So, now you're at university, and you're thinking about heading for grad school ...
More re-runs from Ye Olde Blogge
The following is horribly UScentric, 'cause that's where I am right now.
The general principles are broadly applicable, the actual getting into grad school procedure bit in future post will be both US and THEM centric.
Caveat: these numbers are somewhat dated, but the shift is not large enough yet for me to bother re-searching them.
Each cohort in the US is about 4+ million people, about 4000 of those major in physics. Since participation in the further education in the US is almost 50%, that is 4000 out of about 2 million, or 0.2% of undergraduates (specifically, about 1.2 million bachelors degrees are awarded each year, with physics major 0.34% of those, near historic lows, trend has flattened after many years of decline, and may even be showing some secular rise
(see APS jobs in physics stats.
For what it is worth, about 1200-1500 PhDs in physics are currently awarded each year, almost half to non-US students, so about 1/6 to 1/7 of undergrads end up doing a PhD. The "rule of thirds" you'd infer from the raw numbers (# PhDs = 1/3 # BSc) is surprisingly robust at each step.
The number of astronomy undergraduates is much smaller still, since not a lot of universities (61 according to this article by Cabanela and Partridge in AER) have a separate astronomy department or a separate major (so a lot of people who become astronomers or astrophysicists start as physics majors, or have an astronomy minor).
The number of astronomy PhDs is fluctuating around 120 each year, with significant Poisson noise, as one might expect.
There are 25-30 major research universities which dominate the astronomy PhD production, so classes are small, and the intake is fought over hard.
Having said that, current astronomy undergraduate production is about 300 per year, and has grown significantly (AIP stats summarises). A lot of those are double majors with physics. Naively them about 1/2 of undergrads go on to PhDs, but after you allow for the foreign intake, it is more like 1/4 - 1/5, since some also go into graduate school in physics (and of course other fields, but I am not considering those now).
So, the good news is that if you're in the major, you have a high prior probability of going to grad school. You just have to pass the classes, get good grades, not go broke, survive the insanity of university, enjoy life, and take the GRE exam, the only exam stupider than the SATs...
So, what should you do. First, take all the math classes you can handle, especially if your interest is astrophysics; take calculus of course, through ODE, PDE, Complex Analysis, and some course covering spectral methods (Fourier and Laplace transforms etc). Better know what a Bessel function is when you get to grad school, and know immediately where to start on solutions to second order differential equations. Take also probability theory and statistics, linear algebra, numerical analysis, and computational techniques. If you can stand it, differential geometry, topology, functional analysis, and some advanced classes never hurt anyone.
I know I keep hammering on this point, but the primary limit on career paths within astrophysics is inadequate math preparation - too many students take minimal load of math classes and skip mathematics that is "not relevant" and then find years later that they did need if after all but they don't have the time, inclination or energy to go back and learn on their own.
Did I mention statistics? I'm increasingly convinced that a good survey of applied statistics is the single best thing any student can learn, especially if leavened with some probability theory.
Then take physics. You don't have to take all of it, but would it hurt to do so?
Solid state physics, wave theory, optics and quantum field theory all show up somewhere in astrophysics (all of physics does, that is why astrophysics is the greatest sub-field in physics! ;-) oh, and take relativity if you're at one of the few places it is offered.
What else. Well, the prereqs and college mandated hoops of course.
Don't burn yourself out, but given a choice, wouldn't you rather take a gen ed class on something that is interesting (to you).
Funky minors sound fun and macho, but they can destroy a GPA, a graduation schedule and enthusiasm - approach with care.
Then think about what you like to do when you finally get there? Like to build things, add labs and engineering classes (especially electronic and optics).
Like data? Then add more statistics and computing classes.
Like to think? Go buy a ruled pad and nice black ink pen (no pencils, this isn't kindergarten).
So, you did that, aced all the classes, are student president, captain of some NCAA team, and still have time to party.
Well, a long time ago, there was a rule of thumb - the odds of an incoming undergraduate in physics/astronomy getting a faculty position at a research university is about the same as the odds of an NCAA division 1 football player making the NFL.
But the earning potential is different (not as much as you'd think, lifetime average!).
And in both cases, it is not a bad career move, even if you don't make it all the way, the alternate career paths can be sweet. Oh, and in both cases, where you go to school matters a lot, for your average odds. But remember, there is always a Jerry Rice!
So, end of your junior year, if you can still stand the field, you need to start seriously working on grad school applications, and planning for the GREs. More later...
+1 on everything above.
I would add that being really fluent with computers is also very very valuable in grad school and beyond. That means programming, not just using pre-written applications. I suggest getting fluent in at least Fortran 77 and 90, C, and at least one scripting language (python, perl, ruby, etc). If you have the time, C++ wouldn't hurt, either...
And you really really need at least one course in numerical analysis so you know the right and no-so-right ways of using that programming knowledge to solve mathematical problems.
Computing is an absolute essential. To the languages above, I would add IDL, which is the lingua Franca of astrophysics, particularly observational astronomy. Being highly competent in programming makes for job options and security because there are, astonishingly, lots of non- faculty jobs in astronomy. The faculty job should not be seen as the only end point for a career in astronomy.