Some Applications of Geometric Thinking (IAS/PCMI--The Teacher Program) (Ias/Pcmi - the Teacher Program: Mathematics for Teaching: a Problem-Based Approach)

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Some Applications of Geometric Thinking 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 Some Applications of Geometric Thinking is to help teachers see that geometric ideas can be used throughout the secondary school curriculum, both as a hub that connects ideas from all parts of secondary school and beyond—algebra, number theory, arithmetic, and data analysis—and as a locus for applications of results and methods from these fields. Some Applications of Geometric Thinking is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest. 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. -- Provided by publisher Volume 1. Probability Through Algebra -- Volume 2. Applications Of Algebra And Geometry To The Work Of Teaching / Bowen Kerins, Benjamin Sinwell, Darryl Young, Al Cuoco, Glenn Stevens -- Volume 3. Famous Functions In Number Theory / Bowen Kerins, Darryl Young, Al Cuoco, Glenn Stevens Development Team, Bowen Kerins, Benjamin Sinwell, Al Cuoco, Glenn Stevens. Institute For Advanced Study Park City Mathematics Institute Developed At Education Development Center, Inc. (edc) In Partnership With The Park City Mathematics Institute (pcmi), With Support Of The National Science Foundation. Based On Courses Offered In The Summer School Teacher Program At The Park City Mathematics Institute. Includes Bibliographical References. 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 specific theme developed is the use of complex numbers to investigate some questions that are at the intersection of algebra and geometry.