Bachelor In Mathematics and PhD In Physics

In summary: Micromass, so if I took PDE, ODE, Real Analysis, Complex Analysis, Functional Analysis, Linear Algebra, Differential Geometry, and Abstract Algebra, would that be enough to complete the required courses for the "average" bachelors in mathematics? Too much? Too little? Assuming we're talking about group theory, it comes up a lot in physics. Some examples off the top of my head are: QFT, or in general any field theory (yes, there is more to this, but don't got much time to type), Lie groups used in LQG, and of course they use groups in the standard model! I don't see any reason why this is less important,
  • #1
Bashyboy
1,421
5
Bachelors In Mathematics and PhD In Physics

Hello,

As of now, I am maneuvering through undergraduate work, with the intention of gaining a bachelors in mathematics and (someday) a PhD in physics. For my mathematics courses I have taken, I have done all three calculi, discrete mathematics, and probability and statistics; and this summer, I shall be taking differential equations. Without respect to any particular school, in general, what is the required amount of mathematics courses to complete a bachelors in mathematics; and of the remaining I need to take, what mathematics classes would be pertain to someone who intends to do research in mathematical/theoretical physics?

Thank you dearly for your time.
 
Last edited:
Physics news on Phys.org
  • #2
Bashyboy said:
what is the required amount of mathematics courses to complete a bachelors in mathematics;
There are usually around 15-18 credit hours (5-6 classes) of "core" mathematics that all math majors are required to take. This includes discrete math, real analysis, abstract algebra, probability, linear algebra, differential equations, and perhaps a research requirement.

Then you usually get to choose from ~15 hours of mathematics electives, which could include just about anything, for example complex analysis, differential geometry, numerical analysis, mathematics software, more real analysis and algebra, partial differential equations, topology...

and of the remaining I need to take, what mathematics classes would be pertain to someone who intends to do research in mathematical/theoretical physics?

Not sure on the physics side, but my recommendation is that you AT LEAST minor in physics if you plan to attend graduate school in physics. My friend talked to the physics department at Ga Tech and they said they would consider anyone who didn't have at least 5 upper-division physics courses. I assume these would include E&M, Mechanics, Optics, Solid State, Condensed matter, statistical mechanics.

I urge you to just go ahead and change your major to physics if that is what you want to study. I don't know why you are a math major, but in my case, math was the only STEM degree that my school offers (aside from biology and chemistry), and I didn't want to transfer. It has caused me a LOT of trouble and inconveniences and caused me to postpone my graduation for several semesters while I attend another school part time to get prerequisites for my intended field in graduate school. Save yourself the headache and just major in physics, or double major.
 
  • #3
Take as many analysis classes as you can. Don't stop with one real analysis class. Take complex analysis and functional analysis and more. Be sure to take differential equations classes, such as PDE.
Also, take whatever linear algebra classes they have. And also take differential geometry.

I guess you should also take abstract algebra, but that's way less important for physics.

These are the recommendations I would make for anybody going into mathematical physics. They might not help you get into grad school. But once you got into grad school, you will be happy that you took these classes. The more analysis, linear algebra and differential geometry you took, the better off you will be.
 
  • #4
Micromass, so if I took PDE, ODE, Real Analysis, Complex Analysis, Functional Analysis, Linear Algebra, Differential Geometry, and Abstract Algebra, would that be enough to complete the required courses for the "average" bachelors in mathematics? Too much? Too little?

Also, is Advanced Calculus simply another name for Real Analysis?
 
  • #5
Bashyboy said:
Micromass, so if I took PDE, ODE, Real Analysis, Complex Analysis, Functional Analysis, Linear Algebra, Differential Geometry, and Abstract Algebra, would that be enough to complete the required courses for the "average" bachelors in mathematics? Too much? Too little?

I realize you were asking Micromass, but I figure more input can't hurt. For the "average" bachelors in math, probably yes, this is fine. However, these types of questions should be directed toward your advisor (that is why they are there). It really depends on the school. For example, at my school, the core required coursework includes Calc 1-3, ODEs, Intro to Abstract Math, Intro Real Analysis, Combinatorics, Prob and Stats 1, Applied Linear Algebra, and 2 programming courses. Then you pick a concentration (not necessarily in math) and choose your electives based on that. Other math departments I've looked at require a year of real analysis, a year of abstract algebra, calc 1-3, ODEs, etc.
 
