LEADER 03006nam 2200517 450 001 9910698649203321 005 20240130141652.0 010 $a9783031250026$b(electronic bk.) 010 $z9783031250019 024 7 $a10.1007/978-3-031-25002-6 035 $a(MiAaPQ)EBC7237593 035 $a(Au-PeEL)EBL7237593 035 $a(DE-He213)978-3-031-25002-6 035 $a(OCoLC)1376454184 035 $a(PPN)269655700 035 $a(EXLCZ)9926455994700041 100 $a20230619d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLinear fractional transformations $ean illustrated introduction /$fArseniy Sheydvasser 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer,$d[2023] 210 4$dŠ2023 215 $a1 online resource (242 pages) 225 1 $aUndergraduate Texts in Mathematics,$x2197-5604 311 08$aPrint version: Sheydvasser, Arseniy Linear Fractional Transformations Cham : Springer International Publishing AG,c2023 9783031250019 320 $aIncludes bibliographical references and index. 327 $aMotivation -- I Euclidean and Inversive Geometry -- Euclidean Isometries and Similarities -- Inversive Geometry -- Applications of Inversive Geometry -- II Non-Euclidean Geometry -- Spherical Geometry -- Appendix: Set Theory. 330 $aThe principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning. This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment. 410 0$aUndergraduate Texts in Mathematics,$x2197-5604 606 $aTransformations (Mathematics) 606 $aTransformacions (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aTransformations (Mathematics) 615 7$aTransformacions (Matemātica) 676 $a516.1 700 $aSheydvasser$b Arseniy$01352757 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910698649203321 996 $aLinear Fractional Transformations$93200521 997 $aUNINA