By Andrew McInerney
Differential geometry arguably bargains the smoothest transition from the normal collage arithmetic series of the 1st 4 semesters in calculus, linear algebra, and differential equations to the better degrees of abstraction and evidence encountered on the higher department by way of arithmetic majors. this present day it truly is attainable to explain differential geometry as "the examine of constructions at the tangent space," and this article develops this aspect of view.
This publication, in contrast to different introductory texts in differential geometry, develops the structure essential to introduce symplectic and phone geometry along its Riemannian cousin. the most target of this ebook is to deliver the undergraduate pupil who already has a superb starting place within the typical arithmetic curriculum into touch with the great thing about better arithmetic. particularly, the presentation right here emphasizes the implications of a definition and the cautious use of examples and structures with a view to discover these outcomes.