Bookmark added to your notes.
View Notes

Algebra in Detail

Algebra is one of the various branches in Mathematics. It deals with symbols and variables. Various arithmetical statements and operations such as equations, terms, expressions to draw a relationship between objects which are not constant, and do change over time. These objects in basic algebra are also termed as ‘variables’.

Algebra includes several forms of mathematical representations, such as real numbers, complex numbers, vectors, matrices, and so on. Equations form a crucial part in algebraic applications. Different algebraic rules are used to solve elementary equations to study variables.

Introduction to Algebra

Talking about variables, algebra is used to determine unknown values like proportions, bank interest, percentage, distance, price, etc. It also uses symbols and letters to represent mathematical equations. The equations consist of some constants and some variables. With the help of the constants provided in the equation, we find out the value of the unknown/variable in algebra math.

Students of secondary as well as higher-secondary level must understand how this branch of mathematics works and how the rules are implemented. They must learn algebra with thorough attention as it holds sufficient weightage in the final exams. One of the most helpful platforms to understand this is Vedantu. The App can be downloaded for free to understand algebra for beginners, practice sums, and score well in the exams.

Different Branches in Algebra

Here is a list of the branches and sub-branches of Algebra. These branches are applied accordingly to find the values of two or more variables. These algebraic branches are as follows:

  1. Elementary Algebra

This branch deals with basic properties of numbers, variables, constants, and relations between them. The topics which form a part of elementary algebra include equations, formation, manipulation, evaluation of expressions, equalities, inequalities, equation solving (algebraic as well as linear), and so on.

  1. Advanced Algebra

This is a more detailed and intermediate step in algebra. The equations included in this branch helps study the following:

  • Equalities

  • Inequalities

  • Matrices

  • Conic sections

  • Sequences

  • Series

  • Trigonometry

  • Polynomial equation

  • Graphic functions

  • Rational expression

  • Probability

  1. Abstract Algebra

It deals with truth related to algebraic applications independent of its specific nature. The components included in this branch of algebra are:

  • Sets

  • Binary Operations

  • Identity Element

  • Inverse Element

  • Associativity

  1. Communicative Algebra

This is a branch of algebra deals with communicative rings, including algebraic integer rings, polynomial rings, etc. It can also be said to be a branch of abstract algebra. It includes a study on ring theory, Banach algebra, representation theory, and so on.

  1. Linear Algebra

This is a branch of mathematics which deals with linear equations and their representations through vectors and matrices. Linear algebra forms a fundamental aspect for in every sector of mathematics.

The topics included in this branch of algebra are as follows:

  • Introduction to linear algebra

  • Linear equations

  • Relations

  • Vector spaces

  • Relations and Computations

  • Matrices

  • Matrix decomposition

Students can learn various concepts of algebra online through the Vedantu App. The algebraic topics you can read on this App are:

  1. Basics of algebra.

  2. Adding, subtracting, and multiplying algebraic expressions.

  3. Simplification of algebraic equations, using the BODMAS rule.

  4. Substitution.

  5. Solving inequalities of equations.

  6. Exponents.

  7. Surds.

  8. Square roots.

  9. Cube roots.

  10. Laws of exponents.

  11. Simplifying equations.

  12. Algebraic properties (associative properties, distributive laws, communicative laws).

  13. Cross multiplication.

  14. Polynomials.

  15. Adding, subtracting, multiplying, and dividing polynomials.

  16. Rational expressions.

  17. Long division of polynomials.

  18. Conjugate.

  19. Rationalising denominator.

  20. Quadratic equations.

The Vedantu App covers all the mentioned topics in a detailed manner.

FAQ (Frequently Asked Questions)

1. What are the Different Branches or Types of Algebra?

Ans. There are five different branches or types of algebra. They are elementary algebra, abstract algebra, advanced algebra, communicative algebra, and linear algebra. All these branches have a different formula, different application, and different use in finding out the values of variables.

2. What are Polynomials in Algebra?

Ans. Polynomials are such algebraic expressions which consist of variables as well as coefficients. The variables here can also be termed as indeterminate. Polynomials only include addition, subtraction, and multiplication of the variables. It also includes non-negative or positive integer exponentiation of the required variables. Students also learn factoring polynomials in geometry.

3. What is Algebraic Geometry?

Ans. Algebraic geometry is a branch of mathematics which deals with algebraic properties of geometric shapes and structures. In this branch, communicative algebra or abstract algebraic methods are used to solve geometrical problems. The shapes and structures studied in algebraic geometry are lines, circles, ellipses, curves, parabolas, hyperbolas, and so on.

4. What are the Different Types of Algebraic Expressions?

Ans. Algebraic expressions can also be termed as polynomials. These are mathematical terms which contain variables as well as constants. Different types of algebraic expressions include:

  • Monomial

  • Binomial

  • Trinomial

  • Cubic

  • Linear

  • Quadratic