Mathematics of Finance, Mathematics for Economics, and Management Science

         Now that we have known that accounting and business students have a different need than economics students, it is inappropriate and unfair to give them the same mathematics as the economics students. If Mathematics is given only in one semester for undergraduate students of accounting and business, it should be Mathematics of Finance just like the students of the diploma program. If students of the diploma program learn Mathematics that they need for their career and jobs, why should not the undergraduate students? It is not proper to say that the graduates of undergraduate program are expected to be scholars and conceptors that they should study more concepts than skill or practical knowledge. Some of them may eventually become scholars but most will be absorbed in the financial industry. The teaching of Mathematics for Economics and or Management Science should be given only after students have learned Mathematics of Finance.

         Ideally, students of accounting and business learn mathematics-related courses in three semesters. First they learn Mathematics of Finance, then Mathematics for Economics and Management Science in the following semesters. What I mean by Mathematics for Economics is the study of linear algebra and calculus (Chiang, 2005). It can start from market equilibrium (Daus, 1962), matrices, vectors, to derivatives (partial and total), differentiation, optimization (unconstrained and with equality constraints), and integral. The basic concepts that have been given in high schools such as polynomial functions and set theory need not be reviewed. Differential and difference equations need not be included, either. Whereas the topics in Management Science are optimization with multiple inequality constraints, goal programming, integer programming, sensitivity analysis, decision analysis, game theory, analytical hierarchy process, network flow models, and project management (Taylor, 2007). In Mathematics of Finance, students will learn about flat/stated and effective rates, pricing of discount securities, discount rate vs interest rate, present value, future value, annuity, perpetuity, calculation of various yields and returns, stock indices, savings schedule, loan amortization, and asset (stocks, bonds, and other real assets) valuation (Frensidy, 2006).

Topics Studied in Mathemathics-Related Courses
No	Mathematics of Finance	Mathematics for Economics	Management Science
1	Flat & Effective Interest Rates	Market Equilibrium	Linear Programming
2	Discount vs Interest Rates	Matrices	Integer Programming
3	Yields and Returns	Vectors	Nonlinear Programming
4	Present Value	Linear Equation System	Goal Programming
5	Future Value	Differentiation	Analytical Hierarchy Process
6	Annuity	(Partial & Total) Derivatives	Decision Analysis
7	Perpetuity	Elasticity	Game Theory
8	Savings Schedule	Unconstrained Optimization	Network Flow Models
9	Loan Amortization / Loan	RefinancingOptimization with Equality Contraints	Project Management
10	Asset Valuation	Integral	Project Crashing
11	Pricing of Discount Securities	The Effect of Tax & Subsidy on Market Equilibrium	Sensitivity Analysis

needed to study financial management, intermediate accounting, financial planning, investment, and derivative securities.

            Conversely, Mathematics for Economics teaches more concepts and tools rather than skills. Mathematics for Economics is helpful for someone to study microeconomics, macroeconomics, and econometrics. The application of Mathematics for Economics in accounting and business is limited and can be found in Economic Order Quantity (EOQ) formula and in wine storage case (Chiang, 2005).
            Management Science becomes interesting if someone already knows the rules of unconstrained optimization and optimization with equality constraints using calculus. In other words, the study of optimization is not complete until students know the short-cut method to solve any optimization models using Excel-Solver.

           There is a saying that in studying anything, knowing is not enough; we must apply. For mathematics-related courses this saying also counts. The problem is Mathematics for Economics has little application in accounting and business.            Compared to Mathematics for Economics and Management Science, Mathematics of Finance is more dynamic and fun to study due to several reasons. First it is about money and everyone is concerned when talking about money. Second, it discusses topics and things that do exist. Mathematics of Finance is rich with application examples. Last but not least, one can use many ways to get the solutions to the Mathematics of Finance. He can use a scientific calculator, a financial calculator, or excel. A feature that belongs uniquely to Mathematics of Finance.

Mathematics, Accounting, and bussiness

         Mathematics is indispensable to economics and business. Mathematics is compulsory for students of accounting and business from the diploma program up to the graduate program. For undergraduate students, mathematics-related courses are even given in two to three semesters. They are given under different course names: mathematics for economics, mathematics for business, mathematics of finance, mathematical analysis, quantitative methods, quantitative analysis, and management science. The problem is, in most universities, students of accounting and business only learn mathematics that is of little relevance to them but of high relevance to students of economics. This paper tries to criticize the relevancies of the contents of the mathematics courses for accounting and business students.

         To support the career of accounting and business graduates, mathematics taught to them should be differentiated from mathematics for economics students. For accounting and business students, the topics of set theory, limit, differentiation, partial and total derivatives, matrices, unconstrained and constrained optimization, and integration, all of which are covered in mathematics for economics, are just “nice to know”. But, they fail to be “essential to know.” It is much more important for the students of accounting and business to know how to make a savings schedule for financial/pension planning; calculations of various yields, returns, interest rates, and stock indices; and valuations of any assets and securities (stocks and bonds) using present value approach.

        The above skills are needed by any accountant or finance manager and anyone working in the finance-related institutions such as banks, leasing, insurance, pension funds, and security companies. Such knowledge is also required for any cash surplus (investors) to select the investment with the highest return, given risk; for any cash deficit (borrower) to obtain the cheapest financing; and for anyone dealing with banks.

Source: Budi Frensidy, Accounting Department, Faculty of Economics – University of Indonesia
Presented at the National Seminar on Mathematics 2007, Catholic University of Parahyangan