Gregory V. Bard
Associate Professor of Mathematics
Preserving the look-and-feel of the World Wide Web as it was, in 1998.
Finite and Financial Mathematics
(Click Here to Jump to the Table of Contents)
What is this Book and Who is it For?
I'm currently writing a very unusual textbook for the university 100-level math requirement for
majors such as economics, finance, marketing, business, accounting, and management. The book is for
a course often called Finite Mathematics in the USA and Canada,
but Quantitative Methods in the UK.
Assorted sections could easily be used to create a Quantitative
Literacy course for liberal-arts majors as well, with a flavor of personal-finance education.
(Scroll down, for a table of contents.)
This textbook is intended for freshmen or sophomores, particularly those
majoring in the money-related fields. I define
this broadly, to include finance,
economics, marketing, accounting, management, human resources,
international commerce, hotel & tourism, business administration, and other majors.
(It has been suggested to me that the book is probably very useful for students in the
social sciences as well.
By the social sciences, I would include psychology, education, sociology,
anthropology, archeology, geography, and most especially political science.)
One might imagine that this book is not intended for math majors,
engineering students, nor physics students. However, I find that a lot of topics in probability and combinatorics
were amputated from the high school curriculum long ago, due to the common core. Yet, these topics are very
useful and model circumstances that occur in those subjects. Therefore, even
math majors, engineering students, and physics students can profit from reading those topics, covered in chapters
seven and eight.
The goal is to cover everything that the students would need at the undergraduate level (and at
their jobs in commerce or industry) up to (but not including) calculus. A sequel, covering
Business Calculus, might be written someday.
The topics of the text include functions, cost-benefit analysis, compound interest,
building mathematical models, supply and demand, regressions, non-linear proportions,
exponential growth, logarithms,
perpetuities, annuities, geometric progressions, systems of equations, matrices and their
inverses, the Leontief
Input-Output Model, systems of inequalities, linear programming (both small problems and large ones),
set theory, Venn Diagrams,
combinatorics, probability, and some descriptive statistics.
This textbook has been carefully designed with extremely realistic word problems whenever
possible. I have consulted advanced texts in economics and finance, as well as spoken to
faculty in other departments, and professionals actually working in the above fields.
Care has been
taken to review, rather than assume, knowledge of algebra throughout the textbook.
The lessons have been tested in the classroom numerous times since the project began
in January of 2010.
My coauthor, former student, former research collaborator and chief proofreader,
Joseph Bertino, and myself both carefully check every module,
to avoid or reduce typos, and ensure mathematical accuracy.
Table of Contents
- The Preface: How to Use this Book
- The Prime Directive [Under Renovation]
- Chapter Zero: Diagnostics and Vital Skills
- Scientific Notation and Significant Digits
- Diagnostic One: Calculator Skills
- The Order of Operations and Calculator Skills
- Diagnostic Two: Algebra Skills
- Diagnostic Zero: Fundamentals of Algebra
Chapter One: Algebra Review
- Worksheet: Direct Proportions
- Using the Quadratic Formula to Solve Quadratic Equations
- Intercepts and Rapidly Graphing Lines
- Intersecting Two Lines, Part One
- Intersecting Two Lines, Part Two
- Working with Functions
- Multiplying and Squaring Polynomials or Functions?
