Mathematics Between Friends
Lily Yen

Teaching mathematics through storytelling—a gentle introduction to college mathematics.


I first met Lily Yen in 2003, when we were both invited to coach Canada’s team to the International Mathematical Olympiad. As teachers and researchers of mathematics, as well as being former Math Olympians, Lily and I share a lifelong passion for the subject, as well as the firm belief that mathematics can help students discover their passion and purpose.

Mathematics Between Friends treats the reader to a historical and global tour of the subject. We learn about diverse systems of numerals (including Indigenous numerals) in the chapter on Counting and Coding, and the mathematics of origami in the chapter on Measuring and Tracking. We also discover how mathematics can be applied towards issues of Social Justice, whether it is by closing the income gap in the chapter on Saving, Spending, Borrowing and Giving, and better understanding the opioid crisis in the chapter on Predicting.

In her Introduction to the Instructor section, Lily writes of her hope that the “stories and explorations of each chapter will convince [students] that mathematics is not about crunching numbers or memorizing formulas, but loving how their brains take on challenges and stay focused until a tantalizing problem is fully solved or understood.” It is this focus on conceptual understanding and mastery, told through rich narrative and dialogue, that makes Mathematics Between Friends such a joy to read.

Richard Hoshino
Associate Teaching Professor, Northeastern University
Author of The Math Olympian

About Mathematics Between Friends

Mathematics Between Friends contains six chapters: problem solving, numeration systems, geometry, consumer mathematics, probability, and statistics. The book assumes very little mathematical background, and develops most of what is required either through conversations in the story part or in the sidebar via formal development. If reading both the story and the sidebar material at the same time is unfamiliar, I recommend reading the story in each section first. Once the plot of the story is no longer foreign, one can read the section again, this time, paragraph by paragraph with relevant sidebar material. The symbol ◁ marks the end of a mathematical development. Each chapter is enriched by many internet links (in magenta) both mathematical and otherwise: Readers are encouraged to check out each link to follow their interests. Red texts are links within the book.

Chapters in this book are mostly independent; one may read in any chapter order. The exercises for the last chapter, Understanding Data, include questions which require adequate digital literacy to obtain statistical information on the Internet. Since the information may be time sensitive, with new data replacing the old, the solutions to these questions are based on data available in May of 2022. Answers to exercises labelled [im] are found only in the Instructor's Manual to this book.

Mathematics Between Friends is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.