In this book for in-service and preservice secondary school teachers, the authors present a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. The book’s theme revolves around how to use polynomial algebra as a bookkeeping mechanism that allows participants to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones.

This book is part of "IAS/PCMI-The Teacher Program Series,” published by the AMS. Each volume in the series covers the content of one Summer School Teacher Program year at the Park City Mathematics Institute.