Algebra Branches

The various branches of Algebra based on the use and complexity of the expressions are as such:

1. Pre Algebra
2. Elementary Algebra
3. Abstract Algebra
4. Universal Algebra
5. Linear Algebra
6. Commutative Algebra 
7. Boolean Algebra

Pre Algebra

Pre Algebra includes the fundamental concepts of arithmetic and algebra, such as the order of operations, basic operations with numbers, and simplifying expressions.

Algebra assists in turning day-to-day problems into mathematical expressions that use algebraic techniques and algebraic expressions. Pre-algebra specifically involves creating an algebraic expression for the provided problem statement.

Elementary Algebra or Algebra 1

Goal of elementary Algebra is to find a solution by resolving Algebraic expressions. Simple variables like x and y are expressed as equations in elementary Algebra.

• Equations are divided into polynomials, quadratic equations, or linear equations depending on the degree of the variable.

• Formulas for linear equations are ax + b = c, ax+ by + c = 0, and ax + by + cz + d = 0.

• Based on the number of variables, quadratic equations, and polynomials are subsets of Elementary Algebra.

• For a polynomial problem, the typical form of representation is axⁿ + bx^n-1+ cx^n-2+…..k = 0, while for a quadratic equation, it is ax² + bx + c = 0.

Abstract Algebra 

Abstract Algebra is a branch of mathematics that focuses on Algebraic systems like groups, rings, fields, and modules, rather than on specific numerical computations.

• In abstract Algebra, we do not study specific operations like addition and multiplication but instead study general properties of basic operations, such as associativity, commutativity, distributivity, and the existence of inverses.

• Groups, sets, modules, rings, lattices, vector spaces, and other Algebraic structures are studied in abstract Algebra. 

Universal Algebra

Universal Algebra can be used to explain all other mathematical forms using Algebraic expressions in coordinate geometry, calculus, and trigonometry. In each of these areas, universal Algebra focuses on equations rather than Algebraic models.

• We can think of all other types of Algebra as being a subset of universal Algebra.

• Any real-world issue can be categorized into a particular discipline of mathematics and solved using abstract Algebra.

Linear Algebra 

Linear algebra, a branch of algebra, finds uses in both pure and practical mathematics. It deals with the linear mappings of the vector spaces. It also involves learning about lines and planes. It is the study of linear systems of equations with transformational features.

• It is used in almost all areas of mathematics.

• It deals with the representation of linear equations for linear functions in matrices and vector spaces.

Commutative Algebra 

Commutative algebra is one of the types of algebra that studies commutative rings and their ideals. Both algebraic geometry and algebraic number theory require commutative algebra.

• Rings of algebraic integers, polynomial rings, and other rings are all present.

• Numerous other areas of mathematics, such as differential topology, invariant theory, order theory, and generic topology, make use of commutative algebra. 

Also Read

• Commutative Property in Maths

Algebra is the branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics and includes everything from solving elementary equations to studying abstractions such as groups, rings, and fields.

It helps represent problems or situations in the form of mathematical expressions. It is different from Arithmetic as Arithmetic deals with specific numbers and simple operations such as addition and subtraction. Algebra, on the other hand, introduces more complex operations and includes the use of variables, equations, and functions.