Prepping for physics grad classes... as a science ed student

[SeriousSillyPutty]

First, my angst:

I love physics. (I was a physics major.) But the physics I love is thinking about all the potential energy I've gained by cycling to the top of the hill, and cursing thermodynamics when I have to break at the bottom of a hill b/c of a stop sign, then going again reflecting on how I can make a 90-degree turn without loosing all my speed (even though I've lost all my original velocity) because good ol' friction gives me a boost. That is to say, I love warm fuzzy conceptual physics.

I held my own in the upper-level math-intensive classes (quantum 2, intro to particle physics, etc.) back when I took them, but that was five years ago and I remember nil.

Now, for my PhD program in Science Ed, I'm supposed to earn the equivalent of an MA in physics, which scares me. I keep reminding myself that if I could learn it once I can learn it again, but I haven't done a calculus problem in five years! Physics peeps tend to go straight from UG to PhD programs, so I suspect I'll be the only "old, rusty" person in the class, besides the fact that I probably wouldn't have had the chops to get into my school's physics program to begin with.

Okay, now my questions:

1) What do you think is most important for me to review?

2) If you had someone in your class who wasn't in your cohort, what would make be more or less inclined to work with her on homework and such?

Thanks for any thoughts and feedback!

[SymmetryOfImperfection]

here's what im doing over the summer to review:

just do tens of comprehensive exams, but as open-book problems and with Mathematica assistance. if the comprehensive exams are too hard, do book problems. try to do at least 2 problems per day, distributed as mechanics/EM, then next day do quantum/stat-thermo, but personally I'd want to do 6-8 problems per day though that might be too time consuming. I'd also just read the textbooks for fun, and see if there's anything interesting you missed the first time.

it seems easy at first (only 2-8 problems...) but the idea is to consistently learn a bit by bit and most of all, do it without a teacher, so when it comes time for class, you'll be repeating the same material, and this time, there'd be a professor to help you, and it should go alot easier.

[Eigen]

I'd pick up a copy of "Mathematics for Scientists and Engineers" by McQuarrie. It's what I used to get through grad QM after 3 years without a math class.

Very comprehensive, but not overly worry, great as a reference for helping yourself remember math you no longer know.

[TakeruK]

Do you HAVE to do a MA in physics, or would something like....Astronomy be okay? One of the reasons I chose to be an Physics+Astronomy undergrad instead of just Physics is like you, I prefer conceptual ideas over intense calculus! Not to say that there isn't calculus in Astro, but it's mostly stuff you learn in first year (integrals, some differential equations) and a little bit of 2nd year vector calculus for some things. Nothing at the level of E&M or QM on a regular basis though (some of these ideas are needed to understand some stuff but it's more like you need to understand/follow the derivation/calculation, not do it yourself on an exam or something).

But if Astro is not possible or not your cup of tea, then to answer your actual questions...

1. I think the material covered in the Physics GRE is about the level you need to know. At many schools, the PhD program will require at least one graduate QM course and maybe one graduate EM course (the infamous Jackson). I don't know if you will have to do them as well for Masters level. But if you do, you should review your most recent courses in these topics, I think! If you are looking for books, Griffiths gives a very nice conceptual-turned-mathematical treatment of both these topics. In addition, the book is for undergrads so the first half is usually a 2nd or 3rd year level course while the 2nd half is generally a 4th year course. This is good because it will allow you to start from basics!

I think this is the most advanced material that you would absolutely need before starting. In addition though (maybe before doing the above), a review of freshman physics (especially some mechanics questions) and single- and multi-variable calculus would be good. If I was doing this, I would find my first year books and start doing the problems at the end of the chapter, then review in depth whatever I couldn't do. You might find that once you start getting back into it, you will remember more than you think though!

2. I really like to collaborate on problem sets, and both places I've studied at also had people who thought the same way, so I would be willing/happy to work with anyone in my classes on problem sets! It might be harder for someone who isn't in our cohort because of issues like potentially not having an office in the same area/building or not being on the same mailing lists or not being in the same social group. If I'm working on a problem, and get stuck, I like to just turn to my office mate, or walk down the hall and find someone else who is working on the same thing. If enough people are doing this, we might end up finding an empty room and puzzling it out together. So not being in the same area might make you miss out on these impromptu type study groups!

If you weren't in my cohort, I might not know you as well so there might be some inertia of me just asking to set up a time to work together. Especially if there were others in the class that I already worked with before, I might end up more likely to work with them than a "new" person! As an "outsider" to the cohort, it is probably better if you took the initiative and ask if anyone else has started problem set X and if they wanted to work together etc. If I was a student already in the cohort, I wouldn't have any worries about working with someone outside of the cohort, I just wouldn't be sure if the "outsider" actually wanted to work with us or not!

