Abstract Algebra | ZF Axioms | Math Set Theory | Number Theory | Groups | Quotient Groups | Rings | Commutative Rings | Fields | Group Actions | Modules | Vector Spaces | Linear Operators and Matrices | Inner Product Spaces | Tensors | Exterior Algebras | Theory | Polynomial Rings | Category Theory |
Abstract Algebra
To me, Algebra is a branch of Mathematics that deals with symbols and the rules for manipulating those symbols. It really is the foundation of all Mathematics because it sets up and sets out the written language of math. Without algebra we would have no powerful method of communicating our Mathematical ideas (to humans or computers) and progress would essentially ground to a halt.