The Joy of Finite Mathematics: The Language and Art of Math

“Finite Mathematics” generally refers to a course conventionally required for non-science students. It normally covers several mathematical topics, including basic probability theory, statistics, linear programming, matrices, and more.

This textbook includes the fundamentals of logic, set theory, combinatorics, probability, statistics, geometry, algebra, finance, and more. Aimed at undergraduate students in social sciences, finance, economics, and other areas, this liberal arts math text is said to be “appropriate for preparing students for Florida’s CLAST exam or similar core requirements.” Matched online resources I did not review include PowerPoint slides for instructors and a student manual.

This book includes several topics generally not seen in comparable texts. I am very pleased, even impressed, to see that:

• Readers will encounter here an introduction to reasoning through the motivated presentation of basic logic. The use of a truth table to draw conclusions about a statement is a lost art now, rarely taught in secondary education and early college, at least in America. This dovetails nicely with the authors’ electrical switching (parallel and serial) word problems.
• The book includes well-considered personal finance advice, fulfilling a very present need for practical education. It includes bankruptcy laws, savings instruments, insurance types, budgeting, sales tax, and more. Together with a few pages on considering renting versus leasing versus buying, this chapter is strong in the practicalities of personal finance.
• The syntax of proofs, including \(\forall\) and \(\exists\).
• Induction is covered earlier and at greater depth than is typical.
• There is a deeper introduction to statistics, including the normal distribution, z-scores, and a very good introduction to normal approximation for binomial probabilities.
• A decent bit of geometry filling a gap I typically have to deal with by supplementary material, for example to explain “scalene” and the implication of an axis being “transverse.”
• Set theory that goes deeper than usual, for instance reaching to “closure”, etc.

I am surprised, even perplexed to see excluded:

• The use of matrices, beyond Cramer’s Rule, to solve systems of linear equations, e.g. row-echelon form, Gauss-Jordan method, and inverses.
• The meaning and formulation of the objective function.
• Conic sections and their graphs.
• A fuller exploration of sequences and series. Here, the terse display is called “pattern recognition.”
• Pascal’s triangle and the binomial theorem.
• Conversion between and solving logarithmic and exponential equations.

Study aids for each chapter include end-of-chapter vocabulary and concept reviews, as well as review exercises and a practice test. This is complete enough for independent study.

The authors’ choices of what to include and exclude mean this book may not match a typical curriculum. I see this book as containing enough for perhaps two semesters of first-year college coursework.

Tom Schulte teaches finite mathematics and algebra courses at Oakland Community College in Michigan.