When did you mind really sharpened as a physics students

(in math) when i realized my advisor was not going to solve my research problem for me and i had to think as hard about it as i possibly could do.

it reminds me of my most effective day as a high school tutor, once when i wAS TOO TIRED TO DO THE KID'S HOMEWORK FOR HIM, AND HE BEGAN TO DO IT HIMSELF.

 

That sort of made me laugh. Just goes to show what people will do when they can not depend on someone else.

 

Still waiting - hopefully it is before the dementia kicks in!

 

Haha! I laughed too. It's a good point, though!

I have many years to go before my mind has any sense whatsoever of knowing what I'm doing in math or physics. I feel so confined: it's really exciting to look at others and see what in a few years I should be able to accomplish. Thanks for starting this thread :)

 

Taking upper division electromagnetism as a sophomore undergraduate, I had self-studied the multivariable calculus and differential equations, and I was at the top of my class. But the professor would always give me scores of 8/10 on assignments, since he held the students at my small school to the same level of rigor as he had experienced in the ivy league (so my classmate's scores were even worse).

Anyway, one day I sat in the quiet library basement and told myself I would get a 10 on the next assignment. I used a pen and demanded that my handwriting be perfect, and somehow this caused my brain to forge a new connection with the symbols I was writing. For the first time, I could look directly at written mathematics as if I had gone from being legally blind to having perfect 20/20 vision. I began to interpret all the notation literally, and could see every deductive step in the demonstration. I got a 10, and went on to have a great relationship with that professor.

After that epiphany in the basement my handwriting came from a different place; in my mind, as opposed to from muscle memory in my hand. When I got injured and had to teach class with my non-dominant hand, the students were amazed to no end that I could fill the chalkboard with proofs with my alternate hand without any prior practice. The handwriting looks eerily the same as on the hand I spent dozens of hours "practicing" with in my youth. But practice is nothing, and focus is everything.

P.S. Never belittle the importance of handwriting in math/phys education!

 

That was an interesting story Crosson. I too am interested in self-studying some advanced topics in Calculus, so that I ca later pursue some Biophysics courses. I was interested in knowing if you could send me a PM with some of the books you used to teach yourself. Thanks.

 

I'll answer this in the thread, in case anyone else cares.

I don't buy books, and as I mentioned I was in the library, so I actually used many different books that had minor variations on these generic titles:

Advanced Calculus
Multivariable Calculus
Introduction to Differential Equations

I read 3-5 books on each of those subjects. There is so much overlap that this is much easier than it sounds. In fact I think that the overlap is necessary to give that well rounded view of the subject that you cannot get from one single book. So my recommendation is to go to a university library and read as many books on the subjects you are interested in as you can.

For Biophysics, I think the introduction to differential equations would be the most applicable, which would open the doors to many other books on applied math.

 

Thanks for the answer Crosson.

 

I have to say, I was transformed after meeting a friend who wasn't afraid of correcting my mistake. I had a roommate who would attack me for every time I talk about physics. Almost all the time, when I'm trying to convince him of something, he would not listen to me unless I first write down all of my assumptions. Now, I found that writing out explicitly what are my assumptions in solving physics problem really really really helpful.