# Purposes of Mathematics in Business Management

The principle and foundation of mathematics are the same in all parts of the world. It is considered to be one of the most important languages and the only language that all civilizations, regardless of religion, culture and ethnicity, utilize to communicate numerically and regulate many aspects of their lives to make better decisions. In fact, mathematics forms the foundation of science, technology and engineering, and it is the soul of all businesses. In many fields of management, it is applied to solve a variety of practical management problems with varying complexity, ranging from employee engagement problems to advanced financial analyses. Particularly when it comes to business management, it is extremely vital to have adequate knowledge on business mathematics given that a business generally revolves around dealing with money or the transaction of products that have monetary value.

## 1. Arithmetic

Arithmetic is the study of numbers, emphasizing on the operations of number addition, subtraction, multiplication and division. It is the foundation on which all of the more advanced mathematics are built, such as algebra, trigonometry, geometry and calculus.

## 2. Algebra

Algebra is the branch of mathematics that mainly deals with the application of arithmetical operations and formal manipulations to symbols rather than numbers. It involves the use of arithmetic methods, combined with the exercise of principles of algebra, to solve a mathematical problem involving at least one unknown quantity. Basically, it helps solve problems that are too complex or impossible for the ordinary arithmetic. In business management, it is often used to manipulate and solve various mathematical functions, including revenue, profit, demand, marginal revenue functions. For instance, generally, a revenue function is comparatively the most basic function and it is usually a linear function, which is , where  is the selling price, a constant, of the item and , an independent variable, is the amount of the concerning item sold. When R and K are known variables, this equation can be manipulated into  to find x, the process of which is known as algebra. A profit function is generally a little more complicated, and it is , where  is a cost function and  is the quantity of that particular item sold. For example, if , where  and , is the derived profit function for a particular item, an increase in  will result in a decrease in the value of the profit of each of the items concerned, the result of which can be ascertained through the use of calculus.

## 3. Calculus

Calculus primarily entails applying both the principles of arithmetic and algebra while considering the fundamental theorem of calculus. It involves the study of the rates of change of mathematical functions, exploring the variables and how these variables change by looking at them in extremely small segments, known as infinitesimals. There are two main parts of calculus, differential calculus and integral calculus. Differential calculus is concerned with finding the rate of change in the output of a function at any point. On the other hand, integral calculus involves doing the reverse operation of differential calculus. For instance, to find the marginal profit function of the afore-mentioned profit function, , the function is differentiated with respect to . This function then becomes , which shows that the profit of each of the item decreases as  increases. Calculus is also applied to many types of problems, most of those are pretty similar to one another in terms of function formulation and solving. On the other hand, integral calculus is applied to a different set of problems requiring the summation of a function  with respect to . As an example, if , where  and  are constants, represents the rate of growth of the sales of an item in terms of quantity and is integrated over a period of time , it will give the total number of the item sold over that particular period of time.

Business management requires the use of different mathematical techniques, ranging from just basic arithmetic to a more advanced branch of mathematics. Possessing this knowledge enables the effective management of a business operation, ensuring profit maximization while both reducing the relevant operational and production costs and improving the operation itself.