Gregory V. Bard

Associate Professor of Mathematics
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Finite and Financial Mathematics

(Click Here to Jump to the Table of Contents)

This project is on indefinite hold.

(To find out why, click on "Books I have written," above.)

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 (Click Here)
  • The Prime Directive [Under Renovation]

  • Chapter Zero: Diagnostics and Vital Skills
    1. Scientific Notation and Significant Digits (Click Here)
    2. Diagnostic One: Calculator Skills (Click Here)
    3. The Order of Operations and Calculator Skills (Click Here)
    4. Diagnostic Two: Algebra Skills (Click Here)
    5. Diagnostic Zero: Fundamentals of Algebra (Click Here)

  • Chapter One: Algebra Review
    1. Worksheet: Direct Proportions (Click Here)
    2. Using the Quadratic Formula to Solve Quadratic Equations (Click Here)
    3. Intercepts and Rapidly Graphing Lines (Click Here)
    4. Intersecting Two Lines, Part One (Click Here)
    5. Intersecting Two Lines, Part Two (Click Here)
    6. Working with Functions (Click Here)
    7. Multiplying and Squaring Polynomials or Functions? (Click Here)
    8. Review of Basic Inequalities (Click Here)
    9. Five Problems about Improvements Paying for Themselves (Click Here)
    10. Completing the Square (and Applications) [Under Long-Term Renovation]

  • Chapter Two: Basic Financial, Scientific, and Economic Models
    1. Simple Interest (Click Here)
    2. The Basics of Compound Interest (Click Here)
    3. Introduction to Portfolio Balancing [Under Long-Term Renovation]
    4. Worksheet: Problems about Mixed Commodities (Click Here)
    5. Worksheet: Using and Testing a Model [Under Long-Term Renovation]
    6. Building a Linear Model (Click here)
    7. How Exponents Really Work (Click Here)
    8. Worksheet: Non-Linear Proportions (Click Here)
    9. Linear Break-Even Analysis (Click Here)
    10. Worksheet: Some Challenging Word Problems (Click Here)
    11. Cost-Benefit Analysis (Click Here)

  • Chapter Three: Intermediate Financial, Scientific, and Economic Models
    1. Predatory Lending and the Annual Effective Rate (Click Here)
    2. Advanced Thoughts on Compound Interest [In Preparation]
    3. Worksheet: Exploring Best-Fit Lines (also known as Linear Regressions) [Under Renovation]
    4. Supply and Demand: Part One (Click Here)
    5. Supply and Demand: Part Two [Under Renovation]
    6. Inflation and the True Rate of Return (Click Here)
    7. Radiation, Bacteria, Populations, and Real Estate (Click Here)
    8. Rigorously Deriving the Laws of Logarithms (Click Here)
    9. What is a Logarithm? (Click Here)
    10. The Number e and Continuously Compounded Interest (Click Here)
    11. Worksheet: Solving Problems Using Logarithms (Click Here)
    12. Advanced Topics in Exponential and Logarithmic Functions [Planned]

  • Chapter Four: Perpetuities, Annuities, Arithmetic, and Geometric Progressions
    1. What is an Amortization Table? [Under Repairs]
    2. The Present Value of a Decreasing Annuity [Under Repairs]
    3. The Future Value of an Increasing Annuity [Under Repairs]
    4. Advanced Mortgage Problems [Under Revision]
    5. Long-Term Savings with Inflation [Under Repairs]
    6. The Time Value of Money and NPVs [Under Repairs]
    7. The Internal Rate of Return [Planned]

  • Chapter Five: Systems of Equations and Matrices [Planned]

  • Chapter Six: Inequalities, Linear Programming, and Industrial Engineering [Planned]

  • Chapter Seven: Sets, Probability, and Combinatorics
    1. Introduction to Sets (Click Here)
    2. Basic Venn Diagram Problems (Click Here)
    3. Handout about Inclusive vs Exclusive Or (Click Here)
    4. Intermediate Venn Diagram Problems (Click Here)
    5. Advanced Venn Diagram Problems (Click Here)
    6. A Formal Introduction to Probability (Click Here)
    7. You Can't Just Add Probabilities (Click Here)
    8. The Multiplication and Exponent Principles (Click Here)
    9. The Permutation and Factorial Principles (Click Here)
    10. The Combinations Principle and the Handshake Principle (Click Here)
    11. Worksheet: Which Combinatorial Formula Should I Use? (Click here)
    12. Worksheet: Independence, Repetition, and Bernoulli's Formula (Click here)

  • Chapter Eight: Advanced Topics in Probability and Combinatorics
    1. Advanced Topics in Set Theory (Click here)
    2. Probability, Dice, and Games [Coming Soon]
    3. Probability Tree Diagrams (Click here)
    4. Conditional Probability Notation [Planned]
    5. Bayes's Theorem [Planned]
    6. Expected Value and Insurance [Coming Soon]
    7. Pascal's Triangle and the Binomial Theorem (Worksheet) and also (Reference Card)
    8. Advanced Combinatorial Problems [Planned]
    9. Working with Different Number Bases [Planned]
    10. The Rare Events Theorem [Under Renovation]

  • Chapter Nine: Logic
    1. Truth Tables, Part One [Planned]
    2. A Tiny Taste of Category Theory [Coming Soon]
    3. What is a Contra-positive? A Counter-Example? A Converse? (Click here)
    4. Truth Tables, Part Two [Planned]

  • Appendix A: Things Everyone Should Know
    1. Unit Conversions (Click Here)
    2. Percentages [Planned]
    3. All About Averages [Planned]
    4. What is a Standard Deviation? [Planned]

  • Appendix B: Geometric and Arithmetic Progressions
    1. Loans and Finite Geometric Progressions [Under Repairs]
    2. Arithmetic Progressions [Planned]
    3. Deriving the Annuity Formulas [Planned]
    4. The Money Multiplier and Infinite Geometric Progressions [Under Repairs]
    5. Big-Sigma Notation [Planned]

  • Appendix C: Miscellaneous
    1. Worksheet on Solving Problems Using Logarithms (Click here)
    2. Mini-Worksheet on "Conglomerates, Holding Companies, and Matrix Algebra" (Click here)
    3. Mega-Worksheet on "Leontief Input-Output Analysis" (Click here)

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.
(Indefinite hold notice added on July 26th, 2017.)