  • #6
micromass said:
I guess you should also take abstract algebra, but that's way less important for physics.

Assuming we're talking about group theory, it comes up a lot in physics. Some examples off the top of my head are: QFT, or in general any field theory (yes, there is more to this, but don't got much time to type), Lie groups used in LQG, and of course they use groups in the standard model! I don't see any reason why this is less important, than say, real analysis...

Anyways to OP, if you DO want to stay with math major and then do get a PhD in physics be sure to take PDEs, differential geometry, and a numerical computation course. I don't know of a math program where you wouldn't have to take real analysis, abstract algebra and linear algebra, so of course you're going to take those.

Also, see if the math department offers a course on perturbation theory, it's used a lot in physics, and being a math major, you should want to understand the methods and theory behind it.

Good luck!
 
  • #8
Thank you everyone for your responses.
 
  • #9
micromass - Take as many analysis classes as you can. Don't stop with one real analysis class.

- Take complex analysis and functional analysis and more. Be sure to take differential equations classes, such as PDE.

- Also, take whatever linear algebra classes they have. And also take differential geometry.

- I guess you should also take abstract algebra, but that's way less important for physics.

- The more analysis, linear algebra and differential geometry you took, the better off you will be.

----

In a nutshell all a mathematical physics degree is:

It's just an honours degree in Physics with

- extra analysis
- differential geometry

---
[i'll repeat what i said in - who wants to be a mathematician]i would think that as an undergrad you'd aim for 70% of this outline... and if you take an extra year for your degree, maybe you don't need to take as much in grad school...

But the ideal undergrad degree, would be this:

Mathematical Physics
-------------------------Calculus
------------
Math 151 Calculus I
Math 152 Calculus II
Math 251 Calculus III
Math 252 Vector Calculus I
Math 313 Vector Calculus II / Differential Geometry
Math 466 Tensor Analysis [needs Differential Geometry]
Math 471 Special Relativity [needs Differential Geometry and Butkov] [Butkov needs Diff Eqs and Griffith EM]

Analysis and Topology
--------------------------
Math 242 Intro to Analysis
Math 320 Theory of Convergence [aka Advanced Calculus of One Variable]
Math 425 Introduction to Metric Spaces
Math 426 Introduction to Lebesque Theory
Math 444 Topology

Differential Equations
------------------------------
Math 310 Introduction to Ordinary Differential Equations
Math 314 Boundary Value Problems
Math 415 Ordinary Differential Equations [needs Complex Analysis]
Math 418 Partial Differential Equations [needs Differential Geometry]
Math 419 Linear Analysis [needs Theory of Convergence]
Math 467 Vibrations [needs Symon]
Math 470 Variational Calculus [needs Symon and Differential Geometry]

Complex Analysis
-------------------------
Math 322 Complex Analysis
Math 424 Applications of Complex Analysis

Linear Algebra
--------------------
Math 232 Elementary Linear Algebra
Math 438 Linear Algebra
Math 439 Introduction to Algebraic Systems [aka Abstract Algebra]
minor things

Fluid Mechanics [fluid motion/air motion/turbulence] - engineering like - turbulent gases and liquids
------------------
Math 362 Fluid Mechanics I [needs Vector Calculus and Symon]
Math 462 Fluid Mechanics II [needs Boundary Value Problems]

Continuum Mechanics [aka deformation/stress/elasticity] - engineering like - elastic solids
--------------------------
Math 361 Mechanics of Deformable Media [needs Vector Calculus and Engineering Dynamics]
Math 468 Continuum Mechanics [needs Differential Geometry and Boundary Value Problems]

Probability and Statistics
-----------------------------
Math 272 Introduction to Probability and Statistics
Math 387 Introduction to Stochastic Processes

