Algebra helps in the representation of problems or situations as mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression. All the branches of mathematics such as trigonometry, calculus, coordinate geometry, involve the use of algebra. One simple example of an expression in algebra is 2x + 4 = 8.

Algebra deals with symbols and these symbols are related to each other with the help of operators. It is not just a mathematical concept, but a skill that all of us use in our daily life without even realizing it. Understanding algebra as a concept is more important than solving equations and finding the right answer, as it is useful in all the other topics of mathematics that you are going to learn in the future or you have already learned in past.

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.

Algebra Topics

Algebra is divided into numerous topics to help for a detailed study. Here we have listed below some of the important topics of algebra such as algebraic expressions and equations, sequence and series, exponents, logarithm, and sets.

Algebraic Expressions

An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/). An example of an algebraic expression is 5x + 6. Here 5 and 6 are fixed numbers and x is a variable. Further, the variables can be simple variables using alphabets like x, y, z or can have complex variables like x2, x3, xn, xy, x2y, etc. Algebraic expressions are also known as polynomials. A polynomial is an expression consisting of variables (also called indeterminates), coefficients, and non-negative integer exponents of variables. Example: 5x3 + 4x2 + 7x + 2 = 0.

An equation is a mathematical statement with an ‘equal to’ symbol between two algebraic expressions that have equal values. Given below are the different types of equations, based on the degree of the variable, where we apply the concept of algebra:

  • Linear Equations: Linear equations help in representing the relationship between variables such as x, y, z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
  • Quadratic Equations: A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
  • Cubic Equations: The algebraic equations having variables with power 3 are referred to as cubic equations. A generalized form of a cubic equation is ax3 + bx2 + cx + d = 0. A cubic equation has numerous applications in calculus and three-dimensional geometry.