Mathematics: Algebra, Geometry, and Calculus Overview

Mathematics is a fundamental discipline of science that encompasses various branches such as algebra, geometry, and calculus among others. Each branch has its unique focus and applications, making mathematics essential in everyday life.

Algebra deals with symbols, operations, numbers, variables, equations, and relations between them. It's used extensively in other areas like physics, economics, and biology because it provides a systematic approach to understanding how different quantities relate to each other. Not only does it play a role in practical problems, but also forms a basis for more advanced mathematics like number theory and abstract algebra.

Geometry explores shapes and spatial relationships by using deductive reasoning from basic principles. This subject covers things like angles, lines, triangles, circles, polygons, etc., providing geometrical information regarding objects in space. With the advent of coordinate systems and technology, today we have computer graphics which relies heavily on vector analysis — another area of Geometry.

Calculus develops methods to find out how functions change over time; this includes finding derivatives and integrals of curves. Calculus was developed during the late medieval period. It became very important when people began studying astronomy through the telescope around the year 1000 AD. Today, calculus finds usage everywhere - in pure maths where mathematicians explore mathematical spaces, in finance where investors predict stock prices, and even in architecture where architects design buildings! So essentially all real world situations involve some form of calculus.

In conclusion, mathematics serves as a foundation upon which many scientific disciplines build their theories. Algebra provides us tools for solving complex problems and simplifying calculations while Geometry gives insights into spatial relationships. Finally, Calculus helps us understand changes over time. These subjects work together seamlessly within the field of mathematics, allowing us to solve diverse practical issues ranging from daily tasks to high level theoretical concepts.