Postby TakeruK » Wed Oct 18, 2017 1:11 pm
Highly variant. In my experience, for any particular grad course, there are probably 3 times as many major topics that could be covered than there is time. So, each instructor will pick their own set of topics to cover. Then, since grad courses go into topics in depth, there are 2-3 ways to teach each topic too (e.g. different applications, examples, approaches).
Of course, for some "core" courses there are some key skills that are going to be consistent across all grad classes. But the way it is taught will vary depending on each instructor (i.e. a grad class taught at School X by Prof A will be different from the same class taught 3 years later by Prof B).
Some examples. I took some undergrad/grad cross-level classes in undergrad, took grad classes in my Masters and took grad classes in my PhD (3 different schools).
- I took a grad-level astronomical instrumentation class three times. The first one was taught by a radio astronomer and we learned a lot about measurements with examples to radio telescopes. The second class was taught by 4 different professors covering 4 different regions of the EM field. Since each region only had 2-3 weeks of coverage, it was very much like a survey class---we only learned a little bit about each type of detector. The third class specifically covered optical and infrared detectors. We learned a lot about the fine details of how these detectors actually worked. There was also a field trip to an observatory. And we spent quite a bit of time learning about future detectors and what's state of the art, not just want is already deployed.
- I took a Bayesian statistics class twice (Masters and PhD). The first time was very mathematically/theory focussed. We learned probability theory and derived the main principles of Bayesian statistics. When we learned about Markov Chain Monte Carlo methods, we went through proofs of theorems to show that it worked. The second time was very applications focussed. The class was taught as a toolbox of statistical tools. We didn't really go into detail on proving why each tool worked. Instead, we were taught to familiarize ourselves with each tool, learned what principles drive each tool and we learned when we can use it and when we cannot (i.e. its limitations). When we learned MCMC, the prof showed us examples of MCMC results to show that it worked (we did talk about the theory afterwards, but to a lesser extent). The homework were all coding related and writing algorithms instead of proofs.
Just two examples.
If I was a senior in undergrad, I would not worry at all about trying to test out of grad classes. Unless you already know the school you want to go to will allow it, most grad schools do not allow you to skip their classes. (Full disclosure: when I was a senior undergrad, I was thinking the same way as you and asked my advisor/grad class instructors about this. They told me what I just told you.) After going through grad school myself and experiencing the differences, I agree with school policies to not allow students to test out. It's worth seeing some of the material again and you learn new things every time. For that Bayesian class I mentioned above, I TA'ed that class two more times (so I saw the material 4 times) and each time I learned something new or gained a new perspective.
Instead, my advice would be to take grad classes in the areas you're interested in, if you can. This will expose you to more people/research in the area and give you a better idea of what's going on in your intended area of research. Maybe you'll find it less interesting or find something really cool in that specific subfield that you want to do your dissertation on. Then later, when you take a similar course in your graduate program, having this background knowledge will help you absorb material at a deeper level, further improving your foundation in your intended area of work.