Self-Study Math Master

Hua Luogeng (华罗庚) urged using the daily 10-20 mins intervals while waiting for buses, queues, idle times, make it at least 1 hour a day to read Math books which you carry along with you.
Hua advised on speedy self-learning Math :
1) Choose the Best book on the Topic written by the Master (say, Abstract Algebra), read completely and do the exercises.
2) Read other reference books. Read only those new topics not covered in 1).
If not much new things, return them to bookshelf. This way speed up reading many books in short time.
3) Then read International renown Math Journals.
Beware 90% are copy-cats or rubbish by University lecturers to meet their yearly publishing quota. Only < 10% are masterpieces.
4) Pick one topic to do your independent research.
5) Discuss with friends with better knowledge in the field.
This way you can be a Master in the topic in 4 to 5 years.

Open Cubic Root

Mental Trick

It was discovered by the Martial Art writer Liang Yusheng 武侠小说家 梁羽生 (《白发魔女传》作者), who met Hua Luogeng (华罗庚) @1979 in England:
2³= [8]
8³= 51[2]
3³= 2[7]
7³= 34[3]

The last digit pairs :
[2 <->8] , [3 <-> 7]
Others unchanged.

Example:

$latex \sqrt[3]{658503} = N$
Last three digits 503 <-> ...[7]
First three digits 658:
 (8³ =512)< 658 < (729 = 9³)
=>  8...
Answer : $latex \sqrt[3]{658503} = N$= 87
Note: Similar trick for opening $latex \sqrt[23] {200 digits}$ by an indian lady Ms Shakuntala (83) dubbed "Human computer".

[caption id="attachment_2408" align="alignnone" width="560"] Human computer[/caption]