Glimpses of Algebra and Geometry

Softcover Nachdruck of the original 2. Auflage 2002
ISBN: 978-1-4419-2962-4
Verlag: Springer

Buch, Englisch, 450 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 895 g

Reihe: Undergraduate Texts in Mathematics

Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Toth, Gabor

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

“A Number Is a Multitude Composed of Units”—Euclid.- “. There Are No Irrational Numbers at All”—Kronecker.- Rationality, Elliptic Curves, and Fermat’s Last Theorem.- Algebraic or Transcendental?.- Complex Arithmetic.- Quadratic, Cubic, and Quartic Equations.- Stereographic Projection.- Proof of the Fundamental Theorem of Algebra.- Symmetries of Regular Polygons.- Discrete Subgroups of Iso (R2).- Möbius Geometry.- Complex Linear Fractional Transformations.- “Out of Nothing I Have Created a New Universe”—Bolyai.- Fuchsian Groups.- Riemann Surfaces.- General Surfaces.- The Five Platonic Solids.- Finite Möbius Groups.- Detour in Topology: Euler-Poincaré Characteristic.- Detour in Graph Theory: Euler, Hamilton, and the Four Color Theorem.- Dimension Leap.- Quaternions.- Back to R3!.- Invariants.- The Icosahedron and the Unsolvable Quintic.- The Fourth Dimension.