# Applications of Algebra and Geometry to the Work of Teaching

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*Bowen Kerins; Benjamin Sinwell; 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, Applications of Algebra and
Geometry to the Work of Teaching 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 specific theme developed in Applications of Algebra
and Geometry to the Work of Teaching is the use of complex
numbers—especially the arithmetic of Gaussian and Eisenstein
integers—to investigate some questions that are at the
intersection of algebra and geometry, like the classification of
Pythagorean triples and the number of representations of an
integer as the sum of two squares.

Applications of Algebra and Geometry to the Work of Teaching 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.

#### Readership

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

#### Reviews & Endorsements

The book provides materials and problems that will engage the student in deep and rich discovery of mathematics. This is a book for both parties, teacher and students. Both groups can learn from reading the problems and solving them to develop a greater appreciation of mathematics and the art of solving problems. It is refreshing to see a book with a wealth of problems and also a discussion how they can be used for multiple learning levels. I see the book being used in many areas of instruction, such as projects, competitions, and for practice. I highly recommend this book if you want more interaction with your students and to develop their logical thinking skills.

-- Peter Olszewski, MAA Reviews