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


by R.P.F.
Tags: competitive, field, math, physics
Begoner
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#19
Jul17-11, 02:37 AM
P: 4
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.
R.P.F.
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#20
Jul19-11, 03:25 PM
P: 210
Quote Quote by Ryker View Post
Sorry for going against your wishes, but...

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
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.


Quote Quote by hadsed View Post
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. :)

Quote Quote by Klockan3 View Post
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.
R.P.F.
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#21
Jul19-11, 03:33 PM
P: 210
Quote Quote by deRham View Post
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.

Quote Quote by Begoner View Post
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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#22
Jul19-11, 03:59 PM
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Quote Quote by R.P.F. View Post
Maybe I should restrict the comparison to the field of pure math and experimental physics?
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.
R.P.F.
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#23
Jul19-11, 04:26 PM
P: 210
Quote Quote by George Jones View Post
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...

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.
deRham
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#24
Jul19-11, 09:27 PM
P: 412
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.
Begoner
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#25
Jul20-11, 01:37 PM
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Quote Quote by R.P.F. View Post
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.
nlsherrill
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#26
Jul20-11, 07:27 PM
P: 322
looks like this thread is turning into another "math vs. physics" debate. In regards to the OP's question, there are some areas of physics that are more competitive than some areas of mathematics, and there are some areas of mathematics that are more competitive than some areas of physics. They are both very, very difficult areas of study and shouldn't be compared because they ARE different.
fhewizard
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#27
Jul20-11, 10:57 PM
P: 1
I disagree when it comes to undergrad. I am also a double major physics and math and to me linear algebra was my hardest class (b/c I didn't know how to do proofs then) and it just gets easier from there. Whereas in physics it only gets harder. Quantum mechanics and electronics are one of the hardest while classical mechanics and thermodynamics are not as difficult. I agree with you a grad PhD. student in physics probably has it easier than one in mathematics (because they have to originate their own proofs while in physics you can run experiments), but undergrad is definitely not the case.
deRham
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#28
Jul20-11, 11:21 PM
P: 412
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.
Well, or an idealization of something real-world. Textbook physics isn't quite real world ;) but I get your drift, and it was part of my point too. You do have to do quite a bit more converting in physics.

In advanced mathematics, the level of converting is stepped up significantly, but it's usually from one kind of theoretical to another kind - it's equally hard, but different.
Ryker
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#29
Jul21-11, 01:01 AM
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Quote Quote by fhewizard View Post
I agree with you a grad PhD. student in physics probably has it easier than one in mathematics (because they have to originate their own proofs while in physics you can run experiments), but undergrad is definitely not the case.
Yeah, I suppose experiments do just hang out in hallways waiting for Physics PhD's to pick them up and run them.
Sankaku
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#30
Jul21-11, 11:25 AM
P: 714
Yup, math is so easy that I just head some of the psychology students say "Hey man, lets take this measure theory course, I hear it is an easy A!"

:-P

On a more serious note, I think Physics has much more romanticism associated with it. Some evidence is the existence of this forum, rather than an equivalent math forum. There are probably 20 physics documentaries made and 10 popular books written for every one about mathematics. Perhaps the expectations of people lured into physics are different than those who choose mathematics. I agree with the assessment of 'different' rather than 'harder.'

However, the sociology of teaching comes into play. Universities in the early part of the century had a mandate to get engineers (and later, physicists) trained up for the emerging industrial economy. Courses had to be functional and you didn't want to crush too many of your students. Mathematics, on the other hand, has always struggled with its elitist past and many courses used to be just plain grueling. This wasn't because the subject was harder, just that profs taught it much faster and without as much allowance for people who didn't get it right away. I like to think that this has been changing...
hadsed
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#31
Jul21-11, 11:37 PM
P: 496
Quote Quote by Sankaku View Post
However, the sociology of teaching comes into play. Universities in the early part of the century had a mandate to get engineers (and later, physicists) trained up for the emerging industrial economy. Courses had to be functional and you didn't want to crush too many of your students. Mathematics, on the other hand, has always struggled with its elitist past and many courses used to be just plain grueling. This wasn't because the subject was harder, just that profs taught it much faster and without as much allowance for people who didn't get it right away. I like to think that this has been changing...
I'd also like to add that I feel that math people are more likely to buy into the whole child prodigy supergenius stuff. I guess the super abstract thinking makes sense with insanely creative minds in abnormal circumstances, but I think it gets to an unfair level. Physicists like to point to Richard Feynman and his IQ score of 129, or the fact that Einstein was basically thought to be mentally challenged when he was young. We can look at these people and say, look! they were geniuses. But if you're not Gauss or Euler by the time you're 14, you're never going to be. Further proof is the fact that older mathematicians don't win Field's medals. Though I don't discount the fact that maybe the abstract thinking could be linked to more abnormal cases, like I said before. Still, it can get to be disappointing sometimes.
Ryker
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#32
Jul22-11, 12:03 AM
P: 1,089
Quote Quote by hadsed View Post
Further proof is the fact that older mathematicians don't win Field's medals.
Quote Quote by wikipedia
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age...
Sankaku
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#33
Jul22-11, 12:36 AM
P: 714
Quote Quote by hadsed View Post
...or the fact that Einstein was basically thought to be mentally challenged when he was young.
From reading Isaacson's biography of Einstein, I believe this is a complete myth. He was consistently top of his class in primary school. I suggest you read the book - it is very well written.

This does not invalidate your general point about obsession with genius, however. It is unhealthy and surfaces far too much in these forums...
hadsed
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#34
Jul22-11, 02:50 PM
P: 496
Quote Quote by Ryker View Post
Alright alright, but it's not typical, let's say that.

Anyway, I was generalizing to some degree, but I think everyone recognizes the whole spiel I was trying to describe.
Ryker
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#35
Jul22-11, 03:24 PM
P: 1,089
Yeah, can't comment on that, since I don't know today's big names and how the field of mathematics research actually works. I have a suspicion a lot of what you described is also just false public perception. I can't back it up, though.
Leptos
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#36
Jul22-11, 10:07 PM
P: 172
Notice how few people in modern day get mentioned. And yet we have to keep in mind that the world population is larger than ever, and education's penetration only increases over time. It's possible in the early 1900s that the greatest minds didn't even get educated, but today that's far less likely to occur for obvious reasons.


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