Modern Applied algebra Pdf

The notion of a “category” was first introduced by the famous mathematician Euler, who in 1775 used it to solve an equation of a special type. Today any mathematician at least knows this notion, but it is also required reading for most students, and hence we can say that every “educated person” knows what a category is.

This introductory chapter outlines the basic definitions and results which will be used in greater detail later on. We then introduce some of the main themes that will be developed in the book, especially those relating to algebraic structures of real and complex varieties over finite fields, in order to give the reader a general idea of what is to follow.

Algebra is a branch of mathematics that focuses on solving equations containing variables. Equations are representations of mathematical statements and their solutions. Algebra teaches students to use abstraction to solve problems; it has rules and uses symbols that often have specific meanings. These symbols allow us to talk about math in an abstract way. There are many branches under the larger umbrella of algebra, one of which is called algebraic logic.