Sometimes cliques form, but from my experiences (which may not be representative, I guess), these groups form just out of comfort (instead of being selective) and most physics students are pretty friendly and are happy to accept newcomers, it's just that we might be too shy to ask (but we are glad when we get newcomers, usually!).

Good luck

[SymmetryOfImperfection]

Do you HAVE to do a MA in physics, or would something like....Astronomy be okay? One of the reasons I chose to be an Physics+Astronomy undergrad instead of just Physics is like you, I prefer conceptual ideas over intense calculus! Not to say that there isn't calculus in Astro, but it's mostly stuff you learn in first year (integrals, some differential equations) and a little bit of 2nd year vector calculus for some things. Nothing at the level of E&M or QM on a regular basis though (some of these ideas are needed to understand some stuff but it's more like you need to understand/follow the derivation/calculation, not do it yourself on an exam or something).

But if Astro is not possible or not your cup of tea, then to answer your actual questions...

1. I think the material covered in the Physics GRE is about the level you need to know. At many schools, the PhD program will require at least one graduate QM course and maybe one graduate EM course (the infamous Jackson). I don't know if you will have to do them as well for Masters level. But if you do, you should review your most recent courses in these topics, I think! If you are looking for books, Griffiths gives a very nice conceptual-turned-mathematical treatment of both these topics. In addition, the book is for undergrads so the first half is usually a 2nd or 3rd year level course while the 2nd half is generally a 4th year course. This is good because it will allow you to start from basics!

I think this is the most advanced material that you would absolutely need before starting. In addition though (maybe before doing the above), a review of freshman physics (especially some mechanics questions) and single- and multi-variable calculus would be good. If I was doing this, I would find my first year books and start doing the problems at the end of the chapter, then review in depth whatever I couldn't do. You might find that once you start getting back into it, you will remember more than you think though!

2. I really like to collaborate on problem sets, and both places I've studied at also had people who thought the same way, so I would be willing/happy to work with anyone in my classes on problem sets! It might be harder for someone who isn't in our cohort because of issues like potentially not having an office in the same area/building or not being on the same mailing lists or not being in the same social group. If I'm working on a problem, and get stuck, I like to just turn to my office mate, or walk down the hall and find someone else who is working on the same thing. If enough people are doing this, we might end up finding an empty room and puzzling it out together. So not being in the same area might make you miss out on these impromptu type study groups!

If you weren't in my cohort, I might not know you as well so there might be some inertia of me just asking to set up a time to work together. Especially if there were others in the class that I already worked with before, I might end up more likely to work with them than a "new" person! As an "outsider" to the cohort, it is probably better if you took the initiative and ask if anyone else has started problem set X and if they wanted to work together etc. If I was a student already in the cohort, I wouldn't have any worries about working with someone outside of the cohort, I just wouldn't be sure if the "outsider" actually wanted to work with us or not!

Sometimes cliques form, but from my experiences (which may not be representative, I guess), these groups form just out of comfort (instead of being selective) and most physics students are pretty friendly and are happy to accept newcomers, it's just that we might be too shy to ask (but we are glad when we get newcomers, usually!).

Good luck

Hi, I think I disagree with using Griffith to solve many problems. The answer is, there's no easy to go to solution manual (have to look online so can't do it alone away from the computer). It also leaves partial explanations sometimes. Sometimes I feel like the book simply does not give you enough information to solve a problem and it has literally taken me 5 hours to solve a single problem before, simply because the book didn't have a formula I needed. I'd recommend Quantum Mechanics: Concepts and Applications by Zettili. The book is graduate level, but it has hundreds of solved problems and answers. If that's too much. Quantum Mechanics by Townsend is also OK (though also graduate level; they use it as such at John Hopkins), and it has a very innovative style that starts you off with hard concepts but the easiest math (1/2 spin systems, just 2 states), then moves you onto easier concepts but harder math (1-D wave mechanics, hydrogen atom, etc)

Also, my question is, is there really less math in astro than in areas of physics such as condensed matter? I've always been under the impression that astro was the most intense mathematically due to general relativity.

Edited June 18, 2012 by SymmetryOfImperfection

[TakeruK]

I agree that Griffiths does not always have detailed solutions -- all the steps are there though, just not very many guiding words in between. Personally, I don't mind having a computer nearby (I actually like to solve a problem, then turn over to my laptop and check) when working -- and it might be just me, but I can't really focus in places that I wouldn't have my laptop handy (e.g. bus rides, car, etc.) Anywhere I can do work has desk space big enough for a laptop. Not to mention you can just print out the relevant pages of the solution manual if you know which problems you want to try at a time when you don't have laptop use. It's really easy to get the PDF of the solutions manual online so that you can use it offline too.

