Linear Fractional Transformations
An Illustrated Introduction
Springer International Publishing
ISBN 978-3-031-25002-6
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Bibliografische Daten
eBook. PDF
2023
XV, 231 p. 106 illus., 96 illus. in color..
In englischer Sprache
Umfang: 231 S.
Verlag: Springer International Publishing
ISBN: 978-3-031-25002-6
Weiterführende bibliografische Daten
Das Werk ist Teil der Reihe: Undergraduate Texts in Mathematics
Produktbeschreibung
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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