Numerical Analysis
-----------------------
Math 316 Numerical Analysis I [needs Fortran or PL/I]
Math 416 Numerical Analysis II [needs Differential Equations]

Mechanics - 1
------------
Phys 120 Physics I
Phys 211 Intermediate Mechanics [Symon and Kleppner-Kolenkow]
Phys 413 Advanced Mechanics [Goldstein]

Electricity and Magnetism - 2
------------------------------
Phys 121 Physics II [Halliday-Resnick/Purcell/Kip/Griffith/Lorrian/Stump-Pollack]
Phys 221 Intermediate Electricity and Magnetism
Phys 325 Relativity and Electromagnetism
Phys 326 Electronics and Instrumentation [tube/transistor/ic]
Phys 425 Electromagnetic Theory [with Griffiths and Pollack you can do Jackson]

Waves and Optics - 3
---------------------
Phys 355 Optics

Quantum Mechanics - 4
------------------------
Phys 385 Quantum Physics [Griffiths]
Phys 415 Quantum Mechanics
Phys 465 Solid State Physics - [should be separate but basic QM is needed for these branches]
Phys/Nusc 485 Particle Physics - [should be separate but basic QM is needed for these branches]

Thermodynamics and Statistical Mechanics - 5
--------------------------------------------------
Phys 344 Thermal Physics [Baerlein/Schroeder]
Phys 345 Statistical Mechanics [Reif]

Mathematical Physics
-------------------------
Phys 384 Methods of Theoretical Physics I [Butkov]
Phys 484 Methods of Theoretical Physics II [Butkov]

Plasma Physics
-----------------
Phys 477 Plasma Physics [Chen]
 
  • #10
romsofia said:
Assuming we're talking about group theory, it comes up a lot in physics. Some examples off the top of my head are: QFT, or in general any field theory (yes, there is more to this, but don't got much time to type), Lie groups used in LQG, and of course they use groups in the standard model! I don't see any reason why this is less important, than say, real analysis...

I know that groups are used very frequently in physics. But the point is that I *think* that an abstract algebra course will not be very useful. I say this because I think that an abstract algebra course doesn't really deal with those parts of group theory that are useful in physics.

A group theory course in the math department is usually about finite groups. Things like Lie groups are not treated at all and I don't see how the theory of finite groups is going to be useful in Lie group theory (apart from usual definitions such as subgroups or quotient groups).

Very useful in physics would be representation theory. But the representation theory course I was taught was for finite groups. And again, I don't think that this would be very useful to physicists.

The OP should absolutely do an abstract algebra course though, if only to see what it is about. But I think it might be better to just self-study the group theory you need for physics. I've seen here a lot that it is possible to self-study those things in a very short time period.
 
  • #11
Bashyboy said:
Micromass, so if I took PDE, ODE, Real Analysis, Complex Analysis, Functional Analysis, Linear Algebra, Differential Geometry, and Abstract Algebra, would that be enough to complete the required courses for the "average" bachelors in mathematics? Too much? Too little?

Although I agree with most of micromass's advice but I would take it with a grain of salt.. since he or she is still in high school.

Hercuflea has the right idea. Your extra classes should be at least some physics courses or you'll have to make them up if you intend on pursuing a PhD in physics. Now if you go for a PhD in math with an adviser that does work in mathematical physics this won't be a problem and you could probably get by with no physics courses.. but it would be program dependent.

Physics classes are a different animal than math classes, most of them will be grinding out solutions using approximation techniques or learning about assumptions to the model at hand. Unless it's a "____ for mathematicians" class the solutions and models will be most important not the theory. If this isn't your intention then I highly suggest looking into a math PhD with an adviser that specializes in mathematical physics. They're aren't many of these but I found a couple and almost considered that route too.

If you go the math PhD route then take what others have said and take a good course(s) in probability you'd be surprised how much probability is used in physics and unfortunately many students don't recognize this.
 
  • #12
SophusLies said:
Although I agree with most of micromass's advice but I would take it with a grain of salt.. since he or she is still in high school.

Ad hominem??

Where exactly is my advice wrong??
Either my advice was wrong and then you should point out what was wrong about it. Or my advice was correct. There is no need about snide remarks about my education level.
 
