A Guide To Business Mathematics

Description

The success of business today is dependent on the knowledge and expertise of its employees. The need for mathematics arises naturally in business such as in the work of the actuary in an insurance company, the financial mathematics required in the day-to-day work of the banker and the need to analyse data to extract useful information to enable the business to make the right decisions to be successful. A Guide to Business Mathematics provides a valuable self-study guide to business practitioners, business students and the general reader to enable them to gain an appropriate insight into the mathematics used in business. This book offers an accessible introduction to essential mathematics for the business field. A wide selection of topics is discussed with the mathematical material presented in a reader-friendly way. The business context motivates the presentation. The author uses modelling and applications to motivate the material, demonstrating how mathematics is used in the financial sector. In addition to the role of the actuary and the banker, the book covers operations research including game theory, trade discounts and the fundamentals of statistics and probability. The book is also a guide to using metrics to manage and measure performance, and business economics. Foundations on algebra, number theory, sequences and series, matrix theory and calculus are included as is a complete chapter on using software. Features: • Discusses simple interest and its application to promissory notes/treasury bills. • Discusses compound interest with applications to present and future values. • Introduces the banking field including loans, annuities and the spot/forward FX market. • Discusses trade discounts and markups/markdowns. • Introduces the insurance field and the role of the actuary. • Introduces the fields of data analytics and operations research. • Discusses business metrics and problem solving. • Introduces matrices and their applications. • Discusses calculus and its applications. • Discusses basic financial statements such as balance sheet, profit and loss and cash account. • Reviews a selection of software to support business mathematics. This broad-ranging text gives the reader a flavour of the applications of mathematics to the business field and stimulates further study in the subject. As such, it will be of great benefit to business students, while also capturing the interest of the more casual reader. Cover Half Title Title Page Copyright Page Dedication Contents Preface Overview Organization and Features Audience Acknowledgements Contributors 1. Introduction to Number Theory 1.1 Basic Number Theory 1.2 Fractions and Decimals 1.3 Prime Number Theory 1.3.1 Greatest Common Divisors (GCD) 1.3.2 Euclid's Algorithm for GCD 1.3.3 Least Common Multiple (LCM) 1.3.4 Distribution of Primes 1.4 Ratios and Proportions 1.5 Percentages 1.6 Review Questions 1.7 Summary Notes 2. Algebra 2.1 Simplification of Algebraic Expressions 2.2 Simple and Simultaneous Equations 2.2.1 Simultaneous Equations 2.3 Quadratic Equations 2.4 Indices and Logarithms 2.5 Exponentials and Natural Logarithms 2.6 Review Questions 2.7 Summary 3. Sets, Relations and Functions 3.1 Set Theory 3.1.1 Set Theoretical Operations 3.1.2 Properties of Set Theoretical Operations 3.1.3 Russell's Paradox 3.2 Relations 3.2.1 Reflexive, Symmetric and Transitive Relations 3.2.2 Composition of Relations 3.2.3 Binary Relations 3.2.4 Applications of Relations to Databases 3.3 Functions 3.4 Review Questions 3.5 Summary Notes 4. Sequences, Series and Permutations and Combinations 4.1 Sequences and Series 4.2 Arithmetic and Geometric Sequences 4.3 Arithmetic and Geometric Series 4.4 Permutations and Combinations 4.4.1 Permutations 4.4.2 Combinations 4.5 Review Questions 4.6 Summary 5. Simple Interest and Applications 5.1 Simple Interest 5.2 Computing Future and Present Values 5.2.1 Computing Future Value 5.2.2 Computing Present Values 5.2.3 Equivalent Values and Payment 5.3 Promissory Notes 5.4 Treasury Bills 5.5 Review Questions 5.6 Summary 6. Compound Interest and Applications 6.1 Compound Interest 6.2 Present Value 6.3 Long-Term Promissory Notes 6.4 Equivalent Values 6.5 Analysing the Business Case for a Project 6.6 Review Questions 6.7 Summary 7. Banking and Financial Services 7.1 Central Bank 7.2 Retail Banks 7.3 Financial Instruments 7.4 Basic Mathematics of Annuities 