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Author: David Pengelley Publisher: American Mathematical Society ISBN: 1470472201 Category : Mathematics Languages : en Pages : 216
Book Description
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 We have only recently completely understood this work from her unpublished letters and manuscripts.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Germainis simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primary-source historical documents, an inquiry-based textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician.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: David Pengelley Publisher: American Mathematical Society ISBN: 1470472201 Category : Mathematics Languages : en Pages : 216
Book Description
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: Cheryl Bardoe Publisher: Little, Brown Books for Young Readers ISBN: 0316394297 Category : Juvenile Nonfiction Languages : en Pages : 40
Book Description
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: Dora E. Musielak Publisher: ISBN: 9781496965028 Category : Biography & Autobiography Languages : en Pages : 294
Book Description
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: 0429779879 Category : Mathematics Languages : en Pages : 394
Book Description
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: Reinhard Laubenbacher Publisher: Springer Science & Business Media ISBN: 1461205239 Category : Mathematics Languages : en Pages : 288
Book Description
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: Kendall Haven Publisher: Bloomsbury Publishing USA ISBN: 0313090009 Category : Language Arts & Disciplines Languages : en Pages : 261
Book Description
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: L.L. Bucciarelli Publisher: Springer Science & Business Media ISBN: 9400990510 Category : History Languages : en Pages : 157
Book Description
Why should the story of a woman's role in the development of a scientific theory be written? Is it to celebrate, as some have done, the heroism of a woman's struggle in a man's world? Or is it, rather~to demonstrate that gender is irrelevant to the march of scientific ideas? This book hopes to do neither. Rather, it intends to do justice both to the professional life of a woman in science and to the development of the theory with which she was engaged. Technically, this essay centers on Sophie Germain's analysis of the modes of vibration of elastic surfaces, work which won a competition set by the French Academy of Sciences in 1809. It also evaluates related work on the mathematical theory of elasticity done by men of the Academy. Biographically, it is about a woman who believed in the greatness of science and strove, with some measure of success, to participate in that noble, but wholly male-dominated, enterprise. It explores her failures, analyzes her success, and describes how the members of the Parisian scientific community dealt with her offerings, contributions and demands.
Author: James J. Tattersall Publisher: Cambridge University Press ISBN: 9780521585316 Category : Mathematics Languages : en Pages : 420
Book Description
This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.
Author: Dora Musielak Publisher: American Mathematical Society ISBN: 1470471566 Category : Mathematics Languages : en Pages : 293
Book Description
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: David Pengelley
Author: David Pengelley
Author: Cheryl Bardoe
Author: Dora E. Musielak
Author: Jeffrey Stopple
Author: Karin R Saoub
Author: Reinhard Laubenbacher
Author: Kendall Haven
Author: L.L. Bucciarelli
Author: James J. Tattersall
Author: Dora Musielak