This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincar Conjecture. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.
發表於2024-11-25
Three-Dimensional Geometry and Topology, Vol. 1 2024 pdf epub mobi 電子書 下載
圖書標籤: 拓撲 數學 幾何 Thurston geometry 低維 美國 topology
大二的時候泛泛讀的,天纔的著作,富有激情與創造力。裏麵的很多問題,通過純粹想象而不是邏輯推導的方式去思考很有意思。每次跟美術學院的老哥們吹牛逼的時候,材料大都從這裏來
評分大二的時候泛泛讀的,天纔的著作,富有激情與創造力。裏麵的很多問題,通過純粹想象而不是邏輯推導的方式去思考很有意思。每次跟美術學院的老哥們吹牛逼的時候,材料大都從這裏來
評分大二的時候泛泛讀的,天纔的著作,富有激情與創造力。裏麵的很多問題,通過純粹想象而不是邏輯推導的方式去思考很有意思。每次跟美術學院的老哥們吹牛逼的時候,材料大都從這裏來
評分大二的時候泛泛讀的,天纔的著作,富有激情與創造力。裏麵的很多問題,通過純粹想象而不是邏輯推導的方式去思考很有意思。每次跟美術學院的老哥們吹牛逼的時候,材料大都從這裏來
評分大二的時候泛泛讀的,天纔的著作,富有激情與創造力。裏麵的很多問題,通過純粹想象而不是邏輯推導的方式去思考很有意思。每次跟美術學院的老哥們吹牛逼的時候,材料大都從這裏來
Three-Dimensional Geometry and Topology, Vol. 1 2024 pdf epub mobi 電子書 下載