Career advice -- How much math for physics?

[Mwett]

Good evening,
I'm currently a high school student and I will have to make a decision for my studies very soon. I'm quite interested in physics and often watch documentaries / read books about it (especially about cosmology, quantum mechanics,...). But I wonder if the math wouldn't be too difficult for me if I chose to study in this field. I'm not especially bad at math but I'm not a genius either.
I am thus asking if some other studies involve physics but with less math.
Thanks already.PS: Sorry for my English. I'm from Belgium

 

[vinicius0197]

Hey, welcome to the forum.
First of all, I'm not a physics student. I'm a student of MechE, but I do have some friends in physics and I think I know a little bit about the course.
Math is, of course, very important, but you don't have to be a genius either. You will probably start with Calculus, and I sugest that you give a previous look at it before you decide. Search for the disciplines you will be studying at college.

I don't think you will find any studies in physics with little mathematics... Physics isn't math, but you have to understand math and be able to use it in you physics studies. I really recommend that you give a fair look at calculus - derivatives, integrals - and try to apply that to the simple Newtonian mechanics that you learn at high school. Go after a introductory calculus-based physics textbook

 

[micromass]

Good evening,
I'm currently a high school student and I will have to make a decision for my studies very soon. I'm quite interested in physics and often watch documentaries / read books about it (especially about cosmology, quantum mechanics,...). But I wonder if the math wouldn't be too difficult for me if I chose to study in this field. I'm not especially bad at math but I'm not a genius either.
I am thus asking if some other studies involve physics but with less math.
Thanks already.PS: Sorry for my English. I'm from Belgium

Hello Mwett. I am from Belgium too, so I'm very familiar with the education system here. So if you wish to discuss something, please ask.
First of all, what does "not bad at math" mean? You don't need to be a genius to do math/physics in university. It just takes hard work. If you are unwilling to do mathematics, but still want to go study something with physics, then any "university" education is basically out. You can still do what we call "high school" (hogeschool/haute ecole).

 

[ModusPwnd]

Math is the language of physics. Trying to study physics while minimizing your math is like trying to study literature while minimizing your ability to read and write.

 

[Mwett]

Hello Mwett. I am from Belgium too, so I'm very familiar with the education system here. So if you wish to discuss something, please ask.
First of all, what does "not bad at math" mean? You don't need to be a genius to do math/physics in university. It just takes hard work. If you are unwilling to do mathematics, but still want to go study something with physics, then any "university" education is basically out. You can still do what we call "high school" (hogeschool/haute ecole).

First of all, thanks to all of you for the advice.
I suppose you're from Flanders, I'm from down south :) And my school is not really good, we've never seen much physics (2h/week) since my science teacher is more into biology... So I can't really make a good opinion of the math required for further physics studies.
I'm quite good at math for the moment, but i fear that it won't be enough later. Even though I do like the way of thinking in math.
I was also maybe thinking about chemistry, since I heard that you could do a specialization in physical chemistry. But I don't really know, I'm more into physics.

Thanks Vinicius, I already have a calculus and physics book from a friend and I will look further into it.

 

[S.G. Janssens]

To the Belgians in this topic: How easy or difficult is it in Belgium these days to move from one degree program to the other during or right after the first bachelor year of university? In The Netherlands, this used to be quite well possible (especially when switching between physics, mathematics and chemistry, and to some extent also cs). Now it has become a bit more complicated, due to rules designed to "motivate" students to complete the degree faster.

 

[glaucousNoise]

Quantum mechanics essentially boils down to linear algebra and 19th century calculus. There is a lot of flamboyant, fluffy formalism from the math department which pokes its head up every now and then but is mostly just ignored, and rarely recommended as a supplemental course. I don't know as much about quantum field theory or general relativity but my understanding is that work that actually relates to observable reality boils down to bean counting on super computers and involves only a dash of exotic math like differential geometry or abstract algebra which does not require taking courses in either subject.

Machine learning, statistics, numerical methods, data structures, and other forms of computer science/applied math/statistics are by far the most useful supplements which, at least in America, are often a very malnourished part of the physics curriculum, particularly given how the vast majority of physicists these days are data scientists of one flavor or another (even if they work in academia).

