Finding Ellipses – What Blaschke Products, Poncelet`s Theorem, and the Numerical Range Know about Each Other by Daepp, Ulrich; Gorkin, Pamela; Shaffer, Andrew;

What Blaschke Products, Poncelet's Theorem, and the Numerical Range Know About Each Other

Sorozatcím: Carus Mathematical Monographs;

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A termék adatai:

Kiadó MP–AMM American Mathematical
Megjelenés dátuma 2018. október 30.
Kötetek száma Hardback

ISBN 9781470443832
Kötéstípus Keménykötés
Terjedelem264 oldal
Méret 216x140x19 mm
Súly 488 g
Nyelv angol

Kategóriák

Analízis

Rövid leírás:

Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.

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Hosszú leírás:

Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections--consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.

The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem--a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a $2 \times 2$ matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of $n \times n$ matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products.

The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project.

You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.

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Mostanában megtekintett

Finding Ellipses – What Blaschke Products, Poncelet`s Theorem, and the Numerical Range Know about Each Other: What Blaschke Products, Poncelet's Theorem, and the Numerical Range Know About Each Other

Daepp, Ulrich; Gorkin, Pamela; Shaffer, Andrew;

30 576 Ft

27 518 Ft

20% %kedvezmény