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Linear Fractional Transformations

E-BookPDF1 - PDF WatermarkE-Book
231 Seiten
Englisch
Springer International Publishingerschienen am15.04.20231st ed. 2023
The principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning.
This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.
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E-BookPDF1 - PDF WatermarkE-Book
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Produkt

KlappentextThe principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning.
This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.
Details
Weitere ISBN/GTIN9783031250026
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2023
Erscheinungsdatum15.04.2023
Auflage1st ed. 2023
Seiten231 Seiten
SpracheEnglisch
IllustrationenXV, 231 p. 106 illus., 96 illus. in color.
Artikel-Nr.10466721
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
Motivation.- I Euclidean and Inversive Geometry.- Euclidean Isometries and Similarities.- Inversive Geometry.- Applications of Inversive Geometry.- II Non-Euclidean Geometry.- Spherical Geometry.- Appendix: Set Theory.mehr

Autor

Arseniy (Senia) Sheydvasser is a postdoctoral researcher in the department of mathematics at the Technion. His interests include algebraic number theory, additive number theory, and logic.
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Sheydvasser, Arseniy