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The field of math being more competitive than the field of physics?

  • Thread starter R.P.F.
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Hello guys,

Before I start, I just want to say the what I am going to say below is just my personal opinion. I'd like to hear about it if you disagree. I just hope no one gets offended by this.

I am a math and physics double major and thus spend plenty of time in both departments. Some math majors would take advanced-level physics classes like quantum, QFT and GR and they would end up doing pretty well in the class. When physics majors take advanced-level math classes like real analysis and abstract algebra, they would have a pretty hard time. They usually struggle through the first semester with a 3.3 or 3.0 and you never see them again the second semester. Of course there are exceptions. I know several physics majors who have done well in advanced-level math classes. But in general, I get this feeling that physics majors in my college are not as good as math majors intellectually. (Again, this is just my personal opinion. Please don't be upset or offended by this.)

I first thought this difference was restricted to my school until the time of applying to REUs came. I know several physics majors with GPAs around 3.4(3.3 is the average) got into REUs. I also heard that plenty of math majors with GPAs around 3.8 did not get into anywhere. I know recommendations might be a problem but as far as I know they were great students and should have received very complimentary recommendations. I don't know about physics REUs, but I feel that math REUs are getting unreasonably competitive. The SMALL REU received over 400 applications for 21 positions, half of which were filled by Williams students....

So is this true in general? The field of math is more competitive than the field of physics?
 

I like Serena

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I think it's more a matter of interest and affinity.

People into physics are more into applied math than fundamental math.
People into math that show an interest in advanced physics seem to prefer applied math.

See the connection?

The fact that you're doing a double major in math and physics suggests you prefer applied math as well. Do you? And how much do you like doing proofs in abstract algebra?
 
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I think it's more a matter of interest and affinity.

People into physics are more into applied math than fundamental math.
People into math that show an interest in advanced physics seem to prefer applied math.

See the connection?

The fact that you're doing a double major in math and physics suggests you prefer applied math as well. Do you? And how much do you like doing proofs in abstract algebra?
:rofl: I am actually more into pure math and abstract algebra happens to be my FAVORITE class in college. It is definitely the most challenging class I have ever had. I never had a weekend the past school year because of the class. 'It's alright because I like the way it hurts.'. But yeah I see what you mean. We have very few applied math classes in my school so that might be why that physics majors don't get to show their mathematical skills.
 
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I agree with ILS. It's a matter of what you like. Many people I know (including me) love abstract and pure mathematics, but are pretty useless when it comes to applications and applying the knowledge. If you have an affinity with pure mathematics, then you like details and proofs. If you don't like details (like most physicists), you will not do good in pure mathematics. But that doesn't mean you're intellectually less then a pure mathematician, quite the contrary! I always feel that physicists are much smarter than mathematicians, because they can combine the intuition with mathematical skills.

All I want to say: put a physicist in a pure math class, and he will not do well. Put a mathematician in a lab, and he will also not do well. The real smart people are the ones that do well in both cases.
 

I like Serena

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Hey proof-guy! :smile:

I was just thinking of you, and how I tend to leave the mathematical proof threads more and more to you!
 
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Hey proof-guy! :smile:

I was just thinking of you, and how I tend to leave the mathematical proof threads more and more to you!
But... why would you do that?? Proofs are the most fun :biggrin:
 
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I agree with ILS. It's a matter of what you like. Many people I know (including me) love abstract and pure mathematics, but are pretty useless when it comes to applications and applying the knowledge. If you have an affinity with pure mathematics, then you like details and proofs. If you don't like details (like most physicists), you will not do good in pure mathematics. But that doesn't mean you're intellectually less then a pure mathematician, quite the contrary! I always feel that physicists are much smarter than mathematicians, because they can combine the intuition with mathematical skills.

All I want to say: put a physicist in a pure math class, and he will not do well. Put a mathematician in a lab, and he will also not do well. The real smart people are the ones that do well in both cases.
Yeah I agree with the intuition part. The more I study both subjects, the more different I find mathematical intuition and physical intuition are. I barely have any physical intuitions. I use mathematical muscles to solve problems.
 
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But still..anyone wants to answer the question about competitiveness? Maybe I should restrict the comparison to the field of pure math and experimental physics?
 
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Who really cares. They're both definitely really hard. They both help their own field grow and they're both intellectually stimulating.
 