Last edited:
  • #13
- I say this because I think that an abstract algebra course doesn't really deal with those parts of group theory that are useful in physics.

don't most people learn it through some of their higher up quantum mechanics courses though?

Lie Algebra and Representation Theory wouldn't be touched by most undergrads, and same with group theory too.

I'm under the impression that like 5% of physics degree people will take a complex variables class [usually the honours degrees in physics take it, but not the main stream]

and Abstract Algebra or a higher up class in Linear Algebra is way rarer. Some that focus a lot in QM might take a math elective in that, but it depends if the math courses demand 1-2 classes in Analysis for a rather abstract and pure treatment of it. [Some Abstract Algebra or Linear Courses toss in that hurdle, some don't]

but yeah if you're going for a Physics and Math double honours/Mathematical Physics option...

the Abstract Algebra, Advanced Linear Algebra, and Analysis courses will be optional electives, a few required...

and as you need it in physics, people will be picking up Tinkham's Group theory book, or Lie Algebra for Physics, but i'd think 96% will not touch that till 4th year or more likely grad school, or reading on their own

I'd think people would just take QM I II III
and getting a chapter in those things, will seek out the math classes for them later or the recommended readings in their texts.but i think Differential Geometry would be the course most often done... [though some places will want some analysis or place it way into 4th year math classes rather than something taken right after Calculus IV/Vector calculus]

taking the Differential Geometry and Analysis courses, basically opens the doors to the most textbooks and prerequisites...

just like vector calculus and one/two courses in Differential Equations is about 99% of all you need as an undergrad. [aka normal physics degree with a Rudin/Boundary Values Text or the second half of your Diff Eqns book/Complex variables book]

and most honours physics people will take the the Boundary Values and Complex both anyways, but not the Analysis.

but my guess is 99% of souls would be taking a 300 level Quantum Course after a Modern Physics course, and after that, they say, do i need Abstract Algebra class or text, and one more Linear Textbook...


I think one year of Analysis, a course in Diff Geometry right after Vector Calculus, and Boundary Values right after Differential Equations, will make any scary physics or math prerequisites disappear for people early on...

and the sooner someone has read Symon [Intermediate Mechanics] and Butkov [Mathematical Physics] the smoother it might be, for choosing most any course later on
 
  • #14
micromass said:
A group theory course in the math department is usually about finite groups. Things like Lie groups are not treated at all and I don't see how the theory of finite groups is going to be useful in Lie group theory (apart from usual definitions such as subgroups or quotient groups).

Hmm, yeah that's true. I took abstract algebra from the math department last semester and it was just finite groups/rings. It was undergraduate though (book was Fraleigh, so pretty easy :x).

For Lie groups (I know that micromass knows this, but for others), it's just a differentiable manifold s.t the differentiable structure can work with the group structure (I.E C X C -> C by (a,b)-> ab^-1 would be a diff. mapping). Without knowing group notation/axioms this makes no sense! Could you self study this, I guess so. But, can't I say that about analysis too?

Ok, i think it's about time I understand why real analysis is important for physics! From what I know, analysis is pretty much another name for calculus? Thus, complex analysis is important because it offers more integration techniques for physics students. But why would real analysis be important? Does a physics student need to know proofs for calculus on the reals? How would constructing the reals be any different than say, proving H is a subgroup of G using axioms and group notation?

Maybe I should make a new thread/pm for this.
 
  • #15
romsofia said:
Hmm, yeah that's true. I took abstract algebra from the math department last semester and it was just finite groups/rings. It was undergraduate though (book was Fraleigh, so pretty easy :x).

For Lie groups (I know that micromass knows this, but for others), it's just a differentiable manifold s.t the differentiable structure can work with the group structure (I.E C X C -> C by (a,b)-> ab^-1 would be a diff. mapping). Without knowing group notation/axioms this makes no sense! Could you self study this, I guess so. But, can't I say that about analysis too?

