There are many ways to describe change. Depending on what aspect that is to be described will depend on the individual. Specifically, mathematics describes the process and the quantity of change. Mathematics is a broad spectrum of tools to quantify phenomena and is widely employed by mathematicians alike. There are branches in mathematics that are specialized in tackling the descriptions of change. They are arithmetic, algebra and calculus.

The very first step to describing change is to define the elements in a set. Quantifying the factors will be likened to defining the elements. Numbers are assigned to quantities and appropriate processes are applied. This calls for arithmetic. A simple set of rules that govern the very works of numbers. Addition, subtraction, multiplication and division are the building blocks to arithmetic and play a fundamental role in mathematics.

Having an abundant range of possibilities, the arithmetic system will have an intrinsic system of governing. This is algebra, a further set of tools to manipulate the processes further. More complex processes include expansion, factorization and partial fractioning. Unknowns may also be found through algebra to present involved elements in a more lucid manner. This, however, does not equate to change just yet and is still static in nature; does not describe change.

Now that all elements and processes are set, calculus kicks in to describe change. This is a more dynamic approach to describing change as more techniques are added. Two very important aspects of calculus are differentiation and integration. Differentiation is responsible for measuring the change to algebraic expressions and integration is responsible for deriving the algebraic expressions from a given change. They are both reversible. Further calculus touches on differential equations and transformations, enabling multivariable analysis and handling more complex changes in lesser steps.

Mathematics, however, should not be relied fully as some aspects of reality cannot be described by mathematics. For example, an improper limit may yield a definite number in reality; however, it may yield infinites when adhered strictly to simple arithmetic. It should be at the user’s discretion to see whether a certain branch of mathematics is appropriate for application.

In a nutshell, mathematics provides a wholesome, if not complete, set of tools to describe change. Applied mathematics, for example, takes advantage of it to describe change in our world; fluid dynamics describes large volume of change in fluids and statistics describes uncertainty. It is fairly adequate to solve some problems in reality, albeit some discrepancies with theory and practicality.

References:

Gullberg, Jan, Mathematics From the Birth of Numbers. W. W. Norton & Company; 1st edition (October 1997). ISBN 0-393-04002-X.

Courant, R. and H. Robbins, What Is Mathematics? : An Elementary Approach to Ideas and Methods, Oxford University Press, USA; 2 edition (July 18, 1996). ISBN 0-19-510519-2.