48
  • 3
    To follow up on @user151413's comment: it makes sense to look at the website of physics departments where you might be interested in studying and see whether they do their own math courses, or send their students to the "math for math" courses. Commented Feb 11, 2021 at 9:51
  • 1
    I studied CS at a german university, and even though the math courses were 'math for computer scientists', they were very heavy on proofs. And at least for me as non-mathematician, the proofs we had to do also didn't seem all that simple ;) So I wouldn't just go by the name ('math' or 'math for X'), but see if there's anything available online about past courses.
    – tim
    Commented Feb 11, 2021 at 10:02
  • 1
    @tim It is all relative, from a mathematicians perspective the hierarchy is somewhat like this: maths for mathematicians, then for CS/physics, then for econ and at the bottom math for dentints, veterinarians and similar things that somehow require a math course. So as a CS student you already get pretty heavy math.
    – quarague
    Commented Feb 11, 2021 at 11:54
6

Speaking as a physics PhD student here.

In physics you will apply and use math. You'll learn more math concepts along the way, but you will use math to solve problems. In that way, it is very similar to math in school. You'll learn physics in a much more profound way than they could ever teach in you in school, because you simply lack the math skills in school to do it.

Math is nothing alike anything in school though. You will rarely calculate stuff. You are more interested in showing relations and proof them. You will prove that a solution exists, but not necessarily, what this solution looks like. To me, this was always kind of boring. Sure, proving that a partial differential equation has a solution is a cool thing to do, but I'm much more interested in actually solving it (so thanks to the people who proved it's possible :p )

With that being said, I highly recommend choosing your field of study based on what is interesting for you, as a topic, not as a use of tools. What drove me into physics was to to discover the mechanism of our universe. That you can do it by using math so solve problems is just a bonus. I'd recommend math if you are interested in pure math itself, if you're interested in the reason why certain math operations are defined the way they are, what really lies behind vector spaces, group theory, analysis, linear algebra...

3
  • 1
    So that the other side also gets heard: I would advice the exact opposite. Choose the field based on the tools that it uses. That is what you will interact with every day and I think in the end for most academics actually more relevant to their motivation. I think you will find that if the tools are interesting there are interesting questions to answer in any field. (Or at least after working on problems in the field for a while you will think that all these questions are very interesting. Perhaps we simply become delusional ;))
    – Kvothe
    Commented Feb 11, 2021 at 19:15
  • 1
    To add: People that get motivated to do physics because they are so interested in the secrets of the universe often got discouraged by the difficult math and drop out. People that actually enjoy the math, which is the majority of the work, remain. It is much easier for them to keep up the motivation. Also nowadays the new "secrets of the universe" are hidden quite far away (very little low hanging fruit) so if finding those motivates you you will have to go for years without any pay-off.
    – Kvothe
    Commented Feb 11, 2021 at 19:17
  • It might be worth noting that there's a school in maths in which only existence proofs are taken seriously that also provide an algorithm to construct the solution. It's quite influential at the maths-CS interface; not so much at the maths-physics one. Commented Feb 11, 2021 at 22:44
1

Short: There is a progression in rigor and abstraction that goes like this: High school physics, high school math, university engineering, university physics, university math. There are large differences between different universities and between different schools.

Assuming that an Austrian Matura is similar to a German Abitur or Swiss Matur (I don't know for sure), then even courses for physicists and engineers are going to have more rigorous math than you are used to, but it's a natural progression and if you have a passion for the subject and liked math ok in high school, then you should be fine.

Courses for mathematicians (which you might be required to take if you study physics) are at a level of rigor and abstraction that is not comparable to the math required for a Matura. If you think about enrolling in a program that requires such courses, I suggest you look through some exercise materials for linear algebra I and analysis I or whatever your study program of interest requires - try to solve some and skim the solutions for the rest. You will get a much better idea of what it would be like to study those subjects for real than by reading abstract descriptions of what it was like for other people.

That being said, some schools offer much more preparation than others. There are Gymnasien which offer an optional math course which is actual math, statement, prove, example, repeat. Some offer more hands-on math that will make the transition to an engineering or physics program easier, but won't make much of a difference if you decide on math. Some might offer additional engineering courses, etc.

The universities in Germany are going to assume the least amount of previous knowledge that an Abiturient would have (which varies a lot among Bundeslaender), but starting university life can be a stressful transition and if you have some more than the minimum it's going to make the first weeks or even months a lot easier.

Not the answer you're looking for? Browse other questions tagged .