Mathematics has its place in our everyday life. It helps in getting our problems solved systematically.

Mathematics has various branches: Algebra, Calculus, Trigonometry, Geometry, etc. Each branch has its importance and different applications.

## Key Takeaways

- Algebra is a branch of mathematics that deals with symbols, variables, and the rules for manipulating them, focusing on solving equations and analyzing relationships between variables.
- Calculus is a branch of mathematics that studies change and motion, using concepts like limits, derivatives, and integrals to analyze functions and their rates of change.
- Both algebra and calculus are essential branches of mathematics, but algebra is concerned with solving equations and relationships between variables, while calculus focuses on analyzing change and motion.

**Algebra vs Calculus**

Algebra is the study of equations, inequalities, and functions, used in various fields such as engineering, physics, and computer science. Calculus is the study of continuous change and is used to analyze and model complex systems. It includes differential calculus, integral calculus, and multivariable calculus.

Algebra is a branch of mathematics based on modern arithmetic and modern mathematics. Algebra finds the values of the variables.

Calculus is a branch that is difficult to understand and used in advanced studies. Calculus studies the rate of change of events.

## Comparison Table

Parameter of Comparison | Algebra | Calculus |
---|---|---|

Basic idea | Algebra deals with finding the values of unknown variables. | Calculus deals with finding the rate of change of functions. |

Origin time | Originating in ancient times, development dates back to the medieval period. | Originated during the 17th century. |

Domain of work | Operates within a known domain and obtains the result within that. | Don’t have any specific domain; while solving the problem, one can learn new things, and results may or may not be in the domain. |

Main operations | Solving equations. | Differentiation and Integration. |

Uses | Used in everyday mathematics such as finding distance, displacement, the slope of the line, etc. | Used in complicated fields and advanced studies. |

## What is Algebra?

A branch of mathematics that uses letters and symbols to represent numbers working on predefined rules. These symbols or letters are termed variables.

Therefore, it can be said that Algebra is a relationship between different variables defined by operators known as algebraic equations.

In other words, Algebra is generalized arithmetic where variables represent all the possible numbers in the place. Algebra helps in the formation of correlated equations and then solving them to obtain values of the variables.

The roots of algebra were laid down by the Babylonians, who were also responsible for developing advanced arithmetic. They developed formulas to solve problems using linear or quadratic equations.

During the time of Plato, Greeks developed another tactic to deal with such problems, which they termed Geometric Algebra. A Greek mathematician, Diophantus later became known as the “father of algebra”.

The first complete solution, including zero and negative values to the algebraic equations, was given by an Indian mathematician Brahmagupta in his book Brahmasphitasiddhanta.

During the 16th century, Francois Viete’s works proved to be an essential step towards the development of modern algebra. In the mid-16th century, another event that marked the further development of algebra was the solution of cubic and quadratic equations.

Algebra can be broadly classified into two categories- Elementary Algebra, which mainly consists of the fundamental part of the algebra that is essential to any mathematical study and Abstract or Modern Algebra, which consists of advanced algebra,

professional mathematicians or academicians study it.

Algebra is used in every field of day-to-day life. It has an essential place in statistics, engineering, economics, computer programming, etc.

## What is Calculus?

Calculus is a branch of mathematics that deals with the change of functions that are related to each other. In other words, Calculus is the study of the rate of change of functions.

It was during the 17th century that Issac Newton and Gottfried Wilhelm Leibniz independently developed modern Calculus. Before the invention of Calculus, one could only calculate the values of the variables but couldn’t deduce the rates.

The invention of Calculus became the first achievement of modern mathematics. Newton developed formulas to calculate the rates and series expansion for functions according to the Taylor series of expansion.

There are two branches of Calculus: Differential Calculus, which uses derivatives to find the rate of change of slopes or curves, and Integral Calculus, which sees the quantity for which the rate of change is already known.

Calculus is paramount in physical sciences, actuarial sciences, computer sciences, statistics, demography, etc.

**Main Differences Between Algebra and Calculus**

- Algebra is the branch of mathematics that helps find the values of unknown variables. It is the relationship between different variables. On the other hand, Calculus is the branch of mathematics that helps find the rate of change of entities or functions concerning each other.
- Algebra is the branch that originated during ancient times and was developed in medieval times, whereas Calculus was invented by Issac Newton during the 17th century.
- Algebra is called Old mathematics, while Calculus is known as Modern mathematics.
- Algebra has a specified domain of work; it operates within it and obtains results in the same, while Calculus has no domain of work. One may get unexpected results after solving the problem.
- The main operation of Algebra is to solve the algebraic equations, while Calculus deals with differentiation and integration.
- Algebra is known as everyday mathematics as it helps in solving related to everyday life, while Calculus is used in advanced fields like statistics, actuarial sciences, computer sciences, etc.

**References**