Ok, i think it's about time I understand why real analysis is important for physics! From what I know, analysis is pretty much another name for calculus? Thus, complex analysis is important because it offers more integration techniques for physics students. But why would real analysis be important? Does a physics student need to know proofs for calculus on the reals? How would constructing the reals be any different than say, proving H is a subgroup of G using axioms and group notation?

Maybe I should make a new thread/pm for this.

I don't think real analysis would be useful for all physicists. But the OP specifcally said "mathematical physics", so my responses were tailored to that.

In my opinion, to decently grasp the mathematics behind quantum mechanics, you absolutely need to know real analysis, functional analysis and measure theory. Of course, one can get a very decent understand of QM without all these analysis things, but you'll need them you're into mathematical physics.

Of course, an abstract algebra course will be useful to understand Lie groups and stuff. But only a very small part of the abstract algebra course. I'm no physicist, but I doubt that things like Sylow's theorems or even Lagrange's theorems are used very often in physics. People are of course welcome to show me wrong!

On the other hand, most of real analysis will actually be useful somewhere. But I'm not talking about a first analysis course. A first analysis course will just be "calculus made rigorous" and won't be very interesting. Constructing the reals is certainly not interesting for physics (or even math) students. But later analysis courses will be extremely useful!

Also, I consider real analysis to be more difficult (but also more fun) than abstract algebra. So I think it is very possible to self-study all the abstract algebra you need. But it would be more difficult with analysis. But that is personal.
 
  • #16
OP, what are your goals?

Why are you doing a degree in mathematics for a PhD in physics?

Algebra is fairly useful but not as broadly as analysis courses and linear algebra are.
 
  • #17
romsofia - i think it's about time I understand why real analysis is important for physics! ... But why would real analysis be important? Does a physics student need to know proofs for calculus on the reals?

micromass - I don't think real analysis would be useful for all physicists. But the OP specifcally said "mathematical physics"

---

I think if you're going into mathematical physics, topology would be a cool option [of many options], and there you'd need one textbook [or two small classes] of analysis.

One could argue that for a degree in physics, you don't really need a class in complex variables, but an honours physics person would probably be forced into taking it.

When you get hit with heat and wave equations and other pdf's and you're dealing with courant-hilbert [is that applied analysis after complex analysis, or is it just mathematical physics]

But if you were doing a mathematical physics option, you'll probably be taking Complex Variables and Differnetial Geometry

and weirder crap like fluid mechanics, or topology...Mathematical Physics is just a good way of getting a physics and math degree in one for an extra year's suffering, without getting too crazy into the pure math, but then again you did take analysis and might get tricked into topology...

so there is some truth that maybe a physics degree in some cases needs more math than a 'math degree'

---

for my money, a mathematical physics degree syllabus is a nice way of showing what math is most useful for future physics study.

it also shows you how a lot of doors can open with a course in analysis.

----

again

a. get your vector calculus fast and try differential geometry [aka vector calc II]
b. take your Differential Equations [and finish your book! or get Powers Boundary Value Problems book]

[now you got your physics hurdles solved with a. and b.]

c. take your analysis
d. take your Symon/Butkov/Griffith's EM early!

most any courses will now have almost no hurdles with prerequisites
if you want physics with differential geometry and topology, congrats someone tricked you into being a wannabe mathematical physicist!
 
  • #18
Someone mentioned that I might be in High school--that would be incorrect. I am not working exclusively towards a degree in mathematics; I am doing a double major in mathematics and physics.
 
  • #19
micromass said:
Ad hominem??

Where exactly is my advice wrong??
Either my advice was wrong and then you should point out what was wrong about it. Or my advice was correct. There is no need about snide remarks about my education level.

Well, yes, it is ad hominem. It's not a snide remark either, it's a fact about you which is stated in your profile. Since you are in high school, I'm assuming that you've never taken a graduate class nor gone through the graduate admissions process. I just find it strange, if that previous statement is true, that you talk about graduate school. I'm not trying to be offensive and I'm sorry if that's how you took it. If you have taken a graduate course then I would be assuming that you aren't in high school and I would be under the impression that you're impersonating a minor which I'm not really sure how to react to that..

