what is Algebra?

Aug 09, 2022, 16:45 IST

what is algebra and its branches

Algebra helps in solving the mathematical equations and helps to derive the unknown quantities, just like the bank interest, proportions, percentages. The variables within the algebra are often wont to represent the unknown quantities which are coupled in such how to rewrite the equations. The algebraic formulas are utilized in our lifestyle to seek out the space, the quantity of containers, and to work out the sales prices as and when needed. Algebra is extremely helpful in stating a mathematical equation and relationship by making use of letters or other symbols representing the entities. The unknown quantities within the equation are often solved through algebra. Some of the most topics coming under algebra include Basics of algebra, exponents, simplification of algebraic expressions, polynomials, quadratic equations, etc.

Branches of Algebra

As it is understood that, algebra is that the concept supported unknown values called variables. The important concept of algebra is equations. It follows various rules to perform arithmetic operations. The principles are wont to add up of sets of knowledge that involves two or more variables. It’s wont to analyse many things around us. You’ll probably use the concept of algebra without realizing it. Algebra is split into different sub-branches like elementary algebra, advanced algebra, abstract algebra, algebra, and commutative algebra.

Elementary Algebra

Elementary Algebra covers the normal topics studied during a modern elementary algebra course. Arithmetic includes numbers alongside mathematical operations like +, -, x, ÷. But within the field of algebra, the numbers are often represented by the symbols and are called variables like x, a, n, y. It also allows the common formulation of the laws of arithmetic like, a + b = b + a and it's the primary step that shows the systematic exploration of all the properties of a system of real numbers. The concepts coming under the elementary algebra includes variables, evaluating expressions and equations, properties of equalities and inequalities, solving the algebraic equations and linear equations having one or two variables, and so on.

Advanced Algebra

This is that the intermediate level Algebra. This algebra features a high level of equations to unravel as compared to pre-algebra. Advanced algebra will assist you to travel through the opposite parts of algebra such as:

1.Equations with inequalities

2.Matrices

3.Solving system of linear equations

4.Graphing of functions and linear equations

5.Conic sections

6.Polynomial Equation

7.Quadratic Functions with inequalities

8.Polynomials and expressions with radicals

9.Sequences and series

10.Rational expressions

11.Trigonometry

12.Discrete mathematics and probability

Abstract Algebra

Abstract algebra is one of the divisions in algebra which discovers the truths concerning algebraic systems independent of specific nature of some operations. These operations, in specific cases, have certain properties.

Thus we'll conclude some consequences of such properties. Hence this branch of mathematics called abstract algebra.

Abstract algebra deals with algebraic structures a bit like the fields, groups, modules, rings, lattices, vector spaces, etc.

The concepts of the abstract algebra are below-

a. Sets – Sets is defined because the gathering of the objects that are determined by some specific property for a gaggle. as an example – a gaggle of all the 2×2 matrices, the set of two-dimensional vectors present within the plane and different kind of finite groups.

b. Binary Operations – When the concept of addition is conceptualized, it gives the binary operations. The concept of all the binary operations are getting to be meaningless without a gaggle.

c. Identity Element – The numbers 0 and 1 are conceptualized to supply the thought of an identity for a specific operation. Here, 0 is known as the identity for the addition operation, whereas 1 is known as the identity for the multiplication operation.

d. Inverse Elements – the thought of Inverse elements comes up with a negative number. For addition, we write “-a” because the inverse of “a” and for the multiplication, the inverse form is written as “a-1″.

e. Associativity – When integers are added, there is a property mentioned as associativity during which the grouping from numbers added doesn't affect the sum. Consider an example, (3 + 2) + 4 = 3 + (2 + 4).

Linear Algebra

Linear algebra may be a branch of algebra which applies to both applied also as mathematics. It deals with the linear mappings between the vector spaces. It also deals with the study of planes and features. it's the study of linear sets of equations with the transformation properties. it's almost utilized in all the areas of Mathematics. It concerns the linear equations for the linear functions with their representation in vector spaces and thru the matrices. The important topics covered in algebra are as follows:

a. Linear equations

b. Vector Spaces

c. Relations

d. Matrices and matrix decomposition

e. Relations and Computations

Polynomial

Polynomials are algebraic expressions that contain variables and coefficients. Variables also are sometimes called indeterminate. We will perform arithmetic operations like addition, subtraction, multiplication and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x²+x-11. During this example, there are three terms: x2, x and -12.