Optimization Algorithms on Matrix Manifolds
by P.-A. Absil, R. Mahony, R. Sepulchre
Publisher: Princeton University Press 2007
Number of pages: 240
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis.
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by Ville Turunen - Aalto TKK
In this book you will learn something about functional analytic framework of topology. And you will get an access to more advanced literature on non-commutative geometry, a quite recent topic in mathematics and mathematical physics.
by Reyer Sjamaar - Cornell University
The text covers manifolds and differential forms for an audience of undergraduates who have taken a typical calculus sequence, including basic linear algebra and multivariable calculus up to the integral theorems of Green, Gauss and Stokes.
by Andrew Ranicki - Princeton University Press
One of the principal aims of surgery theory is to classify the homotopy types of manifolds using tools from algebra and topology. The algebraic approach is emphasized in this book, and it gives the reader a good overview of the subject.
by Curtis T. McMullen - Harvard University
Contents: Introduction; Background in set theory; Topology; Connected spaces; Compact spaces; Metric spaces; Normal spaces; Algebraic topology and homotopy theory; Categories and paths; Path lifting and covering spaces; Global topology; etc.