Can a background in applied math prepare me for a PhD in physics?

[FallenApple]

I have my degree in applied math( mostly diff eqs and prob theory) Mostly A's. I have done graduate work in statistics with a mixture of A's and B's. So my math background isn't lacking. However, I've only done two courses in physics. Intro mechanics and E&M both with A's.

At this point, how long would it take to self learn physics to a high enough of a level to get into a PhD program in physics.

I've already started on classical mechanics by Goldstein and it seems to be doable. but I'm learning it at a slow pace. E&M by Griffins, I am picking up on faster.

I've noticed on the GRE physics, for the topics that I do know, it's really easy. For example, I see a incline plane problem, yet it's much simpler than the incline plane problems I've done before, which are in accelerating elevators. So basically I can do 3 star problems from a text like Giancoli.

So given say a year and a half, can I learn all that is needed to start studying a PhD?

Now my problem is that I don't know how to get letters of recs. Virtually no physics professors.

 

[ZapperZ]

I have my degree in applied math( mostly diff eqs and prob theory) Mostly A's. I have done graduate work in statistics with a mixture of A's and B's. So my math background isn't lacking. However, I've only done two courses in physics. Intro mechanics and E&M both with A's.

At this point, how long would it take to self learn physics to a high enough of a level to get into a PhD program in physics.

I've already started on classical mechanics by Goldstein and it seems to be doable. but I'm learning it at a slow pace. E&M by Griffins, I am picking up on faster.

I've noticed on the GRE physics, for the topics that I do know, it's really easy. For example, I see a incline plane problem, yet it's much simpler than the incline plane problems I've done before, which are in accelerating elevators. So basically I can do 3 star problems from a text like Giancoli.

So given say a year and a half, can I learn all that is needed to start studying a PhD?

Now my problem is that I don't know how to get letters of recs. Virtually no physics professors.

Have you also looked at a typical qualifying exam questions? In other words, have you looked at this thread:

https://www.physicsforums.com/threa...if-my-bachelors-degree-isnt-in-physics.64966/ ?

Zz.

 

[Dr. Courtney]

It really depends on the PhD program you aspire to: its level of difficulty, whether they want to see accredited coursework in most of the undergrad physics courses (for admissions), and how accurate your assessment is of your current abilities.

I'd take the PGRE as soon as practical and use that as a gauge for how far you have to go when you talk to admissions folks and faculty at schools on your radar.

 

[FallenApple]

It really depends on the PhD program you aspire to: its level of difficulty, whether they want to see accredited coursework in most of the undergrad physics courses (for admissions), and how accurate your assessment is of your current abilities.

I'd take the PGRE as soon as practical and use that as a gauge for how far you have to go when you talk to admissions folks and faculty at schools on your radar.

I looked at it. I would not pass as of this point since I don't know enough of the topics. But of the topics that I do know, kinematics, forces ampres law etc, it seems simple. They are only a few steps at most. Find the e field at so an so location, find the direction of current due to lenzs law etc.

So I'm guessing since there's so many questions on the test, they aren't going to go too deep into making the questions multistage. But I'm not sure if they are going to do that for quantum releativity etc since I don't know enough to gauge.

Have you also looked at a typical qualifying exam questions? In other words, have you looked at this thread:

https://www.physicsforums.com/threa...if-my-bachelors-degree-isnt-in-physics.64966/ ?

Zz.

I've only looked at some first year mechanics qual questions. From columbia university I believe. One was finding the point of contact a sliding ladder loses touch with a wall and the angle in which this happens.The other was a sphere rolling up an unbolted incline (wedge of mass) where they both move together afterwards and I'm supposed to find the final velocity of the cm of sphere when it's v of cm is momentarily 0 relative to the motion of the wedge .

I used euler legragne and basic methods( conservation of x momentum and energy ) to do those and got the correct answers. But I don't know if these are considered difficult questions or whether they are freebies.

Oh and there was a collision problem of a rolling sphere and another sphere. This one wasn't that bad either.

The other questions I didn't know because I don't know the topics. Some of them involved matrices etc.
And I've only looked at an mechanics qual because I've haven't even opened a book on quantum, nor relativity. I'm not sure if the style of thinking on mech problems even remotely translates to those.

 

[mpresic]

Self learning is unlikely to lead to getting into a doctoral physics program. The best way would be to take a course in graduate mechanics, electrodynamics, (even if you have to pay for it yourself, and not sponsored by your employer) etc. Successful completion at such a course would also help you to get a recommendation from the professor. (By the way, physics graduate admissions committees should also regard good recommendations from mathematics professors in your applied math program approximately on par with physics professors) If a grad course in these subjects is unavailable, then perhaps an advanced undergraduate course will be well regarded by an admissions committee.

You ask about studying for a doctorate. In most schools, even admission into a graduate school is not credentialed enough to begin. After admissions, there are successful completion of graduate courses, and the (dreaded) qualifying exam completion before you can even begin in earnest. (Some students start research before successful completion of the exam).