I was more recommending that the original poster (OP) start solving problems from the first year of physics though, to get the old ideas familiar again. Problems from books like Griffiths / 3rd-4th year level stuff are important if you want to have the skills for physics grad school, but it sounds like OP just needs to take several physics grad classes. So I would think it would be helpful to solve SOME of the Griffiths problems, you definitely don't need to do them all. Maybe looking at your old course notes (and assignments if you kept them) and try to redo them would be a good idea (since you would probably have solutions too).

But thanks for the other suggestions on QM books, if I ever have to do that again (probably not) then I will be sure to look them up!

As for your question about math in astro: I admit I might have been thinking of two different spectrums of astro and physics work. For example, I was thinking of my 2nd year courses, where in astro, the only calculus (or more advanced) math we did was integration (something we learned in 1st year math courses). Astronomy was more about doing order of magnitude estimates, and knowing which concepts to put together in order to solve for some value -- integrating was done for things like finding the total mass from a density profile etc. At the same time, in my second year physics courses, we were doing PDEs in our mechanics classes (PDEs was a 3rd year math course for us, something we never saw before).

The rest of my physics courses were similarly mathematically challenging (EM, QM (omg so many integrals), etc.) but I didn't do condensed matter at all so I don't know what to say about that.

General relativity isn't really a part of astronomy -- it wasn't a requirement for either my undegrad astro+physics degree nor my masters astronomy degree. The main astro-related people who use relativity are people who study cosmology and astrophysicists (which are a cross between astronomers and physicists). Many schools have relativity people in physics or math departments.

Celestial mechanics can get very tricky mathematically when you start adding on more and more terms and refinements to the approximate solutions, so people who are doing purely astro theory stuff can have complicated math. In practice, it's sufficient to just understand how the things are computed and then use packaged tools, unless you want to make the tools yourself.

Research in astronomy definitely requires math, probably as much as most subfields of physics. I was thinking of classes more though (since the situation OP is in sounds like they need to just take the grad classes that a Masters student would take, not actually do a Physics PhD).

In all of my graduate level astronomy courses, the hardest math I had to do was integration. Some problems required re-writing the integral in some form so that I can then look up and say, ah ha, this is a Bessel function with arguments blah... etc. and others required me figuring out how to do Simpson's rule for a numerical integration (answer: simple rectangle rule was close enough after all). I am sure I did not even analytically solve any differential equations in my (observationally-based) astronomy grad courses. Graduate level E&M, on the other hand....

I guess the main point of my "I think the math is easier in astro" comment was that I feel that someone (like the OP) who prefers to consider conceptual problems more than doing nitty gritty math might enjoy/do better in astro grad courses than physics grad courses. The problem with this though, is that there is a lot of jargon and very weird systems in astronomy (e.g. the magnitude systems) that grad level courses may already assume students know from undergrad (not all programs do this though since many astro grad students come from physics undergrads).

Edited June 19, 2012 by TakeruK

[SeriousSillyPutty]

Thanks so much for the feedback!

Yes, you're right that I have to get into reviewing problems. I reviewed a bit of calc, then got caught up in other preparatory stuff (currently researching new laptops, as mine is dying), and I just have to re-dedicate time to practice problems.

Some of my most pleasant memories were from our physics homework groups that started up spontaneously but became a weekly event. The difference was that, at that point, I could hold my own as a contributing member of the group, whereas now I think I'll just be on the receiving end of help. Maybe I can be the plucky comic relief? Or maybe I can bring cookies?

I'm talking to my ed adviser this week, and she talked to the physics prof who's advising from that end of things. It sounds like he's trying to find the easiest classes he can for me that will count, which is appreciated even if somewhat patronizing as well. (Mostly appreciated! Like I said, the conceptual stuff is what I think is fun.)

As a side note, since you all had such good recommendations for me, I just read the first part of "Teaching Introductory Physics" by Arnold B. Arons. I wished I had read it before working in the physics help room as an undergrad, and I think it would be useful for TAs, because most of what he recommends is guiding students through concepts, and that's best done in small settings. Turns out a lot of college students don't really "get" area or ratios, which explains/confirms a lot of the struggles kids (well, pre-med students, I should say) had in intro physics. Good stuff.

[Gneiss1]

I bought a few of the calculus workbooks to get brushed up on anything I may have forgotten and i use MIT opencourseware for everything else. Love that site!