micromass said:
But you don't know more than the average grad student! Not even undergrad stuff! Why do you think you do?
Sure, grad students forget things. I'm sure that there are not many grad students who can immediately write down the product-to-sum formulas from trigonometry (but I'm sure that many grad students can derive these formulas easily when asked to do so!). But memorizing those formulas is completely useless. If it comes to the important stuff (= problem-solving, useful knowledge), then grad students are miles ahead of you.
You say that students rotely memorize their stuff. And you seem to imply that grad students do that. This is a very skewed opinion of reality. One can not get into grad school by simple rote memorization. I'm sure that students fresh from HS memorized everything, but that is entirely different from grad school. If you don't actually understand what you learn and if you just memorize it, then there is no way you can get into grad school (although exceptions exist, of course).
From your posts I really get the feeling that you regard yourself as superior to most students (and even grad students). This alone indicates that your physics knowledge is insufficient. Why? Because the more physics you actually know, the more you realize what you don't know. Studying physics is a humbling experience!
I do understand it. When I just got out of HS, I thought I was pretty good in mathematics and I thought that I knew as much as math professors. Now I can look back at myself and say that I was a naive idiot. I didn't know any math at all. And as I progressed in my academic career, my views of reality became much more realistic. Now I know tons more than I knew in HS, but I realize that I still don't know anything of math.
I'm certain that many students can read grad texts. But the question this is actually a good idea. If you skip undergrad texts, then your understanding will be very shallow. In the best case, you realize that your understanding is not very big and you remedy this by studying what you don't understand very well. In the worst case, you fool yourself and you think that your understanding is adequate (I fear that you are in this scenario).
Also, grad texts are difficult usually because of the math involved and not necessarily because of the physics. Physical intuition must be gained from undergrad texts.
Personally, I know some differential geometry. So I could get a grad text on classical mechanics and maybe I succeed in solving the problems in the text (I doubt it). But when I try to solve a problem in Kleppner, then I don't know how to start. Does that mean that I know classical mechanics? No, I might understand the math, but I don't understand the physics involved. If I want to understand classical mechanics, then I know that I have to work through kleppner first and only then move on to advanced (and perhaps grad) texts. I have the mathematical maturity to work through a grad texts in mechanics, but I realize that this would be wrong way to go.
I actually prefer to remember how to derive formulas than remember the formulas themselves. For example, instead of remembering the formulas given for the derivative of cosecant, secant and cotangent, I remember the quotient rule and apply it to 1/sin, 1/cos, 1/tan, which for 1/sin would be ((sin)(0) - (1)(cos))/(sin)^2 = -(csc)(cot) The problem is that it takes more time this way on a test. I also recall in a chemistry class the professor told the class to memorize like six different equations for converting moles and atoms and grams around when it's all elementary when you just understand the relationships between them.
What exactly do you mean by physical intuition? I thought everybody was born with that? Well maybe for mechanics but in the case of E/M I think more math brings better intuition. I don't have a problem visualizing such mathematical concepts or figuring out how they relate in a physical sense. Every physics class I have ever taken, I felt like it was just basic algebra or even arithmetic in disguise. And the labs are no help either. It seems pointless to do a lab that one can do in one's head or read out of a textbook and picture it like a storybook.
And as for the humbling... rather the reverse occurred. I used to be less than confident in my abilities. Part of it was due to my foster parent telling me I was retarded and unable to comprehend AP material (this coming from a woman who barely passed high school) but then I entered college, thinking I would have a fun time learning a lot in my chemistry class... all I got was, well, a class that was even easier than what I had taken in high school. A total ripoff. When you are getting an A when you don't do the homework or even have the textbook, you KNOW you are in the wrong class. And this was supposedly the section for science majors too, and the other kids found it too hard and many dropped out. And I am like; wow, am I REALLY that much smarter than everyone else? Of course this was a community college that didn't even have entry level physics and calculus classes (not my choice to go there, long story) so it should be taken with a grain of salt. I transferred very next semester to a four year college (one that only had physics minors but it was in town and I could transfer to a bigger one eventually)
This school, well, I just couldn't focus, and so I cried and thought I was going to get bad grades and fail everything... I didn't. I got an A in physics without trying. Soooo, if I'm not fit to study such subjects then I don't know what is to be said about all the engineering majors in that class that wouldn't have passed were it not for the grading curve. But remember this wasn't a very selective school and it being first semester physics being taught second semester means that the class is mostly idiots that weren't equipped to take it first semester anyway so again, take it with a grain of salt.
And then I moved and had to go back to a community college and that's where the disaster happened. I mean, I certainly wasn't failing, but I wasn't performing at anywhere near my level, and I probably overreacted a bit, which resulted in me being withdrawn and put on antidepressants. Wellbutrin was minimally effective, Zoloft made me too lazy and unmotivated, and Strattera gave me borderline psychotic mood swings by the minute. Not fun. I finally decided just to stick to a small dose of Adderall and that has done the best for my mood and focus, though my focus still leaves a lot to be desired.
So yeah, maybe I'm a little speedy for thinking I'm so much better than everyone else, or so it appears I come across anyway. But really, what is more demotivating than being more or less a community college dropout? You think I felt like such an arrogant little snot after that? NO! I more or less moped around for a year! Ok I studied but not very effectively, or so I felt anyway, and I put an tutoring ad on Craigslist and actually got hired. And I must be doing a good job because I have regular clients that hire me again and again and think that I'm better than a college grad (not to mention cheaper); I even tutored somebody for his E/M final; obviously I do not feel that is my strongest subject, buuut I did know it better than him (but then it was his weak subject you know) and he hired me twice so obviously I was doing a good job.
And so I decided... am I going to let this two bit institution make me feel worthless? Am I going to sell myself short and further stunt myself? I am by no means as egotistical as I appear, but the key is to have a healthy level of confidence.
That, and an unhealthy level of obsession. I mean, how can you be obsessed with something and NOT fully understand it? I mean get a little high just from studying and thinking about it and especially the "EUREKA!" moments; those will come into my dreams and excite me so much I wake up at night...
For the last time... I have not entirely skipped the undergrad texts; I just went through them really fast... ok not really fast; I sort of dragged on because I couldn't focus, probably because I was out traveling all the time and it's hard to focus on studying while riding a bus. Also, I felt the understanding I got from some of the undergraduate texts was shallow. Trust me, I know when I read a book and don't understand it; it has happened quite a bit before.