Table of Contents

**What is Algebra?**

A field of mathematics in which numbers are represented by letters and symbols and follow preset rules. Variables are the symbols or letters that are used to describe these values. As a result, it is possible to define algebra as a relationship between different variables defined by algebraic equations, operators on variables.

As a result, Algebra is a generalized form of arithmetic in which variables represent all possible numbers in a given location. Algebra is constructive when constructing associated equations and then solving them to find the variables’ values.

The Babylonians, who are also credited with developing advanced arithmetic, set the foundations for algebra and its branches of study. They devised formulas to solve linear or quadratic equations, which they tested.

Geometric Algebra was a method of dealing with such problems invented by the Greeks during the time of Plato and named after the Greek philosopher. He was born in Greece and became renowned as the “father of algebra” after his accomplishments in mathematics. The first comprehensive solution to algebraic equations, including zero and negative values, was provided by an Indian mathematician named Brahmagupta in his work Brahmasphitasiddhanta, which may be found online.

Francois Viete’s works, published throughout the 16th century, proved to be a significant step forward in creating modern algebra.

Mathematical studies can be separated into two main categories: Elementary Algebra and Abstract or Modern Algebra. The former focuses on the most fundamental aspects of algebra, while the latter focuses on the more advanced elements of algebra. Elementary Algebra is the essential part of algebra required for any mathematical study. At the same time, Abstract or Modern Algebra is the more advanced part of algebra required for any mathematical research.

Algebra is employed in almost every aspect of one’s daily life, and it has a significant role in several fields, including statistics, engineering, economics, and computer programming.

**What is Calculus?**

Issac Newton and Gottfried Wilhelm Leibniz separately invented the modern Calculus in the 17th century, during which time they were both at Cambridge. Before the advent of Calculus, it was only possible to calculate the values of the variables, not to determine the rates of change.

Because of the invention of Calculus, contemporary mathematics may claim to be the world’s first scientific achievement. Newton devised formulas to compute the rates and series expansion for functions based on the Taylor series of development using the Taylor series of evolution.

In differential calculus, the rate of change of slopes or curves can be found using derivatives, but a known quantity can be observed in integral calculus. A slope or curve’s rate of change can be determined using differential calculus, while an unknown amount can be determined using integral calculus.

Among the many domains in which calculus is crucial are the physical and actuarial sciences, computer science, statistics, and demography.

**Difference Between Algebra and Calculus**

- Algebra is a discipline of mathematics that is used to assist in the determination of the values of unknowable variables. On the other hand, Calculus is a field of mathematics that helps determine the pace at which entities or functions change about one another.
- Algebra dated back to antiquity and was further developed during the Middle Ages, whereas Calculus was founded by Isaac Newton in the seventeenth century.
- While Algebra is referred regarded as “Old mathematics,” Calculus is referred to as “New mathematics.”
- On the other hand, Calculus has no defined work area; it operates within it and produces results, whereas Algebra does. Because Calculus has no defined sphere of work, it can acquire unexpected outcomes after solving the problem.
- The primary operation of Algebra is the solution of algebraic equations, whereas the primary activity of Calculus is the differentiation and integration of functions.
- Algebra is referred to as “everyday mathematics” since it is used to solve problems that arise in everyday life. In contrast, Calculus is employed in sophisticated subjects such as statistics, actuarial sciences, computer sciences, and other related fields.

**Comparison Between Algebra and Calculus**

Parameters of Comparison | Algebra | Calculus |

Basic idea | It is the task of algebra to find values for variables that aren’t known. | Getting the rate of change of functions is what calculus is all about. |

Origin time | Since its inception in antiquity, this technology has advanced through the Middle Ages, where it is currently used. | This term first appeared in print in the seventeenth century. |

Domain of work | Has the ability to operate within a known domain and produce the desired result within that domain. | There is no specified domain, but while addressing the problem, one may learn new things, and the outcomes may or may not be relevant to the field in question. |

Main operations | Equations are being solved. | Integration and differentiation are two crucial concepts in cognitive science. |

Uses | Distance, displacement, and the slope of a line are examples of everyday mathematics used. | In complex fields and advanced research, this term is frequently used. |