7.5 Loans and Mortgages 7.6 Foreign Exchange 7.6.1 Forex and Speculation 7.6.2 Foreign Exchange Spread 7.7 Corporate Bonds 7.8 Review Questions 7.9 Summary Notes 8. Trade Discounts and Pricing 8.1 Calculating Discounts 8.1.1 Net Price Factor Approach 8.2 Markups and Markdowns 8.3 Payment Terms and Cash Discounts 8.4 Pricing and Pricing Policy 8.4.1 Setting the Price for a Product 8.5 Review Questions 8.6 Summary 9. Statistics 9.1 Basic Statistics 9.1.1 Abuse of Statistics 9.1.2 Statistical Sampling and Data Collection 9.2 Frequency Distribution and Charts 9.3 Statistical Measures 9.3.1 Arithmetic Mean 9.3.2 Mode 9.3.3 Median 9.4 Variance and Standard Deviation 9.5 Correlation and Regression 9.5.1 Regression 9.5.2 Method of Least Squares 9.6 Statistical Inference and Hypothesis Testing 9.7 Review Questions 9.8 Summary Note 10. Probability Theory 10.1 Basic Probability Theory 10.1.1 Laws of Probability 10.1.2 Bayes' Formula 10.2 Random Variables 10.3 Binomial and Poisson Distributions 10.4 The Normal Distribution 10.4.1 Unit Normal Distribution 10.4.2 Confidence Intervals and Tests of Significance 10.4.3 The Central Limit Theorem 10.5 Bayesianism 10.6 Review Questions 10.7 Summary Note 11. The Insurance Industry 11.1 Basic Mathematics of Motor Insurance 11.2 Basic Mathematics of Health Insurance 11.3 Basic Mathematics of Pensions 11.3.1 Mortality Tables 11.3.2 Life Insurance 11.4 The Actuary 11.5 Review Questions 11.6 Summary 12. Data Science and Data Analytics 12.1 What Is Data Science? 12.1.1 Data Science and Data Scientists 12.1.2 Data Science and Society 12.2 What Is Data Analytics? 12.2.1 Business Analytics and Business Intelligence 12.2.2 Big Data and Data Mining 12.2.3 Data Analytics for Social Media 12.3 Mathematics in Data Science and Analytics 12.4 Privacy 12.4.1 Privacy and Social Media 12.4.2 Privacy and the Law 12.4.3 EU GDPR Privacy Law 12.5 Security 12.6 Review Questions 12.7 Summary Notes 13. Business Metrics and Problem Solving 13.1 The Goal Question Metric Paradigm 13.1.1 Goal 13.1.2 Question 13.1.3 Metrics 13.2 The Balanced Scorecard 13.3 Metrics for an Organization 13.3.1 Sales and Marketing Metrics 13.3.2 Financial Metrics 13.3.3 Customer Satisfaction Metrics 13.3.4 Process Improvement Metrics 13.3.5 Human Resources and Training Metrics 13.3.6 Project Management Metrics 13.3.7 Development Quality Metrics 13.3.8 Quality Audit Metrics 13.3.9 Customer Care Metrics 13.3.10 Cost of Quality Metrics 13.4 Implementing a Metrics Program 13.4.1 Data Gathering for Metrics 13.5 Problem-Solving Techniques 13.5.1 Fishbone Diagram 13.5.2 Histograms 13.5.3 Pareto Chart 13.5.4 Trend Graphs 13.5.5 Scatter Graphs 13.5.6 Metrics and Statistical Process Control 13.6 Review Questions 13.7 Summary 14. Matrix Theory 14.1 Two × Two Matrices 14.2 Matrix Operations 14.3 Determinants 14.4 Eigen Vectors and Values 14.5 Gaussian Elimination 14.6 Applications of Matrices 14.7 Review Questions 14.8 Summary 15. Operations Research 15.1 Linear Programming 15.1.1 Linear Programming Example 15.1.2 General Formulation of LP Problem 15.2 Cost Volume Profit Analysis 15.3 Game Theory 15.4 Queueing Theory 15.5 Review Questions 15.6 Summary 16. Basic Financial Statements 16.1 Balance Sheet 16.2 Profit and Loss Account 16.3 Managing Cash 16.4 Review Questions 16.5 Summary 17. Calculus I 17.1 Differentiation 17.1.1 Rules of Differentiation 17.2 Integration 17.2.1 Definite Integrals 17.2.2 Fundamental Theorems of Integral Calculus 17.3 Review Questions 17.4 Summary Notes 18. Calculus II 18.1 Applications of Calculus 18.2 Fourier Series 18.3 The Laplace Transform 18.4 Differential Equations 18.5 Review Questions 18.6 Summary 19. A Brief Introduction to Economics 19.1 Macroeconomics 19.2 Microeconomics 19.3 GDP 19.4 Utility 19.5 Comparative and Absolute Advantages 19.6 Elasticity of Demand 19.7 Role of Money 19.8 Role of Government in the Economy 19.9 Economic Indicators 19.10 Competition 19.11 Globalization and Terms of Trade 19.12 Mathematics in Economics 19.13 Review Questions 19.14 Summary 20. Software to Support Business Mathematics 20.1 Microsoft Excel 20.2 Python 20.3 Maple 20.4 Minitab Statistical Software 20.5 R Statistical Software Environment 20.6 Mathematica 20.7 Matlab 20.8 Sage Accounting Software 20.9 SPSS Statistics 20.10 SQL and Relational Databases 20.10.1 Structured Query Language (SQL) 20.11 SAS 20.12 Review Questions 20.13 Summary Notes 21. Epilogue References Glossary Index