Making
Change with Mathematics: Conceptions of the Role of Mathematics in Business,
Commerce, and Management Curriculum
Dr.
Yudhvir Singh
Associate Professor, Dept of Commerce, Government
College, Nadaun, Dist-Hamirpur (H.P)
*Corresponding Author E-mail: yvsapc@gmail.com
Today in this
rapid changing technology driven world, job roles and nature have changed
tremendously. It’s time for artificial intelligence and big data analysis. Job
roles are redefined as analyst, consultant, research associate, data miner etc.
which involve advanced mathematical applications. Business, commerce and
management are few among the most popular disciplines among students. But these
subjects lack mathematical applications in its introduction stages. And now in
this changed scenario, reputed global institutions offer higher education
opportunities for students who are having mathematical background. So the
relevance of mathematics is increasing and it is soon become one of the mandatory
subjects for students in all disciplines. Hence this paper examines the role of
mathematics in business, commerce and management curriculum.
Keyword: Mathematics,
Business, Commerce, Management, Curriculum
1.
INRODUCTION:
Mathematics is a
part of science that deals with the logic of shape, quantity and arrangements
(Srinivasa Ramanujan). Mathematics, what
experts sought out different patterns, formulate new conjectures, and establish
truth by rigorous deduction from approximately chosen axiom and definitions. In
addition of these mathematics finds out logical solutions problems. Mathematics
can be said as omnipresent since it is all around us. Its application in daily
life is inseparable and incomparable. Whatever the field we are looking,
whether it is sports or art or communication or engineering or technology, mathematics
is the key element (Elaine J.Ho, 2013)
Business and
management is also meaningless without mathematics. Business is concerned with
buying and selling of goods and services with an aim to make profit. Here the
value of good or service is expressed in money term, which as price, and the
end result which is either profit or loss also expressed in numerical term. That
clearly denotes how important mathematics in business is.
On the other hand,
management is the art of getting things done through others and decision
making. The task of every manager or higher official is to take managerial
decision and mathematical aids them for logical solution for problem concerned.
Decision making is not a single activity; it is a process which consist of
series of inter related tasks. First step is clearly defining the problem, next
step is analysing the alternatives in terms of most suitable model for solution
of the problem. Thus mathematical applications like algorithm, calculus,
algebra, linear programming, statistics, probability etc. are needed for the
full-fledged functioning of business and management.
In case of
curriculum, in India, Business and management is extensively taught in college
and university level. Earlier, the syllabus includes Accounting as only
numerical paper and other subjects like management, marketing,
entrepreneurship, business studies, auditing etc. Then the role of mathematics
and logical thinking came into picture and thus added subjects like business
statistics operations research, and quantitative techniques. Nowadays, to get
admission for graduation as well as post- graduation courses in business, commerce
and management disciplines, reputed institutions made it compulsory to study
mathematics as separate subject in qualifying examination. So that many
commerce and management courses introduces new paper titled business
mathematics in their curriculum.
Thus, the
influence of mathematics in field of business, commerce and management is
increasing day by day a study wants one to explore the role and applications of
mathematics in this field.
2
. OBJECTIVE:
This paper intends
to know the applications of mathematics in business, commerce and management as
well as the role of mathematics in curriculum.
3.
METHODOLOGY:
The design is
exploratory cum descriptive in nature which uses data from secondary sources
and authors’ views are blended with it and presented accordingly.
4.
APPLICATION OF MATHEMATICS IN BUSINESS, COMMERCE AND MANAGEMENT:
Mathematics plays
significant role in our day today life. If we look into various job roles also, the understanding of basic applied
mathematics is some time essential. Jobs like Consultant, Analyst, Director,
CEO, CFO, Economist, Research Associate
etc. requires mathematical and logical skills to perform the duty effectively.
In the field of business, commerce and management also the mathematical
influence is beyond our thoughts. Its application ranges from basic arithmetic such
as fractions, ratios, algebra, probability etc. to advanced mathematical model
building. Business entities and commercial organizations use arithmetic in the
areas of accounting, inventory management,
budgeting, financial analysis and sales forecasting.
In the curriculum
also, as mentioned earlier, new subjects like business mathematics gain
popularity and acceptance since commerce and management higher education
wanting basic mathematical understanding and knowledge. Advancement in
Information and a Communication Technology (ICT) also accelerate the influence
of mathematics, which allows easy learning opportunity for students.