 

[S.G. Janssens]

Quantum mechanics essentially boils down to linear algebra and 19th century calculus. There is a lot of flamboyant, fluffy formalism from the math department which pokes its head up every now and then but is mostly just ignored, and rarely recommended as a supplemental course. I don't know as much about quantum field theory or general relativity but my understanding is that work that actually relates to observable reality boils down to bean counting on super computers and involves only a dash of exotic math like differential geometry or abstract algebra which does not require taking courses in either subject.

Let me be to the point then.

The above is factually wrong and misleading, as anybody who is merely slightly familiar with modern theoretical research in these fields of physics (even if just at the advanced undergraduate or beginning graduate level) will be able to attest. In my opinion, it constitutes bad advice and does a disservice to the OP.

 

[vinicius0197]

I suppose you're from Flanders, I'm from down south :) And my school is not really good, we've never seen much physics (2h/week) since my science teacher is more into biology... So I can't really make a good opinion of the math required for further physics studies.
I'm quite good at math for the moment, but i fear that it won't be enough later. Even though I do like the way of thinking in math.

My school wasn't good either. I had really poor math teachers during high school, so I had to learn by myself. Even so, I'm doing MechE now, and I'm really loving the mathematics I'm seeing there. Calculus, linear algebra, ODEs, you will learn all that stuff at the beginning.

I don't know how is the educational system in Belgium, but where I study, physics has the highest dropout rate among all courses. After all, it's a very difficult course and many students get there without knowing what they will face.

 

[glaucousNoise]

Let me be to the point then.

The above is factually wrong and misleading, as anybody who is merely slightly familiar with modern theoretical research in these fields of physics (even if just at the advanced undergraduate or beginning graduate level) will be able to attest. In my opinion, it constitutes bad advice and does a disservice to the OP.

well, I've taken quantum at the graduate level and work in computational quantum chemistry/biology among other things...

The big caveat you seem to be ignoring is whether or not what the OP wants to do ultimately connects to real world data. Sure, if you munge through Physical Review D or the Journal of Mathematical physics, you'll find many a paper which employs exotic math but which has nothing to do with real world data. Try the Journal of Chemical physics or Journal of Chemical Theory and Computation and you'll find far fewer such papers, which I think says quite a bit about the relative scientific quality of such journals.

 

[micromass]

well, I've taken quantum at the graduate level and work in computational quantum chemistry/biology among other things...

The big caveat you seem to be ignoring is whether or not what the OP wants to do ultimately connects to real world data. Sure, if you munge through Physical Review D or the Journal of Mathematical physics, you'll find many a paper which employs exotic math but which has nothing to do with real world data. Try the Journal of Chemical physics or Journal of Chemical Theory and Computation and you'll find far fewer such papers, which I think says quite a bit about the relative scientific quality of such journals.

This is a very unscientific approach. Sure, you don't need exotic math in QM. And sure, many people can do fine without advanced math in QM. But you are confusing "anecdotal evidence" with "actual evidence". Just because you don't need advanced math, doesn't mean that nobody will. As you yourself admitted, you don't know much about QFT or other stuff. So you should not make statements like this.

 

[Mwett]

Alright, thank you Krylov. Fortunately, because I do like at least a little more math than bean counting...

 

[Mwett]

My school wasn't good either. I had really poor math teachers during high school, so I had to learn by myself. Even so, I'm doing MechE now, and I'm really loving the mathematics I'm seeing there. Calculus, linear algebra, ODEs, you will learn all that stuff at the beginning.

I don't know how is the educational system in Belgium, but where I study, physics has the highest dropout rate among all courses. After all, it's a very difficult course and many students get there without knowing what they will face.

What is MechE ? I'm not familiar with the abbreviations.
When you say physics has the highest dropout rate, does that mean you have to be really clever and/or hardworking to succeed or just many people choose it but realize it's not their thing.

 

[micromass]

What is MechE ? I'm not familiar with the abbreviations.
When you say physics has the highest dropout rate, does that mean you have to be really clever and/or hardworking to succeed or just many people choose it but realize it's not their thing.

MechE is mechanical engineering. In Belgium, in order to study that, one would like have to enroll as a civil engineer and then choose a speciality as a MechE later. Or one might be able to study it in a "high school". In contrast to the US, engineering (at university) in Belgium is a lot more difficult than either physics or math, as it is very rigorous in physics and math and has an extremely high workload.

