By Siavash Shahshahani
Based on writer Siavash Shahshahani's large instructing event, this quantity offers a radical, rigorous path at the conception of differentiable manifolds. aimed toward complicated undergraduates and graduate scholars in arithmetic, the treatment's must haves comprise a robust historical past in undergraduate arithmetic, together with multivariable calculus, linear algebra, user-friendly summary algebra, and element set topology. greater than 2 hundred workouts supply scholars plentiful chance to gauge their abilities and achieve extra insights.
The four-part therapy starts off with a unmarried bankruptcy dedicated to the tensor algebra of linear areas and their mappings. half II brings in neighboring issues to discover integrating vector fields, Lie bracket, external by-product, and Lie by-product. half III, regarding manifolds and vector bundles, develops the most physique of the direction. the ultimate bankruptcy offers a glimpse into geometric constructions by means of introducing connections on the tangent package as a device to implant the second one by-product and the by-product of vector fields at the base manifold. appropriate ancient and philosophical asides improve the mathematical textual content, and important Appendixes provide supplementary material.
Read Online or Download An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals) PDF
Best geometry & topology books
This can be the second one variation of this most sensible promoting challenge ebook for college kids, now containing over four hundred thoroughly solved routines on differentiable manifolds, Lie concept, fibre bundles and Riemannian manifolds. The routines move from basic computations to relatively refined instruments. the various definitions and theorems used all through are defined within the first part of each one bankruptcy the place they seem.
One of many first college-level texts for undemanding classes in non-Euclidean geometry, this quantity is aimed toward scholars acquainted with calculus. subject matters comprise the 5th postulate, hyperbolic airplane geometry and trigonometry, and elliptic airplane geometry and trigonometry. broad appendixes supply history info, and various workouts seem during the textual content.
Focusing methodologically on these old features which are correct to aiding instinct in axiomatic methods to geometry, the booklet develops systematic and smooth techniques to the 3 center features of axiomatic geometry: Euclidean, non-Euclidean and projective. traditionally, axiomatic geometry marks the foundation of formalized mathematical job.
Leonid Ryvkin supplies a prompted and self-sustainedintroduction to n-plectic geometry with a unique concentrate on symmetries. Therelevant algebraic constructions from scratch are constructed. the writer generalizesknown symplectic notions, particularly observables and symmetries, to the n-plecticcase, culminating in fixing the life query for co-moment maps forgeneral pre-n-plectic manifolds.
Extra info for An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals)
An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals) by Siavash Shahshahani