What is Mathematics?

According to the Encyclopaedia Britannica, Mathematics is “the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects”. Aristotle defined mathematics as “the science of quantity’”. Auguste Comte refined this by saying that mathematics a science that can be used to measure objects, spaces and quantities that cannot be directly measured. Most students think that mathematics is that puzzling science that involves numbers, calculations, theorems and their proofs.

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 Mathematics has been evolving for more than two thousand years. The basic concept of this subject is still man’s natural desire to define the natural world around him by arriving at the truth through the process of meticulous and logical reasoning. The first things that come to mind when we think of mathematics are the numbers. And the first four operations that we all learn as children – addition, subtraction, multiplication and division. This is arithmetic that deals with the study of quantity and its manipulations. Algebra belongs to the study of the structure, geometry to the study of space and analysis to the study of change. The set theory, mathematical logic, applied mathematics are also sub-divisions of this subject.

The different divisions of Mathematics

The study of arithmetic begins with the study of the natural numbers, whole numbers or integers, rational numbers, real numbers and complex numbers. Algebra deals with the results of operations or relations between things over time. It uses symbols and letters to represent the variables (those which change) and constants (those that do not change). Combinatronics, number theory, group theory, graph theory and order theory are also part of the structure study in mathematics. The study of space includes subjects such as: geometry, trigonometry, differential calculus, topology, fractal geometry and measure theory. The study of change in mathematics includes the subjects of functional analysis, quantum mechanics, differential equations, calculus, vector calculus, dynamical systems, chaos theory, complex analysis, to name a few. These studies are all categorised in pure mathematics.

Applied mathematics deals with the mathematical methods that are used to study and explain phenomena in other subjects such as science, engineering, business and industrial processes. Statistics is also part of the applied mathematics. It studies the collection, organisation, analysis and presentation of data for use in many fields including science and education and in research.

Computational mathematics deals with solving large and unwieldy calculations. Mathematical physics, mathematical chemistry, mathematical economics, mathematical finance, mathematical biology, fluid dynamics, numerical analysis, optimisation theory, probability theory, cryptography, game theory, and control theory are also par of the applied mathematics family.

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