Math...
I am strong in Math. But the field has to really fit my mind otherwise I have problems. I was decent at Algebra but not great, but once I hit Calculus everything fit my mind like a glove and I started to understand all these connections between areas and everything made sense. In more advanced courses I tend to not quite understand everything I need to, too many new symbols for me to internalize the meaning of.
I don't really take notes beyond what is being written down on the board, it is more a system that I memorize something a little better if I get my whole body involved. But if I really fascinated (or sometimes really lost) I'll just forget the notes and concentrate on what the teacher is saying. If all the information is in the books anyway this is sometimes better.
Also, if I really don't understand something I have to read and reread the explanations in the books and rephrase all the words into something I inherently understand. Or perhaps draw pictures of what is actually going on, even if these pictures are abstract and not filling in all the details it can be a drastic help. If I can't get this to work on the current section, I go backward into something a bit more basic until do the same thing until I can internalize the older stuff. Sometimes going forward into the more advanced stuff helps sometimes, since early things may be going over too many details and you may need to see the big picture of what is going on then attach all the details to this overall view of things.
Math is a great subject though. Its much more creative and interesting than the early classes lead you to believe. Calc really opened my eyes to what Math can really do.
I am weird I guess. I really like literature, math, science, history. Well certain parts of all of that I am really interested in. And I guess there are ways to tie all that stuff in together. Like the acient Mayan mathmatical system which they used to make a calander using the starts. That involves history math science well not literature but I could tie in somethign else I am sure.
But as for notes for science and stuff.
What I try to do is make my own notes a head of time. Or try. Like I am horrible at following lectures so as he is talking I read through the chapter and take my own notes and work through the example problems and when my teacher does an example I write that down and study it later when I write my master copy of cohesive notes. And for all the big homework problems quizs and tests I put those in my master copy of my notes for like finals. Because at least for my teachers the finals are just a rehash of the old test, quiz and homework problems. Its really handing to get like a really nice notebook. I got myself a really cool moleskine. You can't rip out the pages which really helps to keep everything together and makes you want to keep everything neat so its easier to look through your notes really quick. Highligh the really important stuff. So when the test comes you can do a quicker review of the stuff that matters and look at all the correct worked out problems.
That applies to sciences, for math, I never really took notes I really like math but never listen to the guys anyways. So the notes I do write in that class are pretty much a commentary to myself. Haha. Its fun because when you randomly find them later you are wondering what the hell happened?
But that isn't wierd though. There is a stereotype of mathematicians just being interested in math and then maybe science but aside from math, I am probably more interested in literature then science. I think this is common. I mean, I am only really interested in pure math anyway, which is more an art than a science.
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Yeah, Richard Allenby mentions this in the preface to his classic algebra text, Rings, Groups and Fields.
Mathematics is not a linear process and most of the stuff you find in books will not be presented in the same order in which it was originally discovered/invented.
A lot of the time, you have to skip the detail and come back to it later when you have a better understanding of the high level idea and the motivation and direction of the theory. A lot of the time this is the standard pedagogical approach in many math courses anyway e.g. it is traditional to learn the techniques of integral amd differential calculus before taking an analysis course which gives the rigourous proofs and definitions of differentiability, the Riemann Integral and the fundamental theorem of calculus etc.
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Faire est plus digne que seulement étant