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Who really cares. They're both definitely really hard. They both help their own field grow and they're both intellectually stimulating.
Well, as I mentioned, it is kind of hard to get into a math REU. So if physics REUs are in a more reasonable situation, I might apply to physics REUs since I am interested in both math and physics. Or I might choose to be a physicist instead of a mathematician. So if you ask me, then yes, I do care.
 
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Why not just apply to the one you're interested in the most? Wait a better idea is why not apply to both for grad school? You like both alot (assume) and they're both respectable. If you get accepted into both, choose the one you like the most.
 
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Why not just apply to the one you're interested in the most? Wait a better idea is why not apply to both for grad school? You like both alot (assume) and they're both respectable. If you get accepted into both, choose the one you like the most.
I was actually seriously thinking about applying to both for grad school. But that means taking two GREs which sounds pretty unpleasant. Also I think that might make me seem unfocused. So I don't know...:uhh:
 
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Not to mention applying to generally double the amount of grad schools, which almost doubles the work involved. It's more "concentrate on one" than "do both, decide later." The latter strategy only seems to apply for maybe the first few years of undergrad. Later on, if you keep splitting your time equally, you'd have the jack-of-all-trades/master-of-none issue.
 
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But still..anyone wants to answer the question about competitiveness? Maybe I should restrict the comparison to the field of pure math and experimental physics?
Sorry for going against your wishes, but... :biggrin:

To add to what others have said, I think one of the reasons for your observation - if it matches reality, that is - might also be that some physics courses, even at an advanced level, are more accessible in terms of them being tough, but self-consistent. That is, you need great reasoning skills, but most or all of the material is given within the context of the course. On the other hand, depending on the lower-level courses those physics majors have taken, there might be too big of a jump from those to advanced courses. For example, if they haven't been exposed to proofs and/or lack "mathematical maturity" (whatever that means) they could find it harder doing well in a course that is really hard in and of itself, but also requires the prerequisite knowledge they don't have.

Note that I haven't taken any advanced physics or math courses yet, but I could see this being one of the reasons. There's a chance this stab in the dark is a miss, though :smile:

edit: To take another stab in the dark, perhaps math REUs seem more competitive due to higher value being placed on GPA. Perhaps in physics, it's perceived that someone can have a lower GPA, but still be a great physicist due to, say, quality research work or other stuff that person has done. On the other hand, with maths I'd assume that it's seen that if you can't do well in your courses then you aren't the greatest at maths. There's just no "oh, I'm just not the greatest at theory, but I can come up with ingenious experiments" there. Not to my knowledge, at least. So in that sense, math REUs aren't more competitive, it's just that more emphasis is put on GPA, which is a factor that you - as an outsider to the selection process - most readily observe.
 
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Not to mention applying to generally double the amount of grad schools, which almost doubles the work involved. It's more "concentrate on one" than "do both, decide later." The latter strategy only seems to apply for maybe the first few years of undergrad. Later on, if you keep splitting your time equally, you'd have the jack-of-all-trades/master-of-none issue.
There are some fields in physics/math/computer science that require knowledge of all three. I'm working on applications of Bose-Einstein condensate theory (you could call it condensed matter theory or quantum optics theory) to quantum computing. Probably in graduate school I'd like to focus on the more theoretical aspects of it (so that would probably fall under quantum information theory), but this requires knowledge of a lot of subjects in computer science and math (though mostly the former), though the physics also pretty important (and is sometimes necessary). Things like quantum algorithms requires knowledge of algorithms in terms of CS but also how a quantum computer is supposed to work from a physics perspective, or cryptography requires some knowledge of set/number theory for quantum encryption. For this reason, I'll probably apply to both physics and computer science grad schools (though since I'm doing physics research, physics departments will probably be easier to get into for me).

I think quantum computing is one of the more obvious inter-disciplinary subjects, but it really depends on the sub-field too. Everyone knows that particle theory can require a thorough knowledge of abstract algebra, but in some cases, while doing string theory, knowing the fundamentals of physics is much more important than a highly esoteric type of mathematics.
 
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In general the closer you get to applications the less competition there is since there are more willing to pay you for it. I'd guess that the REU's you are talking about are mostly associated with applied physics or (if theoretical) solid state physics.
 
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Of course there are exceptions. I know several physics majors who have done well in advanced-level math classes. But in general, I get this feeling that physics majors in my college are not as good as math majors intellectually.
I think this varies hugely - I've heard the exact opposite being common for a different reason. I believe physics at the undergrad level requires more raw intuition and problem solving than does mathematics, which can require fewer leaps of intuition, and more can be achieved by just working systematically and following basic rules, learning the important theorems, etc.

