Algebra is one of the most ancient parts of mathematics, comprise of geometry, number theory, and analysis. Therefore, Definition of Algebra in maths is a combination of symbols and its rule, including manipulating these mathematical symbols. In this, we will include everything from the elementary equation to the study of the abstraction.
Moreover, algebra is the basics of Mathematics and included in many chapters of maths. It helps us to solve mathematical problems and drives many interests, percentage, ratio, and proportion issues. As a result, the algebra formula is used in our daily life to find out the volume of a container, distance, mass, and sales price of any object. Likewise, the unknown quantity can be determined by algebra.
The basics of Algebra in maths are called Elementary algebra, and the study of abstract or abstract part is called Abstract Algebra or advanced algebra. One of the essentials for studying mathematics or engineering is elementary algebra. Similarly, modern maths is an advanced study by professional mathematicians. The mathematician who does research, in general, is called an algebraist.
What are the different types of Algebra in maths?
Mainly, Algebra in maths is classified into different categories as
Elementary algebra or Algebra 1(one)
Algebra 1 is a branch that deals with the study of variables, constants, and relations between them. In arithmetic, we have operations like +, -,×,÷, and numbers to form an Equation. But in algebra equation, the numbers are often represented as variables in the form of x,y, a, n. It helps us formulate the arithmetic equation such as a+b=c. In short, the conception of elementary algebra contains equations, variables, evaluating an expression, solving the linear equation, and algebraic equation with two or more variables.
Advanced algebra or Algebra 2(two)
Algebra 2 is an intermediate or high school algebra covering the study of functions, relations, and grapes. It is a bridge between the other parts of algebra, Such as:
- Equations with inequalities and equalities
- Sequence and series
- Solving system of equations
- Polynomial and radicals’ equations
- Polynomial functions
- Exponents and logarithms
Abstract Algebra in Maths
Abstract algebra is a branch of mathematics in algebra that deals with more advanced topics of algebra. Further, we will be dealing with the abstract algebraic application of specific nature or algebraic structure such as groups, modules vector specs, etc. This division of algebra contains the following components.
It is a collection of well-defined objects. These sets can be a collection of anything like people, mathematical numbers, etc. To clarify, two sets are equal if and only if those are the same objects. Set is present everywhere in modern mathematics.
- Binary operation
A binary operation is a calculation of two operands to generate another element. It is the addition or subtraction or multiplication or division of two numbers to get an output. In addition, Set plays a vital role in the binary operation as, without it, the operations are meaningless.
In algebra, the associative property makes the calculation of binary operation much easier and faster. So, it is grouping of elements in operation. Moreover, there is a property in maths in which the grouping of numbers multiplication or addition does not affect the sum of products.
- Identity elements
In mathematics, the identity element is a special type of element of a set with respect to a binary operation on that set. So, 0 is the identity element for additive identity, and 1 is the identity element for multiplicative identity.
- Inverse elements
In Abstract algebra, the inverse element comes up with a negative number. These negative number can be illustrated with the help of an example. For example, the real number ‘a’ has an additive inverse given by ‘-a’.
Commutative Algebra in Maths
Commutative algebra is the division of algebra that deals with the study of commutative rings in algebraic number theory and geometry. Most importantly, the algebraic number theory and algebraic geometry depended on commutative algebra. These rings are classified into the polynomial ring, algebraic number field, and many more.
Linear Algebra in Maths
Linear algebra is a branch of mathematics with respect to linear equations, linear maps, and their representation in vector space and matrices. All compute-intensive tasks use linear algebra. So, It is the center of all areas of mathematics. The things taken care in linear algebra are as follows
- Linear equation
- Linear maps
- Vector space
- Matrices and determinants