**Modern Algebra:** Based on the 1931 influential book “Modern Algebra” written by Van de Waerden (the student of E. Noether). Pioneered by the 20th century german Göttingen school of mathematicians, it deals with Mathematics in an abstract, axiomatic approach of mathematical structures such as **Group, Ring, Vector Space, Module and Linear Algebra**. It differs from the computational Algebra in 19th century dealing with Matrices and Polynomial equations.

This phase of Modern Algebra emphasises on the algebraization of *Number Theory: * {N, Z, Q, R, C}

**Post-Modern Algebra:** The axiomatic, abstract treatment of Algebra is viewed as boring and difficult. There is a renewed interest in explicite computation, reviving the 19th century invariant theory. Also the structural coverage (Group, Ring, Fields, etc) in Modern Algebra is too narrow. There is emphasis on other structures beyond Number Theory, such as **Ordered Set, Monoid, Quasigroup, Category, ** etc.

Example:

The non-abelian Group S3 (order 6) has structures appeared in many branches of maths and sciences:

**[Reference]** :

“*Post-Modern Algebra*” by

Jonathan D.H. Smith and Anna B. Romanowska

1999, John Wiley & Sons