Geometry from a Differentiable Viewpoint

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book Geometry from a Differentiable Viewpoint by John McCleary, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: John McCleary ISBN: 9781139793018
Publisher: Cambridge University Press Publication: October 22, 2012
Imprint: Cambridge University Press Language: English
Author: John McCleary
ISBN: 9781139793018
Publisher: Cambridge University Press
Publication: October 22, 2012
Imprint: Cambridge University Press
Language: English

The development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss and Riemann is a story that is often broken into parts – axiomatic geometry, non-Euclidean geometry and differential geometry. This poses a problem for undergraduates: Which part is geometry? What is the big picture to which these parts belong? In this introduction to differential geometry, the parts are united with all of their interrelations, motivated by the history of the parallel postulate. Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as space-time. The presentation is enlivened by historical diversions such as Huygens's clock and the mathematics of cartography. The intertwined approaches will help undergraduates understand the role of elementary ideas in the more general, differential setting. This thoroughly revised second edition includes numerous new exercises and a new solution key. New topics include Clairaut's relation for geodesics and the use of transformations such as the reflections of the Beltrami disk.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

The development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss and Riemann is a story that is often broken into parts – axiomatic geometry, non-Euclidean geometry and differential geometry. This poses a problem for undergraduates: Which part is geometry? What is the big picture to which these parts belong? In this introduction to differential geometry, the parts are united with all of their interrelations, motivated by the history of the parallel postulate. Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as space-time. The presentation is enlivened by historical diversions such as Huygens's clock and the mathematics of cartography. The intertwined approaches will help undergraduates understand the role of elementary ideas in the more general, differential setting. This thoroughly revised second edition includes numerous new exercises and a new solution key. New topics include Clairaut's relation for geodesics and the use of transformations such as the reflections of the Beltrami disk.

More books from Cambridge University Press

Cover of the book Commentary on the Second Geneva Convention by John McCleary
Cover of the book Global Justice, Christology and Christian Ethics by John McCleary
Cover of the book Solidarity in Biomedicine and Beyond by John McCleary
Cover of the book Diagnostic Ultrasound by John McCleary
Cover of the book Principles of Igneous and Metamorphic Petrology by John McCleary
Cover of the book Understanding and Avoiding the Oil Curse in Resource-rich Arab Economies by John McCleary
Cover of the book Artists and Artistic Production in Ancient Greece by John McCleary
Cover of the book Roman Power by John McCleary
Cover of the book Geofuels by John McCleary
Cover of the book Putting Faith in Hate by John McCleary
Cover of the book Witchcraft and Inquisition in Early Modern Venice by John McCleary
Cover of the book The Art and Thought of Heraclitus by John McCleary
Cover of the book English in the Caribbean by John McCleary
Cover of the book Transparency in International Law by John McCleary
Cover of the book Regime Interaction in International Law by John McCleary
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy