Softcover ISBN:  9781470472207 
Product Code:  CLRM/70 
List Price:  $79.00 
MAA Member Price:  $59.25 
AMS Member Price:  $59.25 
eBook ISBN:  9781470473440 
Product Code:  CLRM/70.E 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
Softcover ISBN:  9781470472207 
eBook: ISBN:  9781470473440 
Product Code:  CLRM/70.B 
List Price:  $154.00 $116.50 
MAA Member Price:  $115.50 $87.38 
AMS Member Price:  $115.50 $87.38 
Softcover ISBN:  9781470472207 
Product Code:  CLRM/70 
List Price:  $79.00 
MAA Member Price:  $59.25 
AMS Member Price:  $59.25 
eBook ISBN:  9781470473440 
Product Code:  CLRM/70.E 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
Softcover ISBN:  9781470472207 
eBook ISBN:  9781470473440 
Product Code:  CLRM/70.B 
List Price:  $154.00 $116.50 
MAA Member Price:  $115.50 $87.38 
AMS Member Price:  $115.50 $87.38 

Book DetailsClassroom Resource MaterialsVolume: 70; 2023; 202 ppMSC: Primary 11
Number Theory Through the Eyes of Sophie Germain: An Inquiry Course is an innovative textbook for an introductory number theory course.
Sophie Germain (1776–1831) was largely selftaught in mathematics and, two centuries ago, in solitude, devised and implemented a plan to prove Fermat's Last Theorem. We have only recently completely understood this work from her unpublished letters and manuscripts. David Pengelley has been a driving force in unraveling this mystery and here he masterfully guides his readers along a path of discovery. Germain, because of her circumstances as the first woman to do important original mathematical research, was forced to learn most of what we now include in an undergraduate number theory course for herself. Pengelley has taken excerpts of her writings (and those of others) and, by asking his readers to decipher them, skillfully leads us through an inquirybased course in elementary number theory. It is a detective story on multiple levels. What is Sophie Germain thinking? What do her mathematical writings mean? How do we understand what she knew and what she was trying to do, where she succeeded and where she didn't?
ReadershipUndergraduate students interested in learning number theory and math history.

Table of Contents

Chapters

Introduction

Sophie Germain, number theory, and Fermat’s last theorem

Germain’s plan to prove Fermat’s last theorem

Fermat’s last theorem for exponent four

Germain’s grand plan and a letter to Gauss

Congruence, Germain’s basic lemma, systems of linear congruences, and higher power congruences

Primitive roots

Germain carrying out her grand plan

Large size of solutions and Sophie Germain’s theorem

The demise of the grand plan: A letter to Legendre

Prime patterns in quadratic forms

How Fermat discovered his theorem, and other divisibility delights


Additional Material

Reviews

It takes tremendous erudition for an author to fully understand "Number Theory Through the Eyes of Sophie Germain" and then lucidly explain it to others in a manner that is both captivating and instructive. David Pengelly has done just that in this unique book that will motivate many students to pursue research in this the most pure and enchanting branch of mathematics.
Dora Musielak, MAA Reviews 
“Number Theory Through the Eyes of Sophie Germain” is simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primarysource historical documents, an inquirybased textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician. Work is required of the reader. Readers are carefully guided to discover and prove almost all results for themselves in a sequence of scaffolded exploratory tasks with hints, fully integrated with the narrative. The difficulty of the inquiry tasks varies considerably, but the author provides the reader with appropriately helpful guidance at every step. An introductory number theory course taught with this text would be a remarkable, potentially lifechanging, experience.
Stephen Kennedy, Carleton College and MAA Press 
Teaching with 'Number Theory through the Eyes of Sophie Germain' is a delight. There is truly something for everyone. The newcomer to number theory is given a motivated and accessible path to discovering all the essentials. The experienced number theorist is treated to an exciting journey through Germain's attempt to crack Fermat's Last Theorem. Having used this text for an independent study, I can say that this wonderful book is not for the casual reader. However, the rewards of the effort are well worth it. How often do you find your heart racing while reading a math textbook, eager to discover what happens next?
Sarah Hagen, Davidson Academy Online


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Number Theory Through the Eyes of Sophie Germain: An Inquiry Course is an innovative textbook for an introductory number theory course.
Sophie Germain (1776–1831) was largely selftaught in mathematics and, two centuries ago, in solitude, devised and implemented a plan to prove Fermat's Last Theorem. We have only recently completely understood this work from her unpublished letters and manuscripts. David Pengelley has been a driving force in unraveling this mystery and here he masterfully guides his readers along a path of discovery. Germain, because of her circumstances as the first woman to do important original mathematical research, was forced to learn most of what we now include in an undergraduate number theory course for herself. Pengelley has taken excerpts of her writings (and those of others) and, by asking his readers to decipher them, skillfully leads us through an inquirybased course in elementary number theory. It is a detective story on multiple levels. What is Sophie Germain thinking? What do her mathematical writings mean? How do we understand what she knew and what she was trying to do, where she succeeded and where she didn't?
Undergraduate students interested in learning number theory and math history.

Chapters

Introduction

Sophie Germain, number theory, and Fermat’s last theorem

Germain’s plan to prove Fermat’s last theorem

Fermat’s last theorem for exponent four

Germain’s grand plan and a letter to Gauss

Congruence, Germain’s basic lemma, systems of linear congruences, and higher power congruences

Primitive roots

Germain carrying out her grand plan

Large size of solutions and Sophie Germain’s theorem

The demise of the grand plan: A letter to Legendre

Prime patterns in quadratic forms

How Fermat discovered his theorem, and other divisibility delights

It takes tremendous erudition for an author to fully understand "Number Theory Through the Eyes of Sophie Germain" and then lucidly explain it to others in a manner that is both captivating and instructive. David Pengelly has done just that in this unique book that will motivate many students to pursue research in this the most pure and enchanting branch of mathematics.
Dora Musielak, MAA Reviews 
“Number Theory Through the Eyes of Sophie Germain” is simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primarysource historical documents, an inquirybased textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician. Work is required of the reader. Readers are carefully guided to discover and prove almost all results for themselves in a sequence of scaffolded exploratory tasks with hints, fully integrated with the narrative. The difficulty of the inquiry tasks varies considerably, but the author provides the reader with appropriately helpful guidance at every step. An introductory number theory course taught with this text would be a remarkable, potentially lifechanging, experience.
Stephen Kennedy, Carleton College and MAA Press 
Teaching with 'Number Theory through the Eyes of Sophie Germain' is a delight. There is truly something for everyone. The newcomer to number theory is given a motivated and accessible path to discovering all the essentials. The experienced number theorist is treated to an exciting journey through Germain's attempt to crack Fermat's Last Theorem. Having used this text for an independent study, I can say that this wonderful book is not for the casual reader. However, the rewards of the effort are well worth it. How often do you find your heart racing while reading a math textbook, eager to discover what happens next?
Sarah Hagen, Davidson Academy Online