Moving Things Around

Title

Moving Things Around

Files

Description

A co-publication of the AMS and IAS/Park City Mathematics Institute

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Moving Things Around is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute.

But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves.

The goal of Moving Things Around is to help participants make what might seem to be surprising connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of card shuffles. Another goal is to use these connections to bring some coherence to several ideas that run throughout school mathematics—rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics. The theme of seeking structural similarities is developed slowly, leading, near the end of the course, to an informal treatment of isomorphism.

ISBN

978-1-4704-2926-3

Publication Date

2016

Publisher

American Mathematical Society

City

Providence, RI

Keywords

permutation groups, number theory, rational number arithmetic

Disciplines

Algebra | Analysis | Mathematics | Number Theory