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MathematicalMiniatures(AnneliLaxNewMathematicalLibrary)

MathematicalMiniatures(AnneliLaxNewMathematicalLibrary)

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作者: Svetoslav Savchev 著 , Titu Andreescu 著

出版社: TheMathematicalAssociationofAmerica

出版时间: 2002-11

ISBN: 9780883856451

定价: 286.50

装帧: 平装

页数: 230页

正文语种: 英语

分类: 外文古旧书>英文书>自然科学

Differential geometry has developed in many directions since its beginnings with Euler and Gauss. This often poses a problem for undergraduates: which direction should be followed? What do these ideas have to do with geometry? This book is designed to make differential geometry an approachable subject for advanced undergraduates. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of the non-Euclidean plane. The book begins with the theorems of non-Euclidean geometry, then introduces the methods of differential geometry and develops them towards the goal of constructing models of the hyperbolic plane. Interesting diversions are offered, such as Huygens' pendulum clock and mathematical cartography; however, the focus of the book is on the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds. Although the main use of this text is as an advanced undergraduate course book, the historical aspect of the text should appeal to most mathematicians. Svetoslav Savchev was born in Gabrovo, Bulgaria, and graduated from Sofia University in 1980. He has worked for the journal "Mathematika" since 1981, and is currently vice editor-in-chief. He is the author of several books, and has been engaged in diverse activities for gifted students. Titu Andreescu is the Director of the American Mathematics Competition, a program of the Mathematical Association of America (MAA). He also serves as Chair of the USA Mathematical Olympiad committee, Head Coach of the the USA International Mathematical Olympiad Team, and Director of the Mathematical Olympiad Summer Program.
内容简介:
Differential geometry has developed in many directions since its beginnings with Euler and Gauss. This often poses a problem for undergraduates: which direction should be followed? What do these ideas have to do with geometry? This book is designed to make differential geometry an approachable subject for advanced undergraduates. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of the non-Euclidean plane. The book begins with the theorems of non-Euclidean geometry, then introduces the methods of differential geometry and develops them towards the goal of constructing models of the hyperbolic plane. Interesting diversions are offered, such as Huygens' pendulum clock and mathematical cartography; however, the focus of the book is on the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds. Although the main use of this text is as an advanced undergraduate course book, the historical aspect of the text should appeal to most mathematicians.
作者简介:
Svetoslav Savchev was born in Gabrovo, Bulgaria, and graduated from Sofia University in 1980. He has worked for the journal "Mathematika" since 1981, and is currently vice editor-in-chief. He is the author of several books, and has been engaged in diverse activities for gifted students. Titu Andreescu is the Director of the American Mathematics Competition, a program of the Mathematical Association of America (MAA). He also serves as Chair of the USA Mathematical Olympiad committee, Head Coach of the the USA International Mathematical Olympiad Team, and Director of the Mathematical Olympiad Summer Program.

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