One semester of undergrad left: What class MUST I take before leaving

[d3nat]

Hi all,

(sorry for the length)

I am an Applied Physics major in her senior year (yay!) at a liberal arts college.
I have a double minor in Mathematics and Computational Physical Sciences (aka Programming, but not Comp Sci.)

Because of the way the sciences are set up at my college, it's very hard to take a lot of science classes and be in the Honors Program (which I am.) Since I've already persevered 3 years of it, I'm not dropping the Program.

I have a semester of HELL this fall, but this is enabling me to have a free spot or two spring semester.

I have taken so far for PHYSICS:

Classical Physics I & II
Modern Physics
Intro to Particle Physics (Griffiths)
Laser Physics
Electromagnetism
Astrophysics I
Electrical Circuits
Independent Phys Research I

Dynamics [NEXT SEMESTER]
Independent Phys Research II [NEXT SEMESTER]

The rest of my STEM classes include:

Calc I, II, III
Topics of 3D Math
Linear Analysis/Algebra
Differential Equations [NEXT SEMESTER]

Gen Chem I (debating about taking the second part next semester)

Programming I & II (C++)
Data Structures and Algorithms (Java)

----------

If I can take my last theology requirement online, I'll have one or two free spots depending on if I take an extra class (I've been doing this since sophomore year, so I probably will.)

I'm planning on going to graduate school. What classes SHOULD I take next semester to make me even more prepared.

The professor who usually teaches higher level classes is on sabbatical, but he told me he'll either come into teach a class for me or find someone who can do it (they didn't find a substitute for him this semester.)

Should I take a Stats/Probability class?
More programming?

My research experience includes one REU in HEP, research this fall with MIT continuing on the same broad project (but different area) of my REU, and geophysics research with my adviser this fall (which will be my senior research thesis).
Both my REU and this side-project with MIT are mainly programming in C++, so I feel pretty solid in that area.

Any thoughts or suggestions on what I really should take this spring will be GREATLY appreciated!


(ps: If my college is a tier 1 college, is it appropriate to apply for tier 1 grad programs, or should I shoot a little lower? Thanks!)

 

[espen180]

I think it is important to get a good understanding of the basics. Make sure you have taken classical mechanics in the Lagrangian/Hamiltonian formalism (ALL modern physics is based on these formalisms), electromagnetism at least on the level of Griffiths, and if possible, enough quantum mechanics to know about perturbation theory, scattering, spin dynamics in magnetic fields, many-body systems of (in)distinguishable particles and the electromagnetic field quantization.

 

[vela]

Instead of simply giving the course titles, could you describe what subjects you actually covered and at what level? Are these upper-division courses?

I have to admit your list has left me confused. I don't see how you could get through electromagnetism without first having had differential equations, yet you've put that course off until the end. What's covered in Modern Physics? Is it quantum mechanics? I assume you must have had quantum mechanics before taking particle physics.

Did you take a math methods course for physics?

You might want to take a statistical mechanics course or perhaps thermodynamics.

 

[dydxforsn]

If you're planning on going to graduate school in physics I would recommend more math. Specifically think about taking Differential Geometry, Complex Analysis, or Partial Differential Equations. You can never have enough math.

Also as Vela pointed out, I'm also noticing the distinct lack of statistical mechanics, a very important course (though you've probably already seen some amount of it in astro or modern physics.) Honestly though I recommend just buying Thermal Physics by Kromer and Kittel and reading through it on your own (the first 9 chapters or so). Further you haven't taken a solid state physics course, the biggest branch of physics in terms of the number of people practicing in the field, but really you should take statistical mechanics before you venture onto a solid state physics text (lots of students don't take solid state at the undergraduate level, so that's not odd, but not having a set statistical mechanics course probably is a little.)

Also most students experience a quantum mechanics shock in graduate school, but it looks like your school just offers a basic modern physics course, and I'm sure you got more quantum experience in Griffith's Particle Physics but I would still say that you should expect your quantum mechanics to be a bit weak (again, just possibly/speculatively.)

Finally, you may be lacking in physics laboratory experience as well.

Also I wouldn't take Chem II. General Chemistry in college is best described in the following way: Chem 1 is what reactions CAN happen, and Chem 2 is how fast they happen, and to what extent (how much product can be formed from a set amount of reactants, not all reactions proceed all the way to completion, rather there are many reactants that don't react at all, and an equilibrium state is formed between reactions going one way and the reverse reaction in the other.) Keeping that thought in your mind, just read through the rest of your chemistry book on your own, don't waste your time with annoying chemistry labs if you don't have to >_< Chem 2 also deals with some important topics like thermal physics applied to chemistry and electrochemistry, but I think usually more than half of the course is the addressing of how fast and to what extent reactions occur.

