How much did you know when you entered Grad School?

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deluks917
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a lot of people ask what people should know. However I think it would be interesting to here what people's preparation for grad school really was. Math/Physics/Engineering are all fine. If you are entering in the fall I would also like to here from you.
 
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It's a tough question to quantify. I am entering a physical chemistry program. I'll most likely be doing theory (analytical theory, not computational simulations).

According to my coursework, I am knowledgeable in classical mechanics, physical chemistry, quantum mechanics, thermodynamics, statistical mechanics, spectroscopy, computational chemistry and inorganic chemistry, plus some stuff I am forgetting (not e&m, my big gap).

More personally, I feel I only have a good grasp of thermodynamics, quantum mechanics and stat mech at the undergraduate level. Those are the areas I feel very comfortable self studying, working out problems, filling in gaps, etc.

I am familiar with a lot more topics so when people talk about broadening in spectroscopy, or spin-boson model or lie algrebras, I can follow the terminology without getting lost but I am not particularly comfortable working on those areas by myself.

My math background is solid for a chemistry or physics major. I have a very good background in math, I've taken tons of courses BUT I am not particularly great at math so there are many people with lesser backgrounds who are more capable.
 
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I'm entering a math PhD program this fall after finishing my undergrad last fall (I'm in the US). In terms of preparation, I double majored in math and physics in undergrad and so I have all of the standard coursework for those degrees. I did graduate courses in quantum mechanics, functional analysis, operator theory/algebras, algebra, algebraic geometry/topology, and differential topology/geometry.

I feel like I've forgotten a serious chunk of the physics I knew, though. I basically did all of my physics requirements and then all of my math requirements, instead of doing them at the same time (since I didn't decide to major in math until my 4th year). I feel that some of my early grad-level coursework in math was pretty weak because of that - I barely got by and it routinely took me hours to solve a single problem. So I'm not going to try to test out of any of the intro grad coursework since I think it will be worthwhile for me to relearn it all, and in a more serious manner than I did as an undergrad where I worried about the grade too much.