Anyway, to the OP and what I said earlier, I believe the clear distinction should be made of which PhD you intend to pursue. If it's math then take more math than physics courses to prepare you for graduate level math courses, aka lots of proofs, theorems, etc. If it's physics then you should focus more on physics classes. I did my undergrad as a double major in math and physics as well and there is a huge difference between grad and undergrad level classes. I have also taken both math and physics graduate classes. Since I'm doing a physics PhD the only courses that were absolutely required were physics and a couple of math methods classes in the physics department. I've taken a handful of pure math courses because I really like it but by no means were they required.

I'm guessing that since you said "mathematical physics" you'll be better off in the math department for a PhD. Those people are the ones that add rigor to physics. They might spend their time proving results that might have be taken on faith by physicists. If you do "theory" in the physics department you will be trying to make models of physical phenomena. Some number crunching, programming, maybe even experimental data analysis. Most of all you will learn how to approximate results and come up with a theoretical model. I stress these differences because you probably won't see them in an undergrad environment. Ask you professors that work in the math department that do research in physics vs. professors that are theoretical physicists. There is a notable difference in how they approach the same problems. When you answer which one you enjoy more then you will know side you fall on.
 
  • #20
SophusLies said:
Well, yes, it is ad hominem. It's not a snide remark either, it's a fact about you which is stated in your profile. Since you are in high school, I'm assuming that you've never taken a graduate class nor gone through the graduate admissions process. I just find it strange, if that previous statement is true, that you talk about graduate school. I'm not trying to be offensive and I'm sorry if that's how you took it. If you have taken a graduate course then I would be assuming that you aren't in high school and I would be under the impression that you're impersonating a minor which I'm not really sure how to react to that..

Again, what was wrong about my advice? If you warn the OP to take my advice with a grain of salt, then that means that something was wrong. I'd like to know what it was.
 
  • #21
Soph - Well, yes, it is ad hominem...I'm assuming that...If you have taken a graduate course then I would be assuming that...

How about you tell us where micromass was on the mark, and where he was off, and ignoring who or what he is or might be, what *specific* grain of salt we need to take with his comments...

I get somehting out of your comments, i get something out of his comments. I think his opinions, are *opinions* and i like his comments and some of his lists.

I do need to work a lot more to pull out some of the useful stuff out of your posts though. I appreciate your commentary, but I'd rather you show where you agree and disagree with his specific comments.I do think it's quite strange though that someone would take a math degree and then decide to hop for grad school in physics, with anything from next to nothing with physics classes, to the usual amount, to a fair amount... But there is something to be said for getting a degree in Math, and the ability to catching up for 8-15 months...

I still think that most of the babble can be taken away, if you think of the student, and if they're doing good in their classes and how flexible their course selection is. Sometimes it's hard enough to squeak in extra math classes, let alone take physics.

Or there's only enough credits you can pack into a sememster with physics classes that there's no room for the 'hard math classes'.

IF you're taking a double major, or a mathematical physics option [which is the same thing to a significant extent with less complications], it's way easier and much more flexible.

----

- I believe the clear distinction should be made of which PhD you intend to pursue.

or where you feel more comfortable, classes taken or not.- If it's math then take more math than physics courses to prepare you for graduate level math courses

which 99% of everyone would know

- If it's physics then you should focus more on physics classes.

no great secret there either- I did my undergrad as a double major in math and physics as well

That would also colour your outlook as well- I've taken a handful of pure math courses because I really like it but by no means were they required.

What did you take?
What did you find useful?
What did you find not useful?
Were any of the pure math courses a real chore for you?- I'm guessing that since you said "mathematical physics" you'll be better off in the math department for a PhD.

I think it depends what courses he's taken, and what he *will* take.

My opinion doesn't count for much here, but for my money, i think all bets are off, unless i can see what someone's course history has been, and what they *wish* to fit in.- Ask you professors that work in the math department that do research in physics vs. professors that are theoretical physicists.

At the lower levels, a lot of guidance counsellors just point at what in the course calendar seems to 'fit you best' and feel all you need to do is tick off the courses you took, and just *take* the next classes you got the prerequisites for... and yeah the higher you go, the more you know, and the better for you to know what to ask for 'future direction'.

