## The Algebra of Real Numbers

Algebra begins with a systematic study of the operations and rules of arithmetic. The operations of addition, subtraction, multiplication and… Click here to read more

From basic to higher mathematics

Algebra begins with a systematic study of the operations and rules of arithmetic. The operations of addition, subtraction, multiplication and… Click here to read more

The numbers used to measure real-world quantities such as length, area, volume, speed, electrical charges, probability of rain, room temperature,… Click here to read more

Grouping or classifying is a familiar technique in the natural sciences for dealing with the immense diversity of things in… Click here to read more

In applied mathematics, very large and very small numbers are written in compact form by using integer powers of $$10$$…. Click here to read more

Numbers produced by a calculator are often inexact because the calculator can work only with a finite number of decimal… Click here to read more

Some scientific calculators can be set to round off all displayed numbers to a particular number of decimal places or… Click here to read more

In the later years of his life, the Italian scientist Galileo Galilei (1564 – 1642) wrote about his experiments with… Click here to read more

Often the value of a variable quantity depends on the values of several other quantities, for instance the amount of… Click here to read more

An algebraic expression is an expression formed from any combination of numbers and variables by using the operations of addition, subtraction,… Click here to read more

To find the sum of two or more polynomials, we use the associative and commutative properties of addition to group… Click here to read more

To multiply two or more monomials, we use the commutative and associative properties of multiplication along with the following properties… Click here to read more

When two or more algebraic expressions are multiplied, each expression is called a factor of the product. For instance, in… Click here to read more

If $$p$$ and $$q$$ are algebraic expressions, the quotient, or ratio, $$p/q$$ is called a fractional expression (or simply a… Click here to read more

Two or more fractions with the same denominator are said to have a common denominator. The following rules for adding… Click here to read more

The following rules for multiplication and division of fractions can be derived from the basic algebraic properties of real numbers… Click here to read more

A fraction that contains one or more fractions in its numerator and denominator is called a complex fraction. Examples are:… Click here to read more

An equation containing a variable is neither true nor false until a particular number is substituted for the variable. If… Click here to read more

A linear equation or first-degree in $$x$$ is written in standard form as \[ax + b = 0\] with $$a… Click here to read more

Questions that arise in the real world are usually expressed in words rather than in mathematical symbols. For example: What… Click here to read more

A quadratic equation or second degree equation in $$x$$ is written in standard form as \[a{x^2} + bx + c… Click here to read more

The process of writing an expression as a product of two or more common factors is called the method of… Click here to read more

Sometimes factorization of a given quadratic equation is not possible. When coefficients in the quadratic equation are large numbers, then… Click here to read more

The completing square method is still a long method for solving the quadratic equation, so to make calculations shorter and… Click here to read more

Quadratic equations have many applications in the arts and sciences, business, economics, medicine and engineering. Example: A certain negative number… Click here to read more

The expression $${b^2} – 4ac$$, which appears under the radical sign in the quadratic formula \[x = \frac{{ – b… Click here to read more

An equation in which the unknown appears in a radicand is called a radical equation. For instance: $$\sqrt[4]{{{x^2} – 5}}… Click here to read more

We saw that a point P on a number line can be specified by a real number $$x$$ called its… Click here to read more

A function is a rule, correspondence, or mapping $$x \mapsto y$$ that assigns to each real number $$x$$ (the input)… Click here to read more

The graph of a function f is defined to be the graph of the corresponding equation $$y = f\left( x… Click here to read more

The graph in figure 1 (a) is always rising as we move to the right, a geometric indication that the… Click here to read more

A function $$f$$ of the form $$f\left( x \right) = a{x^2} + bx + c$$, where $$a,\,b$$ and $$c$$ are… Click here to read more

The word sequence denotes certain objects or events occurring in the same order. In itself, a sequence is a set… Click here to read more

An arithmetic sequence or progression (abbreviated as A.P) is a sequence in which each term after the first is obtained… Click here to read more

The sum of an indicated number of terms in a sequence is called a series. The series obtained by adding… Click here to read more

Example: Tickets for a certain show were printed bearing numbers from $$1$$ to $$100$$. The odd number tickets were sold… Click here to read more

Introduction Geometric sequence is a second type of sequence. One important application of geometric progression is computing interest on savings… Click here to read more

The series obtained by adding the terms of a G.P. is called the geometric series. Let $${S_n}$$ be the sum… Click here to read more

A geometric sequence in which the number of terms increases without bounds is called an infinite geometric series. If the… Click here to read more

In this tutorial we discuss the related problems of application of geometric sequence and geometric series. Example: A line is… Click here to read more

Set theory, which was developed by Gorge Cantor (1845-1918) between 1874-1895, is a basic mathematical tool that is used by… Click here to read more

The word matrix was first introduced by English mathematician Jame Sylverter (1814-1897). Another mathematician, Arther Caylay (1821-1895), also developed the… Click here to read more

Matrix: Now we will write formal definition of a matrix. An arrangement of numbers into m-rows and n-columns is called… Click here to read more

There are several types of matrices, but the most commonly used are: Rows Matrix Columns Matrix Rectangular Matrix Square Matrix… Click here to read more

The algebra of matrices includes Addition of Matrices Subtraction of Matrices Multiplication of a Matrix by Scalar Multiplication of Matrices… Click here to read more

Definition of a Set: A set is a well-defined collection of distinct objects, i.e. the nature of the object is… Click here to read more

In set theory the concept of an empty set or null set is very important and interesting. Its definition is… Click here to read more

The concept of a subset is defined as a set $$A$$ which is said to be the subset of a… Click here to read more

Equality of sets is defined as set $$A$$ is said to be equal to set $$B$$ if both sets have… Click here to read more