Friday, March 31, 2017

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.

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