- Review of Basic Inequalities
- Five Problems about Improvements Paying for Themselves
- Completing the Square (and Applications)
[Under Long-Term Renovation]
Chapter Two: Basic Financial, Scientific, and Economic Models
- Simple Interest
- The Basics of Compound Interest
- Introduction to Portfolio Balancing
[Under Long-Term Renovation]
- Worksheet: Problems about Mixed Commodities
- Worksheet: Using and Testing a Model
[Under Long-Term Renovation]
- Building a Linear Model
- How Exponents Really Work
- Worksheet: Non-Linear Proportions
- Linear Break-Even Analysis
- Worksheet: Some Challenging Word Problems
- Cost-Benefit Analysis
Chapter Three: Intermediate Financial, Scientific, and Economic
- Predatory Lending and the Annual Effective Rate
- Advanced Thoughts on Compound Interest [In Preparation]
- Worksheet: Exploring Best-Fit Lines (also known as Linear Regressions)
- Supply and Demand: Part One
- Supply and Demand: Part Two [Under Renovation]
- Inflation and the True Rate of Return
- Radiation, Bacteria, Populations, and Real Estate
- Rigorously Deriving the Laws of Logarithms
- What is a Logarithm?
- The Number e and Continuously Compounded Interest
- Worksheet: Solving Problems Using Logarithms
- Advanced Topics in Exponential and Logarithmic Functions
Chapter Four: Perpetuities, Annuities, Arithmetic, and Geometric
- What is an Amortization Table? [Under Repairs]
- The Present Value of a Decreasing Annuity [Under Repairs]
- The Future Value of an Increasing Annuity [Under Repairs]
- Advanced Mortgage Problems [Under Revision]
- Long-Term Savings with Inflation [Under Repairs]
- The Time Value of Money and NPVs [Under Repairs]
- The Internal Rate of Return [Planned]
Chapter Five: Systems of Equations and Matrices
Chapter Six: Inequalities, Linear Programming, and Industrial Engineering
Chapter Seven: Sets, Probability, and Combinatorics
- Introduction to Sets
- Basic Venn Diagram Problems
- Handout about Inclusive vs Exclusive Or
- Intermediate Venn Diagram Problems
- Advanced Venn Diagram Problems
- A Formal Introduction to Probability
- You Can't Just Add Probabilities
- The Multiplication and Exponent Principles
- The Permutation and Factorial Principles
- The Combinations Principle and the Handshake Principle
- Worksheet: Which Combinatorial Formula Should I Use?
- Worksheet: Independence, Repetition, and Bernoulli's Formula
Chapter Eight: Advanced Topics in Probability and Combinatorics
- Advanced Topics in Set Theory
- Probability, Dice, and Games [Coming Soon]
- Probability Tree Diagrams
- Conditional Probability Notation [Planned]
- Bayes's Theorem [Planned]
- Expected Value and Insurance [Coming Soon]
- Pascal's Triangle and the Binomial Theorem
- Advanced Combinatorial Problems [Planned]
- Working with Different Number Bases [Planned]
- The Rare Events Theorem [Under Renovation]
Chapter Nine: Logic
- Truth Tables, Part One [Planned]
- A Tiny Taste of Category Theory [Coming Soon]
- What is a Contra-positive? A Counter-Example? A Converse?
- Truth Tables, Part Two [Planned]
Appendix A: Things Everyone Should Know
- Unit Conversions
- Percentages [Planned]
- All About Averages [Planned]
- What is a Standard Deviation? [Planned]
Appendix B: Geometric and Arithmetic Progressions
- Loans and Finite Geometric Progressions [Under Repairs]
- Arithmetic Progressions [Planned]
- Deriving the Annuity Formulas [Planned]
- The Money Multiplier and Infinite Geometric Progressions [Under Repairs]
- Big-Sigma Notation [Planned]
Appendix C: Miscellaneous
- Worksheet on Solving Problems Using Logarithms
- Mini-Worksheet on "Conglomerates, Holding Companies, and Matrix Algebra"
- Mega-Worksheet on "Leontief Input-Output Analysis"
When this book is completed, it is my intention to make it free and open-source,
through the Creative Commons. College students are short on cash as it is, and I don't
want to take any of their money.
I am very grateful for the
able assistance of my proofreader, problem writer, and co-author, Joseph Bertino, who
completed his Bachelors degrees in Economics and in Mathematics at
Fordham University (in
New York City) while I was teaching there.
Last Updated: March 2nd, 2017.