A very easy way to improve your writing would be to separate your text into paragraphs.
It doesn’t take any intelligence but just awareness of norms.
It seems that my mind lights up with too many questions when I learn math, many of which are difficult to answer. (My professor does not have much time to meet students for consultations and I don’t think I want to waste his time).
Not everybody is good at math. That’s okay. Scott Alexander who’s an influential person in this community writes on his blog:
In Math, I just barely by the skin of my teeth scraped together a pass in Calculus with a C-. [...]“Scott Alexander, who by making a herculean effort managed to pass Calculus I, even though they kept throwing random things after the little curly S sign and pretending it made sense.”[...]I don’t want to have to accept the blame for being a lazy person who just didn’t try hard enough in Math.
Things such as why dividing by zero doesn’t work confuses me and I often wonder at things such as the Fundamental Theorem of Calculus.
Math is about abstract thinking. That means “common sense” often doesn’t work. One has to let go of naive assumptions and accept answers that don’t seem obvious.
In many cases the ability to trust that established mathematical finding are correct even if you can’t follow the proof that establishes them is an useful ability. It makes life easier.
In many cases the ability to trust that established mathematical finding are correct even if you can’t follow the proof that establishes them is an useful ability. It makes life easier.
While yes, that can make life easier, it also means that if the reason why you can’t follow the proof is because you’re misunderstanding the finding in question, then you’re not applying any error checking and anything that you do that depends on that misunderstanding is going to potentially be incorrect. So, if you’re going into any field where mathematics is important, it can also make life significantly harder.
It’s hard to put in words what I mean. There a certain ability to think in abstract concepts that you need in math. Wanting things to feel like you “understand” can be the wrong mode of engaging complex math.
That doesn’t mean that understanding math isn’t useful but it’s abstract understanding and trying to seek a feeling of common sense can hold people back.
I… think I learnt math in a very different way to you. If I didn’t feel that I understood something, I went back until I felt that I did.
I do not understand the difference between an “abstract understanding” and a “feeling of common sense”. Is a feeling of common sense not a subtype of an abstract understanding (in the same way that a “square” is a subtype of a “rectangle”)?
On the contrary, failing to feel common sense is usually a sign that you don’t really understand what’s going on. Your understanding of an abstract concept is only as good as that of your best example. The abstract method in mathematics is just a way of taking features common to several examples and formulating a theory that can be applied in many cases. With that said, it is a useful skill in math to be able to play the game and proceed formally.
There’s an anecdote about a famous math professor who had to teach a class. The first time, the students didn’t understand. A year later, he taught it again. Learning from experience, he made it simpler. The students still didn’t understand. When he taught it a third time, he made it simple enough that even he finally understood it.
I will concede that in practice it can be expedient to trust the experts with the complications and use ready-made formulas.
A very easy way to improve your writing would be to separate your text into paragraphs. It doesn’t take any intelligence but just awareness of norms.
Math.stackexchange exists for that purpose.
Not everybody is good at math. That’s okay. Scott Alexander who’s an influential person in this community writes on his blog:
Math is about abstract thinking. That means “common sense” often doesn’t work. One has to let go of naive assumptions and accept answers that don’t seem obvious.
In many cases the ability to trust that established mathematical finding are correct even if you can’t follow the proof that establishes them is an useful ability. It makes life easier.
In addition to what CCC wrote http://math.stackexchange.com/questions/26445/division-by-0 is a good explanation of the case.
Accepting feedback and directly applying it is great :)
While yes, that can make life easier, it also means that if the reason why you can’t follow the proof is because you’re misunderstanding the finding in question, then you’re not applying any error checking and anything that you do that depends on that misunderstanding is going to potentially be incorrect. So, if you’re going into any field where mathematics is important, it can also make life significantly harder.
It’s hard to put in words what I mean. There a certain ability to think in abstract concepts that you need in math. Wanting things to feel like you “understand” can be the wrong mode of engaging complex math.
That doesn’t mean that understanding math isn’t useful but it’s abstract understanding and trying to seek a feeling of common sense can hold people back.
I… think I learnt math in a very different way to you. If I didn’t feel that I understood something, I went back until I felt that I did.
I do not understand the difference between an “abstract understanding” and a “feeling of common sense”. Is a feeling of common sense not a subtype of an abstract understanding (in the same way that a “square” is a subtype of a “rectangle”)?
On the contrary, failing to feel common sense is usually a sign that you don’t really understand what’s going on. Your understanding of an abstract concept is only as good as that of your best example. The abstract method in mathematics is just a way of taking features common to several examples and formulating a theory that can be applied in many cases. With that said, it is a useful skill in math to be able to play the game and proceed formally.
There’s an anecdote about a famous math professor who had to teach a class. The first time, the students didn’t understand. A year later, he taught it again. Learning from experience, he made it simpler. The students still didn’t understand. When he taught it a third time, he made it simple enough that even he finally understood it.
I will concede that in practice it can be expedient to trust the experts with the complications and use ready-made formulas.
This doesn’t seem to be true for anything that’s normally analyzed statistically: the stock market, for example, or large-scale meteorology.