There are two approaches:
[math]1.[/math] Leaving unclear paragraphs for *later*.
[math]2.[/math] Tackling doubts mercilessly.
The second approach is exhausting. Where do you find the energy to be productive and do honest math?
>Mathematics is very hard work, and dons tend to be above average in health and vigor. Below a certain threshold a man cracks up; but above it, hard mental work makes for health and vigor (also—on much historical evidence throughout the ages—for longevity). - Littlewood
If you have later...
There are still problems summoning up like shapes in tetris...
Can you count how much science you need to build a snowboard hall for example?
>>8271212
>Where do you find the energy to be productive and do honest math?
I have nothing else to do with it.
It depends, if I'm in class, I usually opt for 1, try to write down the proofs (well, at least enough of each proof to be able to redo them later) and get the general idea. If I'm reading a book, I opt for 2., but as a consequence I rarely read for too long.
I have a good friend who is also very passionate and he does the exact opposite. He always asks the prof (or me or his neighbours) questions in class if something is unclear so as not to leave anything out. However, when reading a book he just skips through and tries to get the general idea.
I have never understood how someone could keep reading with gaps in their understanding. I think I can do that in class because the professor usually gives intuition, willingly or not, about what should be obvious and what is not (even through the intonation as they are speaking).
>>8271292
>I have never understood how someone could keep reading with gaps in their understanding.
It's not quite like that. It happens to me sometimes that I can't wrap my head around something after reading it for 3 times, usually some proof. Then I move on, but revisit it a few pages later, and then it's usually already evident to me.
It's the most time-efficient method I've found.
>>8271310
I have just thought about it and I'm thinking that maybe it's because I rarely write as I read. I have a lot of trouble remembering things that I have not written down (and hence using them as the pages go by).
Maybe it could help OP to work like that (ie. writing down the bulk of what they're reading)
C'mon, faggots. You're studying math, figure out a mathematically efficient way to learn math.
>>8271342
"what's the best way to solve an np-problem"
"just figure it out"
"just"
>>8271331
>Maybe it could help OP to work like that (ie. writing down the bulk of what they're reading)
I write everything down on my white desk then take notes and collect them. The problem is that sometimes a line of textbook can contain hours of math in it. Figuring everything out is very tiring.
>>8271212
I do 2. My classmates do 1. Occasionally when I'm stuck on some pedantic technical detail they will be confused about why I'm spending so much time on it. After explaining they will often not care about the details or they will offer simple solutions that I will quickly poke holes in.
I think in general 2 starts off being slower than 1 but it forces you to become more comfortable with formalism and to have a deeper and broader knowledge base. As a result I feel like 2 lets me blow through unproblematic content very quickly (or at least much faster than classmates) while instantly having to come to a full stop on problematic statements. For this reason I've found it useful to always use multiple textbooks as reference and to avoid authors who handwave excessively (i.e. aim their writing towards group 1 students who don't care about pedantry).
>>8271292
>I have a good friend who is also very passionate and he does the exact opposite. He always asks the prof (or me or his neighbours) questions in class if something is unclear so as not to leave anything out. However, when reading a book he just skips through and tries to get the general idea.
Sometimes I do this as well. When I skip ahead the issue isn't so much that I'm having trouble understanding the concept but rather that I'm having trouble understanding the author's explanation of the concept (unclear wording, some technical detail not mentioned, missing exposition, the point is unclear, etc..). Often cases after skipping ahead I realize what the author is using the concept for and then it becomes clear what the author actually meant to say earlier on (or at the very least it becomes clearer).
Perhaps your friend is different from myself but that at least is my own personal experience.
>>8271419
>The problem is that sometimes a line of textbook can contain hours of math in it. Figuring everything out is very tiring.
Keep your chin up, anon. You'll get better at this over time.
>>8271762
>Keep your chin up, anon. You'll get better at this over time.
Thanks for the support.
So very tiring