Description
Book SynopsisSophie 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. Pengelley has taken excerpts of her writings and, by asking his readers to decipher them, skillfully leads us through an inquiry-based course in elementary number theory.
Trade Review“
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Germain is simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primary-source historical documents, an inquiry-based textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician.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
Table of Contents
- 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
- Bibliography
- Credits
- Index
