Previous edition sold 2000 copies in 3 years; Explores the subtle connectionsbetween Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitateunderstanding: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems INDICE: * "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 Transcendential? * Complex Arithmetic *Quadratic, Cubic, and Quartic Equations * Stereographic Projection * Proof ofthe Fundamental Theorem of Algebra * Symmetries of Regular Polygons * Discrete Subgroups of Iso(R^2) * 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-Poincare Characteristic * Detour in Graph Theory: Euler, Hamilton and the Four Color Theorem * Dimension Leap * Quaternions * Back to R^3! * Invariants * The Icosahedron and the Unsolvable Quintic * The Fourth Dimension * Appendices * Solutions for 100 Selected Problems * Index
- ISBN: 978-1-4419-2962-4
- Editorial: Springer
- Encuadernacion: Rústica
- Fecha Publicación: 31/03/2012
- Nº Volúmenes: 1
- Idioma: Inglés
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