A mathematician friend of mine chose another process you might consider. He worked and published in electromagnetic wave propagation (in random media) with physicists in the same and external organizations. He did not get a Ph D. in physics, but he did get to work in an area he liked at the same level along side with other physicists. He was regarded equally with the subject matter experts in the field, and isn't that more important. Perhaps you could leverage your background in differential equations and probability in a similar way. Actually EM wave propagation in random media (for example) uses differential equations and probability to a great extent.

(Of course this possibility requires a lot of legwork to find the right co-workers to work/publish with and convince them your effort can contribute)

In addition, you may be filling a niche that many physicists do not fill. I find many physicists today, have a limited background in solving partial differential equations analytically. It seems the computer (numerical analysis) has taken over these applications.

 

[Student100]

Why not aim for something more readily within reach of an applied mathematics degree? Such as anyone of the numerous mathematical physics or applied math programs?

It's certainly possible to go grad school for physics, but why sink all that extra time when you basically can contribute in those two areas above that are closely related?

Randomly googled a professor who works in MP: http://www.math.caltech.edu/~rlfrank/

Check out some of his publications, see if that type of research appeals to you. Look at others in different areas, etc.

 

[ZapperZ]

In addition, you may be filling a niche that many physicists do not fill. I find many physicists today, have a limited background in solving partial differential equations analytically. It seems the computer (numerical analysis) has taken over these applications.

This is a rather odd comment. In my experience, we do not solve these differential equations analytically because they are no analytical solutions! I'd like to see someone attempt to solve one of these equations analytically when we design a rf waveguide! Real-world problems are often not that simple!

Zz.

 

[FallenApple]

Self learning is unlikely to lead to getting into a doctoral physics program. The best way would be to take a course in graduate mechanics, electrodynamics, (even if you have to pay for it yourself, and not sponsored by your employer) etc. Successful completion at such a course would also help you to get a recommendation from the professor. (By the way, physics graduate admissions committees should also regard good recommendations from mathematics professors in your applied math program approximately on par with physics professors) If a grad course in these subjects is unavailable, then perhaps an advanced undergraduate course will be well regarded by an admissions committee.

You ask about studying for a doctorate. In most schools, even admission into a graduate school is not credentialed enough to begin. After admissions, there are successful completion of graduate courses, and the (dreaded) qualifying exam completion before you can even begin in earnest. (Some students start research before successful completion of the exam).

A mathematician friend of mine chose another process you might consider. He worked and published in electromagnetic wave propagation (in random media) with physicists in the same and external organizations. He did not get a Ph D. in physics, but he did get to work in an area he liked at the same level along side with other physicists. He was regarded equally with the subject matter experts in the field, and isn't that more important. Perhaps you could leverage your background in differential equations and probability in a similar way. Actually EM wave propagation in random media (for example) uses differential equations and probability to a great extent.

(Of course this possibility requires a lot of legwork to find the right co-workers to work/publish with and convince them your effort can contribute)

In addition, you may be filling a niche that many physicists do not fill. I find many physicists today, have a limited background in solving partial differential equations analytically. It seems the computer (numerical analysis) has taken over these applications.

I was thinking about studying for the qualifying exams and then show up and take to impress a university. Also, would research help?

Im not sure if I can take graduate courses as all the extension classes nearby are stuff like accounting, electronics etc. It's hard to take real classes.

I could go back for applied math. As long as the program has more of a physics/engineering bent to it. I don't want get stuck doing problems for biology or medical research.

As long as I actually learn the physics instead of solving random equations. For example, a while back I was coding hamlitonian monte carlo to estimate the mle of a distribution. I knew the idea of the math behind it, but I didn't understand the physics well enough to see how it connected. I understood it more after I looked into it and realized that I would rather understand how things work more fundamentally. Or the other time in my nonlinear dynamics class I was given an application of using eigenvalues for oscilating systems but it was in the context of having been already set up, so I didn't have to think deeply about.

Is it usual that applied mathematicians get to work on interesting physics problems?

Why not aim for something more readily within reach of an applied mathematics degree? Such as anyone of the numerous mathematical physics or applied math programs?

It's certainly possible to go grad school for physics, but why sink all that extra time when you basically can contribute in those two areas above that are closely related?

Randomly googled a professor who works in MP: http://www.math.caltech.edu/~rlfrank/

Check out some of his publications, see if that type of research appeals to you. Look at others in different areas, etc.

Well, here's what I was thinking. I have enough of a math background that I can handle some of the math in higher level physics. For example, why read lower level calc based quantum when I already have experience with advanced level linear algebra. I could just jump into a quantum text that has more advanced matrix calculations.
So I'm thinking that's why it's possible to just read through upper div texts in about a year or so. A lot of the topics are just rehashes of the same stuff but with more math and deeper concepts.

