Number Theory Through The Eyes Of Sophie Germain

Author : David Pengelley
Publisher : American Mathematical Society
ISBN 13 : 1470472201
Total Pages : 216 pages
Book Rating : 4.07/5 ( download)

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Download or read book Number Theory Through the Eyes of Sophie Germain written by David Pengelley and published by American Mathematical Society. This book was released on 2023-06-29 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 We have only recently completely understood this work from her unpublished letters and manuscripts.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? Number Theory Through the Eyes of Sophie Germainis simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primary-source historical documents, an inquiry-based textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician.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

Author : Shauna L. Hoffman
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.16/5 ( download)

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Download or read book Sophie Germain written by Shauna L. Hoffman and published by . This book was released on 1995 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Dora E. Musielak
Publisher :
ISBN 13 : 9781496965028
Total Pages : 294 pages
Book Rating : 4.27/5 ( download)

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Download or read book Prime Mystery written by Dora E. Musielak and published by . This book was released on 2015-01-23 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovered by Lagrange, Sophie Germain (1776-1831) stood right between Gauss and Legendre, and both publicly recognized her scientific efforts. Unlike her female predecessors and contemporaries, Sophie Germain was an impressive mathematician and made lasting contributions to both number theory and the theories of vibration and elasticity. She was able to walk with ease across the bridge between the fields of pure mathematics and engineering physics. Though isolated and snubbed by her peers, she almost single-handedly changed the notion of the woman scholar. Sophie Germain was the first woman to win the prize of mathematics from the French Academy of Sciences. She is also the first and only woman who contributed to the proof of Fermat's Last Theorem. Prime Mystery: The Life and Mathematics of Sophie Germain paints a rich portrait of the brilliant and complex woman, including the mathematics she developed, her associations with Gauss, Legendre, and other leading researchers, and the tumultuous times in which she lived. In Prime Mystery, author Dora Musielak has done the impossible. She has chronicled Sophie Germain's brilliance through her life and work in mathematics, in a way that is simultaneously informative, comprehensive, and accurate.

Author : Karin R Saoub
Publisher : CRC Press
ISBN 13 : 0429779879
Total Pages : 394 pages
Book Rating : 4.79/5 ( download)

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Download or read book Graph Theory written by Karin R Saoub and published by CRC Press. This book was released on 2021-03-17 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory: An Introduction to Proofs, Algorithms, and Applications Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis. This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results. Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations. Current applications and exploratory exercises are provided to further the reader’s mathematical reasoning and understanding of the relevance of graph theory to the modern world. Features The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths. The third chapter focuses entirely on trees – terminology, applications, and theory. Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach. Hints and Solutions to selected exercises provided at the back of the book. Author Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She earned her PhD in mathematics from Arizona State University and BA from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.

Author : Jeffrey Stopple
Publisher : Cambridge University Press
ISBN 13 : 9780521012539
Total Pages : 404 pages
Book Rating : 4.38/5 ( download)

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Download or read book A Primer of Analytic Number Theory written by Jeffrey Stopple and published by Cambridge University Press. This book was released on 2003-06-23 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.

Author : Cheryl Bardoe
Publisher : Little, Brown Books for Young Readers
ISBN 13 : 0316394297
Total Pages : 40 pages
Book Rating : 4.91/5 ( download)

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Download or read book Nothing Stopped Sophie written by Cheryl Bardoe and published by Little, Brown Books for Young Readers. This book was released on 2018-06-12 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: The true story of eighteenth-century mathematician Sophie Germain, who solved the unsolvable to achieve her dream. When her parents took away her candles to keep their young daughter from studying math...nothing stopped Sophie. When a professor discovered that the homework sent to him under a male pen name came from a woman...nothing stopped Sophie. And when she tackled a math problem that male scholars said would be impossible to solve...still, nothing stopped Sophie. For six years Sophie Germain used her love of math and her undeniable determination to test equations that would predict patterns of vibrations. She eventually became the first woman to win a grand prize from France's prestigious Academy of Sciences for her formula, which laid the groundwork for much of modern architecture (and can be seen in the book's illustrations). Award-winning author Cheryl Bardoe's inspiring and poetic text is brought to life by acclaimed artist Barbara McClintock's intricate pen-and-ink, watercolor, and collage illustrations in this true story about a woman who let nothing stop her.

Author : Kendall Haven
Publisher : Bloomsbury Publishing USA
ISBN 13 : 0313090009
Total Pages : 261 pages
Book Rating : 4.04/5 ( download)

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Download or read book Marvels of Science written by Kendall Haven and published by Bloomsbury Publishing USA. This book was released on 1994-04-15 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: These 50 tales take just minutes to read but amply illustrate scientific principles and the evolution of science through history. Discussion questions and additional references are included and stories are cross-indexed by year of occurrence and by scientist. Focusing on the characters, events, and moments of genius that comprise the story of science, these 50 short reads are ideal for both read-alouds and reading assignments. The tales take just minutes to read but amply illustrate scientific principles and the evolution of science through history. Discussion questions and additional references correlate each story with elements of the science curriculum and provide direction for students to pursue their own discoveries. Stories are cross-indexed by year of occurrence and by scientist.

Author : Dora Musielak
Publisher : American Mathematical Society
ISBN 13 : 1470471566
Total Pages : 293 pages
Book Rating : 4.69/5 ( download)

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Download or read book Sophie’s Diary written by Dora Musielak and published by American Mathematical Society. This book was released on 2022-08-11 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sophie Germain overcame gender stigmas and a lack of formal education to prove that for all prime exponents less than 100 Case I of Fermat's Last Theorem holds. Hidden behind a man's name, her brilliance as mathematician was first discovered by three of the greatest scholars of the eighteenth century, Lagrange, Gauss, and Legendre. In Sophie's Diary, Germain comes to life through a fictionalized journal that intertwines mathematics with historical descriptions of the brutal events that took place in Paris between 1789 and 1793. This format provides a plausible perspective of how a young Sophie could have learned mathematics on her own—both fascinated by numbers and eager to master tough subjects without a teacher's guidance. Her passion for mathematics is integrated into her personal life as an escape from societal outrage. Sophie's Diary is suitable for a variety of readers—both young and old, mathematicians and novices—who will be inspired and enlightened on a field of study made easy, as told through the intellectual and personal struggles of an exceptional young woman.

Author : Reinhard Laubenbacher
Publisher : Springer Science & Business Media
ISBN 13 : 1461205239
Total Pages : 288 pages
Book Rating : 4.34/5 ( download)

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Download or read book Mathematical Expeditions written by Reinhard Laubenbacher and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve -- or attempt to solve -- a great problem, this book helps readers discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.

Author : Peter Gustav Lejeune Dirichlet
Publisher : American Mathematical Soc.
ISBN 13 : 0821820176
Total Pages : 297 pages
Book Rating : 4.79/5 ( download)

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Download or read book Lectures on Number Theory written by Peter Gustav Lejeune Dirichlet and published by American Mathematical Soc.. This book was released on 1999 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.