User:Micheal Hall

What is Algebra?
Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division, with an objective to find the values.

The above algebraic expressions are made up of variables, operators, and constants. Here the numbers 4, 28 are constants, x is the variable, and the arithmetic operation of addition is performed.

Branches of Algebra
The complexity of algebra is simplified by the use of numerous algebraic expressions. Based on the use and the complexity of the expressions, algebra can be classified into various branches that are listed below:


 * Pre-algebra
 * Elementary Algebra
 * Abstract Algebra
 * Universal Algebra

Pre-algebra
The basic ways of presenting the unknown values as variables help to create mathematical expressions. It helps in transforming real-life problems into an algebraic expression in mathematics. Forming a mathematical expression of the given problem statement is part of pre-algebra.

Elementary Algebra
Elementary algebra deals with solving the algebraic expressions for a viable answer. In elementary algebra, simple variables like x, y, are represented in the form of an equation. Based on the degree of the variable, the equations are called linear equations, quadratic equations, polynomials. Linear equations is of the form of ax + b = c, ax + by + c = 0, ax + by + cz + d = 0. Elementary algebra based on the degree of the variables, branches out into quadratic equations and polynomials. A general form of representation of a quadratic equation is ax2 + bx + c = 0, and for a polynomial equation, it is axn + bxn-1+ cxn-2+ .....k = 0.

Abstract Algebra
Abstract algebra deals with the use of abstract concepts like groups, rings, vectors rather than simple mathematical number systems. Rings are a simple level of abstraction found by writing the addition and multiplication properties together. Group theory and ring theory are two important concepts of abstract algebra. Abstract algebra finds numerous applications in computer sciences, physics, astronomy, and uses vector spaces to represent quantities.

Universal Algebra
All the other mathematical forms involving trigonometry, calculus, coordinate geometry involving algebraic expressions can be accounted as universal algebra. Across these topics, universal algebra studies mathematical expressions and does not involve the study of models of algebra. All the other branches of algebra can be considered as the subset of universal algebra. Any of the real-life problems can be classified into one of the branches of mathematics and can be solved using abstract algebra.