Linear fractional transformations : an illustrated introduction / Arseniy Sheydvasser.

Format:

Book

Author/Creator:

Sheydvasser, Arseniy, author.

Series:

Undergraduate Texts in Mathematics, 2197-5604

Language:

English

Subjects (All):

Transformations (Mathematics).

Physical Description:

1 online resource (242 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham, Switzerland : Springer, [2023]

Summary:

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.

Contents:

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.

Notes:

Description based on print version record.

Includes bibliographical references and index.

Other Format:

Print version: Sheydvasser, Arseniy Linear Fractional Transformations

ISBN:

9783031250026

OCLC:

1376454184