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＜電子ブック＞
Linear Fractional Transformations : An Illustrated Introduction / by Arseniy Sheydvasser
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	1st ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XV, 231 p. 106 illus., 96 illus. in color : online resource
著者標目	*Sheydvasser, Arseniy author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Geometry, Differential LCSH:Group theory FREE:Geometry FREE:Differential Geometry FREE:Group Theory and Generalizations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-031-25002-6

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