**IAS/PCMI--The Teacher Program Series**

Volume: 3;
2015;
203 pp;
Softcover
**Print ISBN: 978-1-4704-2195-3
Product Code: SSTP/3**

List Price: $29.00

Individual Member Price: $23.20

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# Famous Functions in Number Theory

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*Bowen Kerins; Darryl Yong; Al Cuoco; Glenn Stevens*

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

Designed for precollege teachers by a collaborative of teachers,
educators, and mathematicians, Famous Functions in
Number Theory 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.

Famous Functions in Number Theory introduces readers to the
use of formal algebra in number theory. Through numerical
experiments, participants learn how to use polynomial algebra
as a bookkeeping mechanism that allows them to count
divisors, build multiplicative functions, and compile multiplicative
functions in a certain way that produces new ones.
One capstone of the investigations is a beautiful result attributed
to Fermat that determines the number of ways a positive
integer can be written as a sum of two perfect squares.

Famous Functions in Number Theory is a volume of the book
series “IAS/PCMI—The Teacher Program Series”
published by the American Mathematical Society. Each
volume in that series covers the content of one Summer School
Teacher Program year and is independent of the rest.

Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

#### Table of Contents

# Table of Contents

## Famous Functions in Number Theory

#### Readership

In-service secondary school teachers; students training to become secondary school teachers.