u/Any_Tower8201

How you people study math?

I'm a self study person and would like to hear some suggestions from people who are doing math professionally.

This is how I study.

I usually study the theory part first and try to understand the core concepts and stuff like that and go for the examples and try them all of my own. Most of the time I come to the answer atleast have a idea how to initiate or set up.

But some time I'll have zero idea even after seeing the result that why they start that answer like that to prove something (it is this fact that I'm not able to start a proof by myself is exactly what bothers me each time) It seems they picked it out of blue and never in a million year I'll start with this argument because I don't see why they start with that idea at first place(I attached example below).Then I start to question that is my theory part even good? Do i really understood it? etc. All these just because I don't exactly see/know how to start a proof.

For eg take the one I showed in the pic. I will never start the procedure of taking BC× on both sides even if I give my self a whole day to prove that result.

Is this how people usually study or I'm Missing some core understanding or something?

It really frustrates me.

TIA :)

I feel like the book made a unnecessary restriction by using arcsine, as the interval before it clearly enable us to use any value for x from Real Numbers Set.

Please let me know if Im out of any conventions or concept here.

Thanks.

The book says in the first photo the last 6 in 10.46cm is uncertain/doubtful digit but still its a significant digit but in the next page when they discuss about a scale with LC as 1cm, they say only 6 and 0 are SD. My question is why it can't be the case that the last '0' in 600 could be the uncertain digit as the scale has cm marking and one could guess it is very near the 60cm marking so their guess it 600 cm. (I realise its not in standard scientific notation, I'm doubtful about the consistency of the book)

Thank You