Math Girls 6: The Poincar

This sixth entry in the highly acclaimed Math Girls series focuses on the Poincaré 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 Königsberg problem that Leonhard Euler investigated in 1736. After that you will learn about interesting objects like the Möbius 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 Poincaré Conjecture. Math Girls 6: The Poincaré Conjecture has something for anyone interested in mathematics, from advanced high school to college students and educators.