I would say the reason for the phenomenon you observe might be the following - I think the kind of reasoning required in the undergraduate math major is very different from what is expected of almost any other semi-mathematical discipline (engineering, physics, etc). There is a raw barrier, which is getting past writing proofs and learning how to think very theoretically. Physics students never learned that, at least not typically. Whereas I think what subjects like engineering and physics require at the undergrad level is less mystical, less strange to the entering college student - it's hard, it's intimidating in terms of the intellectual commitment it requires, but it's more familiar territory. You're still down to earth to an extent - it makes sense that you're writing down equations to describe something physical. Whereas in math, I think undergrads get caught up not understanding why they're even studying what they are studying.

I would say on average, for someone with basic competency in both math and physics, the undergrad physics major is more taxing. But it's simply less common to have basic competency at math, I think, because of the nature of the subject.
 
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In general the closer you get to applications the less competition there is since there are more willing to pay you for it. I'd guess that the REU's you are talking about are mostly associated with applied physics or (if theoretical) solid state physics.
I second this. Along with what someone else said. The more experimental, the more open people are to letting you in without a perfect GPA. The more theoretical, the less of a chance you have to do "other things" to bolster your academic reputation.
 
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My experience has been the exact opposite. I've taken quite a few math classes and have never received less than an A- in any of them; however, in the one introductory physics course I took, I was lucky to scrape by with a C+. I think physics requires some knowledge about how things work in addition to purely abstract mathematical knowledge; moreover, some physics problems are Putnam-like, in that they require a clever insight, whereas a brute force approach works for many mathematical proofs. Also, quantitatively speaking, physics graduate students have a higher GRE score, on average, than math graduate students.
 
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Sorry for going against your wishes, but... :biggrin:

To add to what others have said, I think one of the reasons for your observation - if it matches reality, that is - might also be that some physics courses, even at an advanced level, are more accessible in terms of them being tough, but self-consistent. That is, you need great reasoning skills, but most or all of the material is given within the context of the course. On the other hand, depending on the lower-level courses those physics majors have taken,Note that I haven't taken any advanced physics or math courses yet, but I could see this being one of the reasons. There's a chance this stab in the dark is a miss, though :smile:
Yep. That is consistent with my observation. The students who stand out in an advanced physics class are usually math students who are interested in physics and physics students who have good mathematical sophistication.


There are some fields in physics/math/computer science that require knowledge of all three. I'm working on applications of Bose-Einstein condensate theory (you could call it condensed matter theory or quantum optics theory) to quantum computing. Probably in graduate school I'd like to focus on the more theoretical aspects of it (so that would probably fall under quantum information theory), but this requires knowledge of a lot of subjects in computer science and math (though mostly the former), though the physics also pretty important (and is sometimes necessary). Things like quantum algorithms requires knowledge of algorithms in terms of CS but also how a quantum computer is supposed to work from a physics perspective, or cryptography requires some knowledge of set/number theory for quantum encryption. For this reason, I'll probably apply to both physics and computer science grad schools (though since I'm doing physics research, physics departments will probably be easier to get into for me).

I think quantum computing is one of the more obvious inter-disciplinary subjects, but it really depends on the sub-field too. Everyone knows that particle theory can require a thorough knowledge of abstract algebra, but in some cases, while doing string theory, knowing the fundamentals of physics is much more important than a highly esoteric type of mathematics.
I really love the theoretical aspects of QIP. I am starting a small project on quantum linear optics. :)

In general the closer you get to applications the less competition there is since there are more willing to pay you for it. I'd guess that the REU's you are talking about are mostly associated with applied physics or (if theoretical) solid state physics.
I believe that is true. I worked a while for a professor who does experimental physics. I felt that I could have done the research without taking any college physics or math classes. It was mostly assembling apparatus taking measurements.
 
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I think this varies hugely - I've heard the exact opposite being common for a different reason. I believe physics at the undergrad level requires more raw intuition and problem solving than does mathematics, which can require fewer leaps of intuition, and more can be achieved by just working systematically and following basic rules, learning the important theorems, etc.

