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Linear fractional transformations = ...

Sheydvasser, Arseniy.

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Linear fractional transformations = an illustrated introduction /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Linear fractional transformations/ by Arseniy Sheydvasser.
其他題名:	an illustrated introduction /
作者:	Sheydvasser, Arseniy.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xv, 231 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Transformations (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-031-25002-6
ISBN:	9783031250026

Linear fractional transformations = an illustrated introduction /
Sheydvasser, Arseniy.

Linear fractional transformationsan illustrated introduction /[electronic resource] :by Arseniy Sheydvasser. - Cham :Springer International Publishing :2023. - xv, 231 p. :ill., digital ;24 cm. - Undergraduate texts in mathematics,2197-5604. - Undergraduate texts in mathematics..

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.

ISBN: 9783031250026

Standard No.: 10.1007/978-3-031-25002-6doiSubjects--Topical Terms:

544232
Transformations (Mathematics)

LC Class. No.: QA601 / .S54 2023

Dewey Class. No.: 516.1

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520 $a 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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