"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) |
Mobius 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 Mobius 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 |
"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 |