Glimpses of Algebra and Geometry

* '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) * 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