- There is a notable difference in how they approach the same problems. When you answer which one you enjoy more then you will know side you fall on.

I think that's the important part! If you know what you enjoy more, that answers 90% of the problems. I still think you get more out of studying a Math Program , a Physics Program , and then comparing it to a Double Major in Math and Physics, or if you're lucky a Mathematical Physics option which might toss some extra hints what to take.

I just think it's sort of useless to ponder this stuff, unless you actually sit down with a Syllabus for Analysis and got the textbook on your shelf and say 'oh so that's what it's all about', and the same goes for a 'Math Methods Book in Physics/Butkov/Symon/Griffith QM/Griffith EM book'

300-400 dollars for half a dozen math and physics books, and a course calendar is all you need, and figure it out semester by semester how much you like the classes/hate the classes/struggle at the classes/worry

I just think choosing a Math PhD or Physics PhD is sort of 'pointless' in many cases because unless you actually own a copy of Royden's Analysis and flake out with stress about it, and you own a copy of Jackson's Electrodynamics and flake out with stress about it, you are just groping in the dark. If you look at the textbooks early enough, and ponder the good and the bad, you'll tailor your own path and follow your muse without needing help later on with direction.-----

micromass - Again, what was wrong about my advice? If you warn the OP to take my advice with a grain of salt, then that means that something was wrong. I'd like to know what it was.

mm - Take as many analysis classes as you can.
mm - Don't stop with one real analysis class.
mm - Take complex analysis
mm - Take functional analysis and more.
mm - take differential equations classes, such as PDE.
mm - take whatever linear algebra classes they have
mm - take differential geometry
mm - you should also take abstract algebra, but way less important

soph - I agree with most of micromass's advice
soph - take saltI make it easy lola. Take Special Relativity [Differential Geometry check]
b. Take Topology [Analysis check]
c. Take all Math Classes that uses Differential Equations [PDE/Vibrations/Calculus of Variations ugh and check]
d. play with Turbulent Flow and Deformation [oh you're a scary engineer now check]

------

So don't get discouraged micromass, you are actually making specific suggestions and all that matters is if people agree with you, or disagree with you. And if they do either, it is hoped that they offer better advice, for all concerned.
 
  • #22
SophusLies said:
Well, yes, it is ad hominem. It's not a snide remark either, it's a fact about you which is stated in your profile. Since you are in high school, I'm assuming that you've never taken a graduate class nor gone through the graduate admissions process. I just find it strange, if that previous statement is true, that you talk about graduate school. I'm not trying to be offensive and I'm sorry if that's how you took it. If you have taken a graduate course then I would be assuming that you aren't in high school and I would be under the impression that you're impersonating a minor which I'm not really sure how to react to that..
There are more things in heaven and earth, SophusLies, Than are dreamt of in your philosophy.
 
  • #23
There's a lot more to mathematical physics besides analysis. I'm in grad school for mathematical physics (in a math department), but I spend about an equal amount of time thinking about algebraic and analytic things (which feels to be the norm for algebraic geometry used in physics). So really, you should take whatever math classes seem interesting to you. They all get used somewhere, even if it is in a niche topic. Though this might not work as well if you're more interested in the physics. I'm just more interested in the math and don't care which area of physics they are applied in.
 
  • #24
Monocles: There's a lot more to mathematical physics besides analysis. So really, you should take whatever math classes seem interesting to you. They all get used somewhere, even if it is in a niche topic. Though this might not work as well if you're more interested in the physics. I'm just more interested in the math and don't care which area of physics they are applied in.

Pretty good comment...

I think the analysis is really there, so people don't choke later on in the extra math classes...

some people can take differential geometry classes and your calculus background is good enough for 12 weeks, another school might choose a text or supplement things where you'd struggle a lot without zooming through all of Rudin/Strichartz/Bartle/Binmore, or when the Differential Geometry class might extend for 24 weeks [2 courses] and do one textbook cover to cover.

i think in most situations, you arent going to be hit with much math work that needs analysis, but some places might just use harder textbooks for Diff Geo or Differential Equations or some Linear Algebra and the lack of analysis would weed out the typical physics degree person's math background.

