Description
Springer Glimpses Of Algebra And Geometry 2002 Edition by Gabor Toth
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 Table of contents : * '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 of the Fundamental Theorem of Algebra * Symmetries of Regular Polygons * Discrete Subgroups of Iso(R^2) * Moebius 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 Moebius 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