4.1.
FINANCIAL MANAGEMENT:
Financial
management is one of the core areas in business and commerce. Financial
management is concerned with procurement and effective utilization of funds.
Financial management is more quantitative discipline in which various
mathematical applications are there. Some of them are:
* Calculation of
rate of return of Cost of Capital
* Deciding Capital
Structure
* Asset Valuation
* Portfolio
Management
* Derivative
Trading
* Risk Management
* Security Pricing
etc.
4.2.
ACCOUNTING:
Accounting is the
language of business. The result of
business is communicated through accounting language to users or stakeholders
of the business. Accounting uses
quantitative data and thus heavily depends on mathematical principles and
techniques. Mathematical formulas are used for computation of profit,
loss, income, expenditure, depreciation etc.
Accounting
discipline is further sub divided into financial accounting, cost accounting,
corporate accounting and management accounting. In financial accounting, the
net result of business is exhibited with the help of Profit and Loss account
and Balance Sheet. The accounting is based on an equation which is mathematical
one. The equation is A=L+C, “A” stands for Assets, “L” stands
for Liabilities and “C” stands for Capital. By using mathematical
relation, A=L+C, we can calculate total cost and decide whether to make or buy
the product. The total cost formula for business is T=a + bx , where ”T” is TOTAL COST, “a” is fixed cost,
“b” is cost per unit and “x” is number
of units produced. Profit is calculated by subtracting total cost from total
revenue and helps in analyzing the financial health of business. Prices are
determined by adding some profit margin to cost.
In cost
accounting, calculation cost pertains to cost centres, ascertainment of
Economic Order Quantity (EOQ), setting of stock levels etc. involve
mathematical applications. In corporate accounting, accountings of companies
are dealt with. It requires mathematical application in case of business
combinations like amalgamation, absorption, external reconstruction, calculation of purchase
consideration, computation of value of goodwill, liquidation statement of
affairs etc. Management accounting
mainly deals with managerial decision making. It involves financial statement
analysis, fund flow statements, cash flow statements, budgetary control, ratio
analysis etc. Ratio equations are derived from mathematical techniques and
helpful in business comparison.
4.3.
SECURITY ANALYSIS AND PORTFOLIO MANAGEMENT:
One of the
important areas in business and commerce is security market. It includes
capital market and money market. Various short -term and long – term securities
are traded in these markets. As we know, security market offers huge return at
the same time it possess huge risk element too. So before investing money in
financial or security markets, it is better to analyse the risk return trade
off and select the best possible portfolio which gives maximum return with
minimum risk. Portfolio here refers to group of securities. For analysis
purpose, various mathematical models are used; they are Capital Asset Pricing
Model (CAPM), Single Index Models, Fama -French Model, Treynor ratio, Jensen’s
Index etc. With these mathematical models, we can make investment which in turn
benefits the investors.
4.4.
PRODUCTION PLANNING AND PRICING:
Production
planning is one of the preliminaries of establishment of business. In this
regard, it involves estimation of cost of materials, cost of production,
machine life, depreciation, labour hour rate, wages and salaries, packing and
storage cost, determination of different stock levels etc. which involves
rigorous mathematical applications. After production, next step is regarding
how much has to be charged as price. Because the survival and expansion of business
is solely depends on the earning from sales. Profit is difference between cost
price of the product and selling price. If you need high profit at initial
stage, you should go for skimming price policy which is charging high price at
initial stage. It is possible only when the business having less competition. If
there is competition, it is better to go for penetration pricing which impose
low price at beginning. Once the profit margin is decided, to calculate selling
price, divide using percent or decimals.
For example, if
you want to decide the retail price, if product cost is Rs.100 to produce and
your required profit margin is 40 percent deduct .40 from 1, which gives .60 as
remaining, denotes 60 percent. In order to determine the selling price of the product,
divide 100 by .70, which rounds to Rs.142.86.
4.5.
STATISTICS AND PROBABILITY:
After realizing
the importance of statistics in business field, a separate subject known as
business statistics is introduced in the commerce and management curriculum.
Statistics assist business in forcasting demand and supply, market
fluctuations, trend analysis, ratio analysis, financial statements,
interpretation etc. There is need to predict the uncertainty and should provide
for the future. There comes the need of probability applications. It is a sub
area of statistics and essential for predication and estimation of risk return
of business investments. It serves as a tool for decision making for the top
level management.