If you want to get topological, with Special Relativity, i think that can toss some motivation there for people to take more math classes from the bare minimum most physics people do. And if you take like 4-5 more courses that lean on differential equations and vibrations, the analysis will help when reading stuff on Fourier series, Legengre polynominals, convergence, Hermitian polynominals etc. All depends on how stiff the class and textbook is.

i think ideally you dip your toes into the three big parts:

tensors
differential equations
topology

and a touch of fluid mech/continuum [gets out the vector calc for things deforming or getting turbulent]

but i think it's totally totally on people dipping their toes into something 12-15 weeks at a time, and saying, oh i'll take that one step deeper - it's sort of interesting

not all undergrads are going to take Stochastic Methods, not all are going to attempt topology, or some might get scared of the calculus of variations. Others are going to sample all three.

Heck, it's the most flexible and wide option there is!
amazing what 1-2 classes in em, differential equations, and analysis does, it opens up the kitchen sink of courses.What didn't you take as an undergrad?

like on that list of courses i posted a few weeks ago, I'm sure a lot of people wouldn't touch 25% or 50% of the math, but almost all of the physics.
 
  • #25
RJinkies said:
If you want to get topological

Oh my god, I think I just thought of the next youtube nerdy dance phenomenon!
 
  • #26
no no, nobody dances since the Frug, if you want to talk about nerdy stuf...be thankful noone's called a topo textbook 'twist and shout' either...

though i do cringe when some Springer books want to turn some geometrical shapes into happy faces, and the inside looks like the Rosetta Stone
 

1. What is the difference between a Bachelor's in Mathematics and a PhD in Physics?

Bachelor's in Mathematics is an undergraduate degree that typically takes 4 years to complete, while a PhD in Physics is a graduate degree that takes an additional 4-5 years after completing a Bachelor's degree. The Bachelor's in Mathematics provides a broad foundation in mathematical concepts, while a PhD in Physics focuses on a specific area within the field of physics and requires original research.

2. Can I pursue a PhD in Physics with a Bachelor's degree in a different field?

Yes, it is possible to pursue a PhD in Physics with a Bachelor's degree in a different field. However, you may be required to complete prerequisite courses in physics and mathematics before starting the PhD program. It is also important to have a strong foundation in mathematics and physics to be successful in a PhD program.

3. What career opportunities are available with a Bachelor's in Mathematics and PhD in Physics?

A Bachelor's in Mathematics and PhD in Physics can lead to a variety of career opportunities in both the public and private sectors. Some common career paths include research scientist, data analyst, financial analyst, engineering consultant, and university professor. These degrees also provide a strong foundation for pursuing advanced degrees in other fields such as engineering, computer science, or economics.

4. How long does it take to complete a Bachelor's in Mathematics and PhD in Physics?

A Bachelor's in Mathematics typically takes 4 years to complete, while a PhD in Physics takes an additional 4-5 years. However, the time to complete a PhD may vary depending on the individual's research progress and dissertation completion.

5. What skills will I develop through a Bachelor's in Mathematics and PhD in Physics?

Through a Bachelor's in Mathematics and PhD in Physics, you will develop strong analytical, problem-solving, and critical thinking skills. You will also gain a deep understanding of mathematical and physical concepts, as well as the ability to conduct research, analyze data, and communicate complex ideas effectively. These skills are highly valued in a variety of industries and are essential for success in advanced academic and research positions.

Similar threads

  • STEM Academic Advising
Replies
2
Views
569
  • STEM Academic Advising
Replies
16
Views
2K
  • STEM Academic Advising
Replies
11
Views
521
  • STEM Academic Advising
Replies
1
Views
693
  • STEM Academic Advising
Replies
1
Views
508
  • STEM Academic Advising
2
Replies
53
Views
4K
  • STEM Academic Advising
Replies
19
Views
2K
  • STEM Academic Advising
Replies
12
Views
774
Replies
35
Views
3K
  • STEM Academic Advising
Replies
24
Views
2K
Back
Top