Algebra in Detail
Algebra is one of the various branches of 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 ‘variables’.
Algebra includes several forms of mathematical representations, such as real numbers, complex numbers, vectors, matrices, and so on. Equations form a crucial part of 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:
Elementary Algebra
This branch deals with the 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.
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
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
Communicative Algebra
This is a branch of algebra that 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.
Linear Algebra
This is a branch of mathematics that deals with linear equations and their representations through vectors and matrices. Linear algebra forms a fundamental aspect 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:
Basics of algebra.
Adding, subtracting, and multiplying algebraic expressions.
Simplification of algebraic equations, using the BODMAS rule.
Substitution.
Solving inequalities of equations.
Exponents.
Surds.
Square roots.
Cube roots.
Laws of exponents.
Simplifying equations.
Algebraic properties (associative properties, distributive laws, communicative laws).
Cross multiplication.
Polynomials.
Adding, subtracting, multiplying, and dividing polynomials.
Rational expressions.
Long division of polynomials.
Conjugate.
Rationalizing denominator.
Quadratic equations.
The Vedantu App covers all the mentioned topics in a detailed manner.
FAQs on Algebra
1. What are the Different Branches or Types of Algebra?
There are five different branches or types of algebra. They are elementary algebra, abstract algebra, advanced algebra, commutative algebra, and linear algebra. All these branches have different formulas, different applications, and different uses in finding out the values of variables.
Pre-Algebra - Helps in transforming real-life problems into algebraic expressions
Elementary Algebra - Helps in solving the algebraic expression into a viable answer.
Abstract Algebra uses advanced levels of algebra with abstract concepts other than mathematical ones like rings and vectors
Universal Algebra uses mathematical concepts involving trigonometry, calculus and coordinate geometry
2. What are Polynomials in Algebra?
Polynomials are algebraic expressions that 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. A polynomial expression includes at least one variable and also includes constants and positive exponents as well. They are the building blocks in rational expressions and are used to express numbers as a result of mathematical expressions.
3. What is Algebraic Geometry?
Algebraic geometry is a branch of mathematics that deals with the algebraic properties of geometric shapes and structures. In this branch, commutative 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. Algebraic geometry is extremely vast and difficult so whoever wishes to pursue and specialize in this field of study must master the concepts to move ahead. They are mainly used in advanced research like designing experiments and hypothesis testing.
4. What are the Different Types of Algebraic Expressions?
Algebraic expressions can also be termed polynomials. These are mathematical terms that contain variables as well as constants. Different types of algebraic expressions include:
Monomial - This algebraic expression contains only one term. Eg. 4xy, 6x, etc.
Binomial - This algebraic expression contains two terms. Eg. 7x+49, 4a+3b, etc.
Trinomial - This algebraic expression contains three terms. Eg. 8x2+7x+49, 3a+4b+5c, etc.
Cubic - This algebraic expression is an expression of third degree. The general formula is f (x) = ax3 + bx2 + cx1 + d
Linear - Here, either a constant or variable is raised to the first power.
Quadratic - It is an algebraic expression of second degree in x.
5. Where can students study Algebra?
For students in high school, books like NCERT, RD Sharma, and RS Aggarwal have the best concept-based explanations which are concise and aptly explained in simple effective language. They contain many exercises which can be solved by examining the examples thoroughly before the exam. In case a student wants more notes online, they can follow Vedantu for more such study materials which can be easily accessed by the students and can be downloaded from the official website in PDF format for free.