Description: Review of fundamental structures of algebra (groups, rings, fields, modules, algebras); Jordan-Holder and Sylow theorems; Galois theory; bilinear forms; modules over principal ideal ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of the recent work by ...

The field of algebraic geometry investigates the profound interplay between polynomial equations and geometric structures, providing a rich framework that unites abstract theory with practical ...

Algebraic geometry is a branch of mathematics which, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of polynomials.

Several fields of mathematics have developed in total isolation, using their own 'undecipherable' coded languages. Mathematicians now present 'big algebras,' a two-way mathematical 'dictionary' ...

If one manages to graduate from high school without the rudiments of algebra, geometry and trigonometry, there are certain relatively high-paying careers probably off-limits for life – such as careers ...