Geometry: from Isometries to Special Relat...

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Beschreibung

This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein¿s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz¿Minkowski plane, building an understanding of how geometry can be used to model special relativity.

Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz¿Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided.

Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.

Über den Autor

Nam-Hoon Lee received his Ph.D. in mathematics from the University of Michigan in Ann Arbor after studying physics at Seoul National University as an undergraduate. His research interests include algebraic geometry, differential geometry, and the theory of relativity. He is now Professor of Mathematics Education at Hongik University in Seoul, South Korea.

Zusammenfassung

Explores Euclidean and non-Euclidean geometries, culminating in a mathematical model for special relativity

Introduces students familiar with calculus to the rigorous foundations of plane geometry: Euclidean, spherical, hyperbolic, and relativistic

Offers a pathway from classical to abstract geometries by focusing on isometries

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Inhaltsverzeichnis

Euclidean Plane.- Sphere.- Stereographic Projection and Inversions.- Hyperbolic Plane.- Lorentz-Minkowski Plane.- Geometry of Special Relativity.- Answers to Selected Exercises.- Index.

Details

Erscheinungsjahr:	2020
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xiii 258 S. 74 s/w Illustr. 18 farbige Illustr. 258 p. 92 illus. 18 illus. in color.
ISBN-13:	9783030421007
ISBN-10:	3030421007
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Lee, Nam-Hoon
Auflage:	1st ed. 2020
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG Undergraduate Texts in Mathematics
Maße:	241 x 160 x 20 mm
Von/Mit:	Nam-Hoon Lee
Erscheinungsdatum:	29.04.2020
Gewicht:	0,626 kg

Artikel-ID: 117963925