But I wonder if my assessment of this is correct.

 

[Student100]

Well, here's what I was thinking. I have enough of a math background that I can handle some of the math in higher level physics. For example, why read lower level calc based quantum when I already have experience with advanced level linear algebra. I could just jump into a quantum text that has more advanced matrix calculations.
So I'm thinking that's why it's possible to just read through upper div texts in about a year or so. A lot of the topics are just rehashes of the same stuff but with more math and deeper concepts.

But I wonder if my assessment of this is correct.

No one doubts your math background. You've had more math than I have, and you're probably much better at it too. The issue is that working through a couple upper division texts is not necessarily equivalent to an upper division education in physics. Neither in time invested solving problems, or breadth of study, these are important.

It's certainly doable, and with motivation you can grind through the texts, study for the PGRE, and get accepted somewhere, probably within 2ish years. So if you're dead set, you can do it.

I'm just wondering, why do it? Do you even know yourself? It seems late to want to jump from one science to another. You've probably not had any time to actually work with a physics research group, to see what actually goes on(it isn't neat and pretty, it's messy and ugly at times). Haven't had any physics instructor feedback or guidance, and on and on. You may discover you don't really care for physics, or physics research, in which case grad school becomes impossible to suffer through. Compound that with an ability, to right now, apply to graduate programs in applied mathematics and combine mathematics while studying physical models (certain physicists do this work too) and I don't see the point of extra time invested learning the breadth of undergrad physics with so many other unknowns.

I don't want to dissuade you per say, but these are things you have to ask yourself. It's doable.

As far as LOR, you will probably need math professors whom you did work with, or studied math applications relevant to physics write them for you. Email any you can think of now, while you're fresh in their memory. Talk to them, get their opinion, see if you can take courses at your at your previous university on a part time basis in physics. See if anyone has any work for you, etc.

 

[jtbell]

I was thinking about studying for the qualifying exams and then show up and take to impress a university.

Will a university actually let you do this, without already having been admitted to their graduate program? I'm genuinely curious. When I started grad school at Michigan, they did not have a written qualifying exam, so I had "only" an oral exam with the profs that I had chosen for my dissertation committee, after finishing most of my coursework. While I was there, Michigan did institute a written qualifying exam, but people in my entering year were grandfathered under the old rules.

 

[FallenApple]

Will a university actually let you do this, without already having been admitted to their graduate program? I'm genuinely curious. When I started grad school at Michigan, they did not have a written qualifying exam, so I had "only" an oral exam with the profs that I had chosen for my dissertation committee, after finishing most of my coursework. While I was there, Michigan did institute a written qualifying exam, but people in my entering year were grandfathered under the old rules.

Well i was think about just auditing some classes and establishing connections. Maybe if I show that i can do a few of the qualifying exams, then I would be able to get a good letter of rec.

 

[FallenApple]

No one doubts your math background. You've had more math than I have, and you're probably much better at it too. The issue is that working through a couple upper division texts is not necessarily equivalent to an upper division education in physics. Neither in time invested solving problems, or breadth of study, these are important.

It's certainly doable, and with motivation you can grind through the texts, study for the PGRE, and get accepted somewhere, probably within 2ish years. So if you're dead set, you can do it.

I'm just wondering, why do it? Do you even know yourself? It seems late to want to jump from one science to another. You've probably not had any time to actually work with a physics research group, to see what actually goes on(it isn't neat and pretty, it's messy and ugly at times). Haven't had any physics instructor feedback or guidance, and on and on. You may discover you don't really care for physics, or physics research, in which case grad school becomes impossible to suffer through. Compound that with an ability, to right now, apply to graduate programs in applied mathematics and combine mathematics while studying physical models (certain physicists do this work too) and I don't see the point of extra time invested learning the breadth of undergrad physics with so many other unknowns.

I don't want to dissuade you per say, but these are things you have to ask yourself. It's doable.

As far as LOR, you will probably need math professors whom you did work with, or studied math applications relevant to physics write them for you. Email any you can think of now, while you're fresh in their memory. Talk to them, get their opinion, see if you can take courses at your at your previous university on a part time basis in physics. See if anyone has any work for you, etc.

Well, I need to be able to apply math to something. Many of the math/stats majors have significant knowledge in other fields so they can do collaberations. Since physics is my favorite subject to apply math to, I figure why not learn a bunch of it.

 

[mal4mac]

Wouldn't it be possible to to do a PhD in Applied Math and find a physics professor who wants some equations solved? With a degree in applied math, mostly A's, you don't need to impress anyone by taking physics exams on your own, in your spare time... in fact, that's likely to appear "too much" and rather eccentric. That said, going through classical mechanics by Goldstein and E&M by GRIFFITHS, seems reasonable and would be enough to show a physics professor you are keen about physics and not just about solving equations. No need to finish them... just say you're going through them during your interview, that should be enough to impress!