[general] regarding permission

Dear All,

I am interested in designing a mathematical computation package for Octave.
Hence I have
collected a lot of reading material for this purpose.

However I am a bit confused where :
I want to know if I can use the formulas or some algorithms present in the
text ( Springer books, research papers ) in my code and then present it in
Octave as open source  ( cite them ), is this method correct or do I need
any kind of permission from the publisher or the authors ?

I want to ask the if the experienced authors of libraries/packages know
all the maths/algorithms when they designed their libraries/packages or
they took help from other sources like me ?

Any response is appreciated !

Best wishes, Mudit