u/imnothere314

I hold a completed masters degree and was thinking about trying to get into a PhD program in the next couple years as my life becomes more conducive to it. I seem to be seeing a lot of direct to PhD type programs and as such have been having a bit of hard time finding information about what it might entail to get into and complete a PhD program when you already have a masters in the field. If anyone has info on what they've seen or experienced in terms of program and/or financial requirements (for example amount of required courses, general phd costs, timelines, etc.). Would also love any general advice in terms of figuring out potential dissertation topics, applications, or programs you've heard good things about. US based, undergrad/masters are in applied math so would be looking in that general field i.e. mathematics / OR / Stats / Data.

I was recently rewatching Community and came to S6E1 where frisbees collapse the cafeteria roof in the opening scene. Sorry if that spoiled it for you but it's been out for years and happens in the first like minute of the episode and is not all that critical. Anyways I was curious about the feasibility so took a stab at some of the math below. Would love to hear additional thoughts about the requirements of the neglect needed to allow frisbees to collapse a roof.

Engineering and building code knowledge are limited but Google told me that most residential buildings are built to accommodate 20lbs per square foot of snow weight before having issues.

A regulation ultimately frisbee disc is 175 grams and has a diameter of 10.75 inches. This yields a surface area of about 0.6 sqft. To get 20 lbs of frisbee requires about 9075 grams or about 52 frisbees.

If we assume frisbees are landing in mostly the same area and create a pile, we can approximate the pile with a nice pyramid. Given that a frisbee takes about about half a square foot and it would take 52 frisbees stacked on top of each other to get to the 20lbs, I think it's safe to say it would require a pyramid that is 26 frisbees tall. Let the pyramid be built such that you have one frisbee on top, four beneath that, 9 beneath that and so on. Then we would have sum_n=1 to 26 of n^2 frisbees or 5,571 frisbees needing to make it to the roof in the same general area to cause collapse.

In the episode they show Leonard throwing a frisbee and they give the aesthetic of being in the 60s or 70s I'd say. Therefore implying that frisbees have been getting thrown up without cleaning for about 45 years (based on S6 being set in 2014-2015).

Putting this together, we need at least 5,571 frisbees in the same area to likely cause the roof to collapse (especially considering structural degradation over the time frame) and we have 45 years to accomplish that which gives us an average of 124 frisbees per year or 2.5 a week since community colleges are active close to year round. Needless to say we are at less than one a day on average which seems more than feasible.

In conclusion it seems logical that should they have never cleaned or replaced the roof since the frisbee thrown by Leonard in the flashback that a sufficient amount of frisbees would have made it on to the roof of greendale university in order to collapse it at the start of season 6. Now given that a frisbee takes up about 1.5 L of space, I'm pretty sure you'd need at least half a million to fill up the cafeteria as it appeared so it gets a little iffy there.