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.
Author(s): Gerard O'Regan
Edition: 1
Publisher: CRC Press
Year: 2023
Language: English
Commentary: TruePDF
Pages: 413
Tags: Business Mathematics
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