Also, I like the fact that you've taken a course on lasers and circuit analysis, those are very practical and important skills. I know I forgot most of my circuit skills from basic university physics, an additional circuits course would have served me well >_<

At the end of the day, if I were you I would probably take PDE, Differential Geometry, or statistical mechanics.

Edit* Also I'm assuming your dynamics course will cover the calculus of variations and Lagrangian/Hamiltonian formalisms in mechanics, which will serve you WELL in graduate school. If you haven't seen these things, make SURE that course covers them, they're techniques that you will see again and again for the rest of your career.

 

[ZombieFeynman]

I see a distinct lack of math. Should you go to graduate school at a top tier school, your mathematical maturity will be seriously lacking compared to your classmates. You should take more math.

 

[d3nat]

Did you take a math methods course for physics?

You might want to take a statistical mechanics course or perhaps thermodynamics.

No, I haven't taken a math methods for physics, though I think it might be offered this Spring. Last time it came around I was studying abroad. Do you recommend that?

I was leaning towards a Stats Mechanics course myself. I don't think a Thermo course is offered at my college, but I'm sure I could request one if I wanted to.

 

[d3nat]

If you're planning on going to graduate school in physics I would recommend more math. Specifically think about taking Differential Geometry, Complex Analysis, or Partial Differential Equations. You can never have enough math.

Also as Vela pointed out, I'm also noticing the distinct lack of statistical mechanics, a very important course (though you've probably already seen some amount of it in astro or modern physics.) Honestly though I recommend just buying Thermal Physics by Kromer and Kittel and reading through it on your own (the first 9 chapters or so). Further you haven't taken a solid state physics course, the biggest branch of physics in terms of the number of people practicing in the field, but really you should take statistical mechanics before you venture onto a solid state physics text (lots of students don't take solid state at the undergraduate level, so that's not odd, but not having a set statistical mechanics course probably is a little.)

Also most students experience a quantum mechanics shock in graduate school, but it looks like your school just offers a basic modern physics course, and I'm sure you got more quantum experience in Griffith's Particle Physics but I would still say that you should expect your quantum mechanics to be a bit weak (again, just possibly/speculatively.)

Finally, you may be lacking in physics laboratory experience as well.

Also I wouldn't take Chem II. General Chemistry in college is best described in the following way: Chem 1 is what reactions CAN happen, and Chem 2 is how fast they happen, and to what extent (how much product can be formed from a set amount of reactants, not all reactions proceed all the way to completion, rather there are many reactants that don't react at all, and an equilibrium state is formed between reactions going one way and the reverse reaction in the other.) Keeping that thought in your mind, just read through the rest of your chemistry book on your own, don't waste your time with annoying chemistry labs if you don't have to >_< Chem 2 also deals with some important topics like thermal physics applied to chemistry and electrochemistry, but I think usually more than half of the course is the addressing of how fast and to what extent reactions occur.

Also, I like the fact that you've taken a course on lasers and circuit analysis, those are very practical and important skills. I know I forgot most of my circuit skills from basic university physics, an additional circuits course would have served me well >_<

At the end of the day, if I were you I would probably take PDE, Differential Geometry, or statistical mechanics.

Edit* Also I'm assuming your dynamics course will cover the calculus of variations and Lagrangian/Hamiltonian formalisms in mechanics, which will serve you WELL in graduate school. If you haven't seen these things, make SURE that course covers them, they're techniques that you will see again and again for the rest of your career.

To be honest, I'm somewhat scared (as tacky as that sounds) to take a solid states course. I feel like I'd be overwhelmingly confused. I feel like I might be better of waiting until grad school if I have to take a class like that.

Thanks for the tip about Chem. I took it this semester since it counts as an honors credit (the ONLY science that does -_-) and because I thought it might be a good idea as a physics major to have at least a basic understanding of chemistry.

I have seen/worked with Lagrangian/Hamiltonians, but my Dynamics class will be covering them again. I already own the book, and I've briefly perused it.

Thank you for your suggestions and input. It was extremely useful. I do feel like my math skills are on the weaker side, so I'm leaning towards a class in that.