 

[Mwett]

OK. I have considered engineering but I think that the applications are too practical for me, I'd rather have something more theoretic.

 

[micromass]

OK. I have considered engineering but I think that the applications are too practical for me, I'd rather have something more theoretic.

OK, but more theoretic kind of means more math.

Can you tell me exactly which math you're very comfortable with and which math you should be comfortable with by reviewing a bit?

 

[Mwett]

I know that.. That's why I've got a problem.
I don't really have problems now, since we haven't seen much (currently seeing log and exponentials). I'm quite comfortable with everything for the moment but I feel like I'm going to have trouble later. I was told it was very different from what we're seeing in high school.

 

[micromass]

I know that.. That's why I've got a problem.
I don't really have problems now, since we haven't seen much (currently seeing log and exponentials). I'm quite comfortable with everything for the moment but I feel like I'm going to have trouble later. I was told it was very different from what we're seeing in high school.

Which year are you in now? In how many years will you going to university?

 

[Mwett]

It's my last year before University.

 

[glaucousNoise]

This is a very unscientific approach. Sure, you don't need exotic math in QM. And sure, many people can do fine without advanced math in QM. But you are confusing "anecdotal evidence" with "actual evidence". Just because you don't need advanced math, doesn't mean that nobody will. As you yourself admitted, you don't know much about QFT or other stuff. So you should not make statements like this.

The evidence was provided in the form of two journals in which one can find papers which successfully model data. A statistical analysis of such papers, I predict, would find practically no papers which are making progress on real world problems by making the mathematics more abstract and convoluted, since making the mathematics more abstract and convoluted, intuitively, should retard rather than enhance progress. By contrast, I argued, with evidence in the form of two journals, that thumbing through their pages would find hardly any cases where real world data was modeled in a better fashion; in fact, many of the papers wouldn't model any data at all, which is should make the OP extremely concerned about the nature of the fields in question.

Alright, thank you Krylov. Fortunately, because I do like at least a little more math than bean counting...

It's all discrete bean counting at the end of the day if you believe in the scientific method. Differential equations may seem fancy but they wind up as discretized difference equations 99% of the time. The best bang for your buck comes from learning how to program a computer to more efficiently and accurately count said beans, which involves a combination of knowledge about algorithms and the artful ability to make correct assertions about the beans in question, which is not a skill that can be taught in any course.

 

[micromass]

You're in your last year now, and you're only seeing logs and exponentials now? That is not good. Not good at all.
I take it you have never encountered stuff like derivatives and integrals then? And what about trigonometry (sine, cosine stuff)?

Listen, it's not too late you for yet. But you will have to put in a lot of effort right now to be able to be prepared for university. I would advice you to get some good book on "calculus" and also on "general physics" and study it very deeply and put in much effort in this. Otherwise, you will not make it in time. Belgian universities are not very forgiving if you lack prerequisites.

 

[micromass]

It's all discrete bean counting at the end of the day if you believe in the scientific method. Differential equations may seem fancy but they wind up as discretized difference equations 99% of the time. The best bang for your buck comes from learning how to program a computer to more efficiently and accurately count said beans, which involves a combination of knowledge about algorithms and the artful ability to make correct assertions about the beans in question, which is not a skill that can be taught in any course.

Spoken like a true computational physicist. Now can you please stop hijacking this thread with your rubbish?

 

[vinicius0197]

What is MechE ? I'm not familiar with the abbreviations.

Mechanical Engineering.

When you say physics has the highest dropout rate, does that mean you have to be really clever and/or hardworking to succeed or just many people choose it but realize it's not their thing.

Many people just realize that they had a fanciful idea about the course and decide to quit, but like I said, it's a difficult course. It's not impossible, but it is difficult. You really have to like what you are studying, and I would say that is more important to be hardworking than clever. I know a lot of people there are clever, but lazy, and hardworking people overcome them.