4.6.
LINEAR PROGRAMMING:
Linear programming
is applied in many complex business problems to find out solutions. It is
mainly used for marketing mix problems, distribution modeling, company restructuring, routing and scheduling etc. In
linear programming, the problems may be either in the nature of maximization of
profits or minimization of costs. With help of mathematical models and logical
steps, we will reach at a solution which is optimal (Lewis, 2008)
4.7.
OPERATIONS RESEARCH:
Operation research
is a military term used in US military operations. Later on this mathematical
application gain popularity in business discipline. Hence it is also known by
the names Management Science or Decision Sciences or Management Optimization
Techniques. It is concerned with decision making under pressure or uncertain
situations. The basis of decision will be regarding profit maximization, cost
reduction, strategic management, performance appreciation,
or any other better management practices. Operation Research mainly involves
application of mathematical models in real life situations and find out the
optimal solution for problem concerned.
The techniques
involved in operation research are as follows:
*Inventory Model-This technique deals
with how much to order at a point in time, and when to place an order, the main
objective of this model is minimize the total cost of inventory which includes
the cost of holding, cost of storage, cost of ordering.
*Allocation Model- This technique used
to allocate the resources to activities so as to optimize a measure of
effectiveness or maximum utilization of resources. Waiting for a line or queuing
line method. These models establish a trade- off between costs of providing
service and waiting time of a customer in the queuing system.
*Game
Theory-This
model used to categorize the behavior of two or more competitors competing to
achieve their conflicting goals. It explains the type of strategy which would
yield the best or worst outcomes.
*Network
Models-
These models are applied to the management of large scale projects. Here
PERT/CPM techniques help in identifying delay and project critical path. It
leads to efficient use of resources.
*
Sequencing Model- These models are used to determine the
sequence or order in which a number of tasks can be performed by a number of
service facilities. In such a way that some measure the performance is
optimized.
4.8.
CALCULUS:
Calculus is the
study of the rate of changes, e.g. velocities, interest rate, return on asset. It
is invented by Sir Issac Newton and Gottfriend Wilhelm V0on Leibniz. The key
areas of calculus are viz. differential calculus and integral calculus. These
are two unrelated areas which are connected with fundamental theorem of
calculus. Differential calculus play key role in decision making in production management,
e.g. supply of raw material, wage rates and taxes etc.
In calculus, the
case when “y” is a function of “x” or in other words, one variable(y) is
dependent on other variable(x) and
derivative of “y’ with respect to “x” i.e. dy/dx measures the change of variable “y” with respect to
change in variable “x”. Derivative enables a firm to make important production
decisions. It is also called the marginal function. Demand can be assumed as a function
of price. This operator is also helpful in calculating minimum cost and maximum
profit. Also, the total cost of production and marketing depends on number of
units in mathematical relations, which
can be described as c(x) is cost function v(x) is variable cost and F is fixed
cost. Revenue function R(x) is represented as R(x)= xp(x), where “x” is number
of units and “p” is the rate per unit. Hence knowledge of derivative is
essential for understanding the economic relations. Another integral operator
is used to calculate the total revenue in case of marginal revenue is given. It
also aid in calculation of profit and taxes to be paid which are important for
any business.
5.
CONCLUSION:
The role played by
mathematics in the field of business, commerce and management is remarkable. If
we try to extract and set aside mathematical element from these fields, the
area becomes meaningless. Linear programming and operation research made
complex business problems into simple solutions; calculus and algebra
applications of mathematics are essential in profit, revenue and tax
computation. Program Evaluation and Review Techniques (PERT) and Critical Path Method
(CPM) helps in project scheduling and cost crashing; without mathematical
principles and formulas, accounting will be waste of time, product pricing will
decide the future of business which depends on mathematical analysis and
forecasting. Thus in a nutshell, the field of business, commerce and
management, from the beginning to end is heavily relying upon mathematical applications.
Mathematics is one of the major ingredient in building management and business
education which is required for self- reliant and self-actualization which the
country is clamoring for. By including mathematics in curriculum, the students
get more opportunities for their higher education and most importantly, their logical,
critical thinking capacity and problem solving analytical skills will be
improved.
6.
REFERENCES:
1. Lewis, C (2008), Linear Programming: Theory
and Applications.
2. www.assignmentpoint.com/business/business
-mathematics/application-of-mathematics i-in-
business.html