 

[d3nat]

I see a distinct lack of math. Should you go to graduate school at a top tier school, your mathematical maturity will be seriously lacking compared to your classmates. You should take more math.

Yes, I'd agree with you there. The math department doesn't really offer to many courses besides the basic Calc 1-3, linear analysis, diff q's, and then just some special topics classes.

In your opinion, what math classes would you recommend? I'm on very good terms with the math department, and I'm sure I could get them to do a special topics course in a specific area if I asked early on.

I'm also going to try to take a math course over this upcoming summer. Whether or not that will happen is debatable. Do you think my "lack of" math will prohibit my chances of getting into a nice grad program?

Thanks

 

[dydxforsn]

To be honest, I'm somewhat scared (as tacky as that sounds) to take a solid states course. I feel like I'd be overwhelmingly confused. I feel like I might be better of waiting until grad school if I have to take a class like that.

Heh, well you definitely want foundations in statistical mechanics before you do solid state physics, they follow a lot of the same lines, so this course is kind of by default scratched off your list of potential courses to take. If you don't have stat. mech. then the course can be a killer, it wasn't easy (though let's be honest, E&M/calculus of variations/quantum are the killers of undergraduates), in fact I'm still not sure I quite understand chapter 8 and onward in the Kittel's Solid State Physics (you study electron conduction in solids quite a bit towards the middle/end of the course and move from a simple model where electrons are free to move around the solid without interactions with the solid lattice to a model in which the electrons interact with a period potential (interactions with the atomic lattice). Really at the undergraduate level the bulk of the course and the more difficult sections are along these lines :/ Though solid state physics is one of those subjects that just goes on and on and on and on. In any other major it would be a completely new major..)

Thanks for the tip about Chem. I took it this semester since it counts as an honors credit (the ONLY science that does -_-) and because I thought it might be a good idea as a physics major to have at least a basic understanding of chemistry.

Yeah my Chem II professor in college pointed out that basic statement about chemistry to me and suddenly I could see the matrix. It's also noteworthy that of the 4 things that Chem II really covers (kinetics/equilibria/thermal/electrochemistry), the first is a simple differential equation that you can solve with Cal II methods and pretty much derive the first couple weeks of the course, then you get to equilibria and the law of mass action which is often derived in statistical mechanics (if you have a fairly in depth course), then comes thermal physics applied to chemistry which is really just a study of the gibbs free energy and basic entropy (you'll get it in stat. mech./thermal physics), and finally electrochemistry is actually kind of interesting at the end of the semester, but just read about it >_< That is unless you want to do 10^5 titration labs just to get a couple hours of useful information out of the course (though it's good to have the ongoing practice with chemical taxonomy and the such, but you're going to forget all of that anyway and only remember the big ideals when you graduate like me...) Don't get me wrong I loved Chem II and you're completely right about it being important, but I would hardly classify it as fulfilling your topic title of "MUST take classes". It's simply a nice background for physics majors. What you should really be gearing up for is the classes you know you will have to take immediately in graduate school, which is going to be your standard graduate mechanics/E&M/Quantum/math methods/stat. mech. and then probably QFT and etc. You should be preparing for your attack on these courses really and lay the foundation for your graduate education with good performance in your first year.

I have seen/worked with Lagrangian/Hamiltonians, but my Dynamics class will be covering them again. I already own the book, and I've briefly perused it.

Good, as somebody mentioned previously this stuff becomes central in all of your physics courses, not just mechanics.

Thank you for your suggestions and input. It was extremely useful. I do feel like my math skills are on the weaker side, so I'm leaning towards a class in that.

Yeah, no problem. Definitely think about what would help with the beginning graduate courses I mentioned. PDE will help you across the board and stat. mech. is up there as well in usefulness. At the end of the day you know you can't go wrong with more math. I honestly think it's the biggest thing that graduate admissions offices will raise and eyebrow at if they see a lack of it on your transcript (other than obvious omissions of something like upper level mechanics, E&M, or a quantum course.)

I think PDE is the course for you (PDE is also a course heavy on Fourier series/transforms if you've only had a cursory glance at those subjects in other courses it might also influence your decision.)

 

[SophusLies]

Take a PDE class, that's where you learn physics as close to real life as possible. Hopefully, it will involve some numerical methods so you can utilize those programming class you've already taken. Even though I took a handful of CS classes, I never felt like I understood computational work until I applied it to my discipline(physics/math).