Hello..
Can anyone tell me any practical application(s) of "groups/rings/fields ", the bulding blocks of ABSTRACT algebra ?
I know they are merely unifying threads that connect different areas in Mathematics,
but as a seperate entity ..... where can they be of any significance ?
Is it that they are only developed to deeply dig into the definition of them or do they help in solving a particular pratical situation ?
as in .... for example a matrix ...its totally a mathematical tool which can used in many applications...viz; solving a set of linear equations , defining optimistic solutions ,etc.
For a layman, matrix or a set is understandable ..like set of integers,states in a country or matrix of coefficients of numbers etc .. heir definiton has been precise to be used in numerous ways .....
whereas groups/rings /fields ..they themselves are inter-connected , how do we explain these to a layman for him to understand ?
I'm sorry , i'm totally confused at this ...help me!