
Famous Functions in Number Theory
American Mathematical Society (Publisher)
Published on 30. October 2015
Book
Paperback/Softback
224 pages
978-1-4704-2195-3 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
387 gr
ISBN-13
978-1-4704-2195-3 (9781470421953)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Bowen Kerins, Education Development Center Inc., Waltham, MA, USA.
Darryl Yong, Harvey Mudd College, Claremont, CA, USA.
Al Cuoco, Education Development Center Inc., Waltham, MA, USA.
Glenn Stevens, Cambridge, MA, USA.
Darryl Yong, Harvey Mudd College, Claremont, CA, USA.
Al Cuoco, Education Development Center Inc., Waltham, MA, USA.
Glenn Stevens, Cambridge, MA, USA.
Content
Problem sets
Facilitator notes
Teaching notes
Mathematical overview
Solutions
Facilitator notes
Teaching notes
Mathematical overview
Solutions