I would say the reason for the phenomenon you observe might be the following - I think the kind of reasoning required in the undergraduate math major is very different from what is expected of almost any other semi-mathematical discipline (engineering, physics, etc). There is a raw barrier, which is getting past writing proofs and learning how to think very theoretically. Physics students never learned that, at least not typically. Whereas I think what subjects like engineering and physics require at the undergrad level is less mystical, less strange to the entering college student - it's hard, it's intimidating in terms of the intellectual commitment it requires, but it's more familiar territory. You're still down to earth to an extent - it makes sense that you're writing down equations to describe something physical. Whereas in math, I think undergrads get caught up not understanding why they're even studying what they are studying.

I would say on average, for someone with basic competency in both math and physics, the undergrad physics major is more taxing. But it's simply less common to have basic competency at math, I think, because of the nature of the subject.
I think undergrad math also requires a lot of intuition. When you are given a problem, your intuition tells you where to go. Without mathematical intuition, you might not find the right theorems to use or the right field to search in. For examples, a lot problems can be solved easily topologically but are darn hard to solve algebraically. The mathematical intuition helps you recognize the problem and pick out the 'right' way to do it.
Of course physics also requires a whole lot of intuition. It is quite different from mathematical intuition though.

My experience has been the exact opposite. I've taken quite a few math classes and have never received less than an A- in any of them; however, in the one introductory physics course I took, I was lucky to scrape by with a C+. I think physics requires some knowledge about how things work in addition to purely abstract mathematical knowledge; moreover, some physics problems are Putnam-like, in that they require a clever insight, whereas a brute force approach works for many mathematical proofs. Also, quantitatively speaking, physics graduate students have a higher GRE score, on average, than math graduate students.
May I ask what are the most advanced math class you take? :)
 

George Jones

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Maybe I should restrict the comparison to the field of pure math and experimental physics?
:confused: :grumpy: Only experimental physics students are physics students?

I took a topology class that used Munkres as its text. There were two (and only two) physics students in the class, and they got the two highest marks on the final exam.
 
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:confused: :grumpy: Only experimental physics students are physics students?

I took a topology class that used Munkres as its text. There were two (and only two) physics students in the class, and they got the two highest marks on the final exam.
Easy, man. I was just saying *maybe* I should restrict the comparison to a smaller group because I know theoretical physics, experimental physics, applied math and pure math are very different...:tongue:

I definitely believe the situation varies a lot. Those two students must have already taken a bunch of advanced math classes before topology so they had the mathematical sophistication required. I believe that mathematical sophistication played an important role in their careers. :wink:
 
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When you are given a problem, your intuition tells you where to go. Without mathematical intuition, you might not find the right theorems to use or the right field to search in.
Like you said, the type of intuition mathematics requires is distinct from physics. And I think the basic point I made was that it seems that while both require intuition, at the undergraduate level, the physics seems to require more leaps. Mathematics exercises seem to be straightforward mostly once you have the idea of what the section is about, unless you register for an honors course or something, and are challenged with especially hard problems.

I think the heart of what I am saying is that mathematical intuition seems simply more systematic. Which means when the ideas presented are relatively manageable, which is generally true at the undergrad level, the major to those who are not opposed to thinking the math way requires a lot less work than many other technical ones.

Of course, when you get to higher level mathematics, quickly the students who can do it drop in number, because the pace at which you are expected to learn grows very rapid, and the level of mastery you are expected to have also deepens. A combo of greater technicality and deeper ideas makes mathematics infinitely more challenging - it is the depth of the ideas and translating them in technical detail that makes higher level math tough, not the leaps of intuition so much, at least as far as I can tell - I think the sort of intuition you employ changes very little as you go.

The thing is you can do a lot at the undergrad level with just fairly decent mathematical intuition.
 
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May I ask what are the most advanced math class you take? :)
I've taken my fair share of standard undergraduate courses, such as a course on linear algebra using Hoffman and Kunze, a course on topology (half point-set and half algebraic) using Munkres, and a course on measure theory using Stein. However, how advanced the courses themselves were doesn't matter; what does matter is the relative difficulty of the math courses I've taken as compared to the physics course I took. In this respect, the physics course was considerably more difficult: it required not only a theoretical understanding of the subject, but an ability to apply this understanding to concrete problems, aided by one's intuition about the physical world. In contrast, one simply needs a theoretical understanding of a mathematical subject: one needn't convert a real-world situation into mathematical formalism to arrive at a solution, but can simply manipulate formal statements until one arrives at a solution, never having to deal with reality in the process.
 

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