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Published by American Mathematical Society, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
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Published by American Mathematical Society, US, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
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Hardback. Condition: New. 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.
Published by Amer Mathematical Society, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
Seller: Revaluation Books, Exeter, United Kingdom
Hardcover. Condition: Brand New. 268 pages. 8.50x5.50x0.75 inches. In Stock.
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Published by American Mathematical Society, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
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Published by American Mathematical Society, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
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Add to basketCondition: New. pp. 392 2nd Edition.
Published by American Mathematical Society, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
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Published by American Mathematical Society, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
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Add to basketCondition: New. 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.
Published by American Mathematical Society, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
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Published by American Mathematical Society, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
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Add to basketHardcover. Condition: very good. Used items may not include media like access codes or CDs. Fast shipping! Expedited orders take 1-3 business days! Media mail may take up to 5 business days.
Published by American Mathematical Society, US, 2018
ISBN 10: 147044383X ISBN 13: 9781470443832
Language: English
Seller: Rarewaves.com USA, London, LONDO, United Kingdom
Hardback. Condition: New. 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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Add to basketCondition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. New to the second edition:A useful appendix of formal definitions that can be used as a quick referenceSecond edition includes new exercises, problems, and student projectsAn electronic solutions manual for instructors and individual.
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Add to basketGebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. New to the second edition:A useful appendix of formal definitions that can be used as a quick referenceSecond edition includes new exercises, problems, and student projectsAn electronic solutions manual for instructors and individual.
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Condition: New. Print on Demand pp. 392 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam.
Seller: Majestic Books, Hounslow, United Kingdom
Condition: New. Print on Demand pp. 392 Illus.