I think it's more about being applied. Are you certain that you have the profile of a physicist? Think about this situation: you are in the lab, trying to attest to the validity of the law of ideal gases, more know as PV = nRT. You can do that with a adjustable mercury barometer. You can then decrease the volume of a column of air inside the barometer, raising the pressure as consequence, keeping the temperature constant. So you keep pressure constant, and see the dependece between temperature and volume. You can then make some curve fitting, adjust all your data and stare at some beautiful results. You get a function for the volume in function of the temperature, and if you extrapolate the volume to zero, you find the zero absolute. Isn't that awesome? It's a simple example, but if you like doing even that, probably physics is the path for you.

 

[Mwett]

You're in your last year now, and you're only seeing logs and exponentials now? That is not good. Not good at all.
I take it you have never encountered stuff like derivatives and integrals then? And what about trigonometry (sine, cosine stuff)?

Listen, it's not too late you for yet. But you will have to put in a lot of effort right now to be able to be prepared for university. I would advice you to get some good book on "calculus" and also on "general physics" and study it very deeply and put in much effort in this. Otherwise, you will not make it in time. Belgian universities are not very forgiving if you lack prerequisites.

We started trigonometry two years ago and continued last year (formulas for sum of sinuses, difference, product,...), we also saw derivatives last year, integrals is in the program for this year, probably as soon as we're finished with logarithms. This year we also saw matrices and complex numbers.
I already borrowed a calculus book, three general physics books and one book about discrete and combinatorial mathematics (don't know if useful, my friend said I could need it if I wanted to do programming). I have to look further into them.

 

[Mwett]

Mechanical Engineering.Many people just realize that they had a fanciful idea about the course and decide to quit, but like I said, it's a difficult course. It's not impossible, but it is difficult. You really have to like what you are studying, and I would say that is more important to be hardworking than clever. I know a lot of people there are clever, but lazy, and hardworking people overcome them.

I think it's more about being applied. Are you certain that you have the profile of a physicist? Think about this situation: you are in the lab, trying to attest to the validity of the law of ideal gases, more know as PV = nRT. You can do that with a adjustable mercury barometer. You can then decrease the volume of a column of air inside the barometer, raising the pressure as consequence, keeping the temperature constant. So you keep pressure constant, and see the dependece between temperature and volume. You can then make some curve fitting, adjust all your data and stare at some beautiful results. You get a function for the volume in function of the temperature, and if you extrapolate the volume to zero, you find the zero absolute. Isn't that awesome? It's a simple example, but if you like doing even that, probably physics is the path for you.

I would absolutely love to do this. I already have a summer job (which is more like a intership) where I get to do set-ups with lasers to test some car parts and I really appreciate it.

 

[micromass]

We started trigonometry two years ago and continued last year (formulas for sum of sinuses, difference, product,...), we also saw derivatives last year, integrals is in the program for this year, probably as soon as we're finished with logarithms. This year we also saw matrices and complex numbers.
I already borrowed a calculus book, three general physics books and one book about discrete and combinatorial mathematics (don't know if useful, my friend said I could need it if I wanted to do programming). I have to look further into them.

OK, this is more reassuring. It is just weird since logarithms are usually covered way before the final year. Things must have changed since I was in high school.
Anyway, I have studied at three different (flemish) universities. So I am very familiar to what physics students tend to get in Belgium. The first year of university will cover mathematical analysis. This is usually very different from calculus as seen in high school. So my advice is to get some familiarity with analysis and proofs already. Study a general calculus book and general physics books will not do you much good now. Try to get an introduction to mathematical analysis and work through that, and also try to get more familiar to proofs. As for physics, it usually starts at university from the basics but at an accelarated pace. So if you are already familiar with general physics in high school, then I advice you to study a more indepth text. I suggest you get Kleppner & Kolenkow and work through that. It will not be easy, but it will be a better preparation than any general physics book will give you at this stage (provided you already have seen quite some physics in high school).

 

[Mwett]

OK, this is more reassuring. It is just weird since logarithms are usually covered way before the final year. Things must have changed since I was in high school.
Anyway, I have studied at three different (flemish) universities. So I am very familiar to what physics students tend to get in Belgium. The first year of university will cover mathematical analysis. This is usually very different from calculus as seen in high school. So my advice is to get some familiarity with analysis and proofs already. Study a general calculus book and general physics books will not do you much good now. Try to get an introduction to mathematical analysis and work through that, and also try to get more familiar to proofs. As for physics, it usually starts at university from the basics but at an accelarated pace. So if you are already familiar with general physics in high school, then I advice you to study a more indepth text. I suggest you get Kleppner & Kolenkow and work through that. It will not be easy, but it will be a better preparation than any general physics book will give you at this stage (provided you already have seen quite some physics in high school).

