Math Girls 6 - Hiroshi Yuki

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Résumé :
This sixth entry in the highly acclaimed Math Girls series focuses on the Poincar? Conjecture, a fundamental problem in topology first proposed in 1904. While the problem is simply stated and easily understood, it resisted proof throughout the twentieth century. Russian mathematician Grigori Perelman finally completed that effort, publishing a series of papers in 2002 that provided missing details for an argument that includes a solution. In this book, you will join Miruka and friends as they learn about topology from its very beginnings: the Seven Bridges of K?nigsberg problem that Leonhard Euler investigated in 1736. After that you will learn about interesting objects like the M?bius strip and the Klein bottle, topological spaces and continuous mappings, homeomophism and homotopy, and non-Euclidean geometries. Along the way, you will also learn about differential equations, Fourier series, the heat equation, and a trigonometric training regimen. The book concludes with an introduction to Hamilton's Ricci flow, a crucial tool in Perelman's work on the Poincar? Conjecture. Math Girls 6: The Poincar? Conjecture has something for anyone interested in mathematics, from advanced high school to college students and educators....

Biographie:
Best-selling author Hiroshi Yuki has written over thirty books on mathematics, programming, and cryptography in Japan. His English-translated works include the Math Girls and Math Girls Talk About... series. He lives in Tokyo.

Sommaire:
This sixth entry in the highly acclaimed Math Girls series focuses on the Poincar? Conjecture, a fundamental problem in topology first proposed in 1904. While the problem is simply stated and easily understood, it resisted proof throughout the twentieth century. Russian mathematician Grigori Perelman finally completed that effort, publishing a series of papers in 2002 that provided missing details for an argument that includes a solution. In this book, you will join Miruka and friends as they learn about topology from its very beginnings: the Seven Bridges of K?nigsberg problem that Leonhard Euler investigated in 1736. After that you will learn about interesting objects like the M?bius strip and the Klein bottle, topological spaces and continuous mappings, homeomophism and homotopy, and non-Euclidean geometries. Along the way, you will also learn about differential equations, Fourier series, the heat equation, and a trigonometric training regimen. The book concludes with an introduction to Hamilton's Ricci flow, a crucial tool in Perelman's work on the Poincar? Conjecture. Math Girls 6: The Poincar? Conjecture has something for anyone interested in mathematics, from advanced high school to college students and educators....