Linear Fractional Transformations | Buch

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Cover: 9783031250019 | Linear Fractional Transformations | An Illustrated Introduction | Buch

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Sprache: Englisch

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Beschreibung

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.

Über den 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.

Zusammenfassung

Highly visual and beautifully illustrated

Exercises are organized into sections pertaining to various topics

Assumed little mathematical knowledge

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.

Details

Erscheinungsjahr:	2023
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	248
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xv 231 S. 10 s/w Illustr. 96 farbige Illustr. 231 p. 106 illus. 96 illus. in color.
ISBN-13:	9783031250019
ISBN-10:	303125001X
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Sheydvasser, Arseniy
Auflage:	2023
Hersteller:	Springer International Publishing Undergraduate Texts in Mathematics
Maße:	241 x 160 x 19 mm
Von/Mit:	Arseniy Sheydvasser
Erscheinungsdatum:	17.04.2023
Gewicht:	0,586 kg

preigu-id: 126063210