In physics we're currently seeing waves (mechanical and later electromagnetic) and that's all we're going to see this year.. Last years we've mainly seen gravity, electrostatics, speed and acceleration.
Speaking of Universities, are there any recommendations ? Wallonia or Flanders, I speak both (quite) good.

 

[glaucousNoise]

Spoken like a true computational physicist. Now can you please stop hijacking this thread with your rubbish?

so, what you're trying to say is, you are not a physical scientist, and therefore, are not qualified to be giving the OP advice on what subjects are relevant to physical scientists?

At any rate the OP appears to be a starry eyed philosopher attracted to physics as so many are by "documentaries and [popular science] books" so s/he probably is beyond helping anyway.

 

[micromass]

In physics we're currently seeing waves (mechanical and later electromagnetic) and that's all we're going to see this year.. Last years we've mainly seen gravity, electrostatics, speed and acceleration.
Speaking of Universities, are there any recommendations ? Wallonia or Flanders, I speak both (quite) good.

There are quite a lot of differences between the universities. However, the visitation committees make sure that all universities do have about the same level. So you won't go wrong in any university.
However, there are some important distinction between universities. For example, there are universities which are very small-scaled (eg the Vrije Universiteit Brussel has very small class sizes), versus very large universities like the Katholieke Universiteit Leuven. This distinction is very important in my opinion. Small-scaled institutions will typically allow you to have a very very close contact with professors. It happened a lot that I could just walk in some professors desk and talk about some random stuff, and they would enjoy this quite a bit (although it does depend on the professor). In large universities, there is a way more formal distinction between professor and student. But those universities do have more resources like money.
Also, the kind of education you receive will be a quality education is all institutions you choose. But they will typically have very different focus. This will become apparent only very gradually, but it may end up being very important. I can sadly enough not tell you much about the focus of different universities. But you should google the "visitatiecommissie fysica" (or whatever it is in french) and read it through carefully. You will get slight hints on what different universities think is important, for example, you will find that one university might favour mathematics more, while others favour experimentation more (for example).

 

[micromass]

so, what you're trying to say is, you are not a physical scientist, and therefore, are not qualified to be giving the OP advice on what subjects are relevant to physical scientists?

Did I say that?

At any rate the OP appears to be a starry eyed philosopher attracted to physics as so many are by "documentaries and [popular science] books" so s/he probably is beyond helping anyway.

Lose the attitude dude. We know who you are. It's been very obvious to all of us ever since you returned. You won't last very long yet again if you keep this up.

 

[Mwett]

Thanks a lot for the advice micromass.
Do you know if some universities in Belgium have a research program ? Just for information.

 

[micromass]

Thanks a lot for the advice micromass.
Do you know if some universities in Belgium have a research program ? Just for information.

What do you mean with "research program"? You mean whether the physicists at the university perform research? Yes, all of them do.

 

[vinicius0197]

You're in your last year now, and you're only seeing logs and exponentials now? That is not good. Not good at all.
I take it you have never encountered stuff like derivatives and integrals then? And what about trigonometry (sine, cosine stuff)?

Educational system in Belgium must be much different from Brazil. Here, students only get to see derivatives and integrals at college.

Tipically, last year in high school would cover complex numbers, probability and statistics, analytical geometry and combinatory analysis, with matrices, trigonometry, exponentials and logarithms being taught the year before.

 

[Mwett]

What do you mean with "research program"? You mean whether the physicists at the university perform research? Yes, all of them do.

During their studies or after? In some Universities they have some students working as researchers for the school after their studies.

 

[micromass]

During their studies or after? In some Universities they have some students working as researchers for the school after their studies.

Yes, this seems very popular in the US. But it is almost unheard of in Belgium, as far as I'm aware. It's certainly not as popular here as in the US, and if it happens at all then it's just a minority.
So you'll have to contact different professors for this. But don't be surprised if they look at you funny.