000			00388nam a2200145Ia 4500
999			_c170406 _d170406
020			_a0387953450
040			_cCUS
082			_a512.12 _bGAB/G
100			_aToth, Gabor
245		0	_aGlimpses of algebra and geometry/ _cGabor Toth
250			_a2nd ed.
260			_aNew York: _bSpringer, _cc2002.
300			_axxii, 450 p. : _bill. ; _c25 cm.
440			_a(Undergraduate texts in mathematics)
505			_a1. "A number is a multitude composed of units"-Euclid -- 2." ... There are no irrational numbers at all"-Kronecker -- 3. Rationality, elliptic curves, and Fermat's last theorem -- 4. Algebraic or transcendental? -- 5. Complex arithmetic -- 6. Quadratic, cubic, and quantic equations -- 7. Stereographic projection -- 8. Proof of the fundamental theorem of algebra -- 9. Symmetries of regular polygons -- 10. Discrete subgroups of Iso (R²) -- 11. Möbius geometry -- 12. Complex linear fractional transformations -- 13. "Out of nothing I have created a new universe"-Bolyai -- 14. Fuchsian groups -- 15. Riemann surfaces -- 16. General surfaces -- 17. The five platonic solids -- 18. Finite Möbius groups -- 19. Detour in topology: Euler-Poincaré characteristic -- 20. Detour in graph theory: Euler, Hamilton, and the four color theorem -- 21. Dimension leap -- 22. Quaternions -- 23. Back to R³! -- 24. Invariants -- 25. The Icosahedron and the unsolvable quintic -- 26. The fourth dimension -- Appendixes: -- A. Sets -- B. Groups -- C. Topology -- D. Smooth maps -- E. The hypergeometric differential equation and the Schwarzian -- F. Galois theory.
650			_aGeometry
650			_aAlgebra
942			_cWB16