Undergraduate Texts in Mathematics

Geometry: from Isometries to Special Relativity

Autoren: Lee, Nam-Hoon

Vorschau
  • 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
Weitere Vorteile

Dieses Buch kaufen

eBook 18,18 €
36,99 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
  • ISBN 978-3-030-42101-4
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: EPUB, PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 24,60 €
48,14 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Softcover 24,60 €
48,14 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Über dieses Lehrbuch

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 die Autor*innen

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.

Inhaltsverzeichnis (6 Kapitel)

Inhaltsverzeichnis (6 Kapitel)
  • Euclidean Plane

    Seiten 1-22

    Lee, Nam-Hoon

  • Sphere

    Seiten 23-45

    Lee, Nam-Hoon

  • Stereographic Projection and Inversions

    Seiten 47-85

    Lee, Nam-Hoon

  • Hyperbolic Plane

    Seiten 87-127

    Lee, Nam-Hoon

  • Lorentz–Minkowski Plane

    Seiten 129-182

    Lee, Nam-Hoon

Dieses Buch kaufen

eBook 18,18 €
36,99 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
  • ISBN 978-3-030-42101-4
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: EPUB, PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 24,60 €
48,14 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Softcover 24,60 €
48,14 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
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Bibliografische Information

Bibliographic Information
Buchtitel
Geometry: from Isometries to Special Relativity
Autoren
Titel der Buchreihe
Undergraduate Texts in Mathematics
Copyright
2020
Verlag
Springer International Publishing
Copyright Inhaber
Springer Nature Switzerland AG
eBook ISBN
978-3-030-42101-4
DOI
10.1007/978-3-030-42101-4
Hardcover ISBN
978-3-030-42100-7
Softcover ISBN
978-3-030-42103-8
Buchreihen ISSN
0172-6056
Auflage
1
Seitenzahl
XIII, 258
Anzahl der Bilder
74 schwarz-weiß Abbildungen, 18 Abbildungen in Farbe
Themen