Algebra

Algebra is one among the oldest branches in the history of mathematics dealing with the number theory, geometry, and its analysis. The definition of algebra states sometimes as the study of the mathematical symbols and the rules involving the manipulation of these mathematical symbols. Algebra includes almost everything right from solving elementary equations to the study of the abstractions. Algebra equations are included in many chapters of Maths, which student will learn in their academics.

Algebra 1 and algebra 2 are the Maths courses included for students in their early and later stages of academics respectively. Like, algebra 1 is the elementary algebra practiced in classes 7,8 or sometimes 9, where basics of algebra are taught. But, algebra 2 is the advanced algebra, which is practiced in high school level. The algebra problems will involve expressions, polynomials, the system of equations, real numbers, inequalities, etc. Know more algebra symbols that is used in maths.

In BYJU’S, students will get the complete details of algebra including its equations, terms, formulas, etc. Also, solve examples based on algebra concepts and practice worksheets to get a better understanding of the fundamentals of algebra.

Algebra

Algebra helps in to solve the mathematical equations and to derive the unknown quantities, like the bank interest, proportions, percentages. The letter variables in the algebra can be used to represent the unknown quantities which are coupled with the ability to rewrite the equations making it easier in finding the data for a given set of equations.

The algebraic formulas are used in daily life like finding the distance, find the volume in containers, or to figure out the sales prices as and when needed. Algebra is very helpful in stating a mathematical equation and relationship by making use of letters or other symbols representing as entities. The values of the equations of unknown quantities can be solved through algebra.

Some of the main topics coming under algebra include Basics of algebra, exponents, simplifying of algebraic expressions, polynomials, quadratic equations, etc.

Parts of Algebra

Introduction to Algebra

Exponents

Simplifying

Polynomials

Quadratic Equations

Branches of Algebra

Algebra

As discusses, Algebra is divided into different sub-branches;

  • Algebra 1 or Elementary Algebra- Elementary Algebra covers the traditional topics studied in a modern elementary algebra course. Arithmetic includes numbers along with mathematical operations like +, -, x,  ÷. But in the field of algebra, the numbers are often represented by the symbols and are called variables such as x, a, n, y. It also allows the common formulation of the laws of arithmetic such as, a + b = b + a and it is the first step that shows 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, logarithmic and Exponential equations, etc.

  • Algebra 2 or Advanced Algebra- This is the intermediate level Algebra or you can say prerequisite of Algebra 1. This algebra has a high level of equations to solve as compared to pre-algebra.
  • Abstract Algebra – Abstract algebra is one of the divisions in algebra which discovers the truths relating to algebraic systems independent of specific nature of some operations. These operations in specific cases have certain properties. Thus we can conclude some consequences of such properties. Hence this branch of mathematics called abstract algebra.

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

The concepts of the abstract algebra are below-

  1. Sets – Sets is defined as the collection of the objects that are determined by some specific property for a set. For Example- A set of all the 2 by 2 matrices, the set of two-dimensional vectors present in the plane and different form of finite groups.
  2. Binary Operations – When the concept of addition is conceptualized, it gives the binary operations. The concept of all the binary operations will be meaningless without a set.
  3. Identity Element – The numbers 0 and 1 are conceptualized to give the idea of an identity element for a specific operation. Here, 0 is called as the identity element for the operation addition, whereas 1 is called the identity element for the operation multiplication.
  4. Inverse Elements – The idea of Inverse elements comes up with the negative number. For Addition, we write -an as the inverse of a and for the purpose of multiplication the inverse form is written as  a−1.
  5. Associativity – When integers are added, there is a property known as associativity in which the grouping up of numbers added does not affect the sum. Consider for Example – (3 + 2) + 4 = 3 + (2 + 4)
  • Linear Algebra – Linear algebra is a branch of algebra which applies to both applied as well as pure mathematics. It deals with the linear mappings between the vector spaces. It also deals with the study of planes and lines.
  • Commutative algebra– Commutative algebra is one of the branches of algebra that studies the commutative rings and its ideals. The algebraic number theory, as well as the algebraic geometry, depending on the commutative algebra.

This was just a brief discussion on Branches of Algebra. Now get model solutions for chapter Algebra in detail and step-by-step procedure to all questions in an NCERT textbook at BYJU’S.



Practise This Question

Given below is a pattern made using squares. Observe the pattern and tell the number of squares in the next figure in the sequence. Also find the general form which represents the number of squares in the sequence.