Linear fractional transformations : an illustrated introduction / Arseniy Sheydvasser.

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Linear fractional transformations : an illustrated introduction / Arseniy Sheydvasser.

9783031250026 (electronic bk.)
3031250028 (electronic bk.)
303125001X
9783031250019

Cham, Switzerland : Springer, 2023.

English

1 online resource (230 pages) : illustrations (black and white, and color).

10.1007/978-3-031-25002-6 doi

QA601

516/.1

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.

Includes bibliographical references and index.

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Description based on print version record.

Undergraduate texts in mathematics.

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