# Mathematics for Finance

 Module code: ACFI 1303 Module description It is generally acknowledged that economic events shape our everyday life in an unparalleled way. As a social science, economics is required to determine, address and precisely monitor the consequences of such social phenomena and when possible to contribute in their ex-ante prediction. To do so, economists tend to use the language of mathematics due to its logic and precision in argumentation; as well as, its ability to simplify extensive and complex narratives in an orderly linguistic. This module aims to familiarise students with the mathematical tools and methods which are necessary for understanding and explaining economic relationships; and, to create the foundations for understanding the complex mathematical models used in finance applications that they will be exposed later in the programme. Indicative module content is likely to include the following: Mathematical Preliminaries Linear Relationships and Applications in Economics Translations of Linear Functions, Elasticity, Budget and Cost Constraints Solving Simultaneous Linear Equations Equilibrium and Break Even Analysis Quadratic and Cubic Functions Exponential, Logarithmic and Hyperbolic Functions Financial Mathematics Slope of a Curve and Differentiation Optimization for Functions of One Variable Curvature and other Applications Derivatives of other Standard Functions Derivatives and Elasticity Partial Differentiation and Unconstrained Optimization Constrained Optimization and Lagrange Multipliers The Power Rule for Integration, Integration and Natural Exponential Functions Integration and Algebraic Substitution Definite Integrals and Estimation of Area under a Curve First-order Differential Equations and Applications Linear Programming, Introduction to Matrix Algebra Contact hours per student per year Lectures: 22 hours Tutorials: 22 hours Assessments Competency test (open book) (40 mins): 40% Unseen exam (60 mins): 60% Additional costs: No extra costs other than purchase of books