| Softcover ISBN: | 978-1-4704-7220-7 |
| Product Code: | CLRM/70 |
| List Price: | $79.00 |
| MAA Member Price: | $59.25 |
| AMS Member Price: | $59.25 |
| eBook ISBN: | 978-1-4704-7344-0 |
| Product Code: | CLRM/70.E |
| List Price: | $75.00 |
| MAA Member Price: | $56.25 |
| AMS Member Price: | $56.25 |
| Softcover ISBN: | 978-1-4704-7220-7 |
| eBook: ISBN: | 978-1-4704-7344-0 |
| 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: | 978-1-4704-7220-7 |
| Product Code: | CLRM/70 |
| List Price: | $79.00 |
| MAA Member Price: | $59.25 |
| AMS Member Price: | $59.25 |
| eBook ISBN: | 978-1-4704-7344-0 |
| Product Code: | CLRM/70.E |
| List Price: | $75.00 |
| MAA Member Price: | $56.25 |
| AMS Member Price: | $56.25 |
| Softcover ISBN: | 978-1-4704-7220-7 |
| eBook ISBN: | 978-1-4704-7344-0 |
| 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 |
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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 self-taught 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 We have only recently completely understood this work from her unpublished letters and manuscripts.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 inquiry-based 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.
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Table of Contents
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Chapters
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Introduction
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Sophie Germain, number theory, and Fermat’s last theorem
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Germain’s plan to prove Fermat’s last theorem
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Fermat’s last theorem for exponent four
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Germain’s grand plan and a letter to Gauss
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Congruence, Germain’s basic lemma, systems of linear congruences, and higher power congruences
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Primitive roots
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Germain carrying out her grand plan
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Large size of solutions and Sophie Germain’s theorem
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The demise of the grand plan: A letter to Legendre
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Prime patterns in quadratic forms
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How Fermat discovered his theorem, and other divisibility delights
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Additional Material
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Reviews
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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 primary-source historical documents, an inquiry-based 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 life-changing, 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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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a courseAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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 self-taught 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 inquiry-based 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 primary-source historical documents, an inquiry-based 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 life-changing, 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
