Topology of Singular Fibers of Differentiable Maps by Osamu Saeki

By Osamu Saeki

The quantity develops a radical concept of singular fibers of time-honored differentiable maps. this can be the 1st paintings that establishes the foundational framework of the worldwide learn of singular differentiable maps of unfavourable codimension from the point of view of differential topology. The ebook comprises not just a normal thought, but additionally a few particular examples including a few very concrete functions.

This is a truly fascinating topic in differential topology, because it indicates a gorgeous interaction among the standard idea of singularities of differentiable maps and the geometric topology of manifolds.

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A Course in Point Set Topology by John B. Conway

By John B. Conway

This textbook in aspect set topology is geared toward an upper-undergraduate viewers. Its mild speed could be worthwhile to scholars who're nonetheless studying to write down proofs. necessities contain calculus and no less than one semester of research, the place the scholar has been correctly uncovered to the guidelines of easy set idea similar to subsets, unions, intersections, and services, in addition to convergence and different topological notions within the actual line. Appendices are integrated to bridge the space among this new fabric and fabric present in an research path. Metric areas are one of many extra wide-spread topological areas utilized in different components and are accordingly brought within the first bankruptcy and emphasised through the textual content. This additionally conforms to the method of the ebook to begin with the actual and paintings towards the extra basic. bankruptcy 2 defines and develops summary topological areas, with metric areas because the resource of proposal, and with a spotlight on Hausdorff areas. the ultimate bankruptcy concentrates on non-stop real-valued features, culminating in a improvement of paracompact spaces.

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Perfect Rigor: A Genius and the Mathematical Breakthrough of by Masha Gessen

By Masha Gessen

A gripping and tragic story that sheds infrequent mild at the certain burden of genius
 
In 2006, an eccentric Russian mathematician named Grigori Perelman solved the Poincare Conjecture, a very advanced topological challenge that had eluded the simplest minds for over a century. A prize of 1 million cash was once provided to somebody who may possibly get to the bottom of it, yet Perelman declined the winnings, and in doing so encouraged journalist Masha Gessen to inform his tale. Drawing on interviews with Perelman’s academics, classmates, coaches, teammates, and co-workers in Russia and the United States—and knowledgeable through her personal heritage as a math whiz raised in Russia—Gessen exposed a brain of unmatched computational energy, one who enabled Perelman to pursue mathematical recommendations to their logical (sometimes far-off) finish. yet she additionally chanced on that this very energy grew to become out to be Perelman's undoing and the cause of his withdrawal, first from the realm of arithmetic after which, more and more, from the area generally.

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