Glimpses of algebra and geometry/
Toth, Gabor
Glimpses of algebra and geometry/ Gabor Toth - 2nd ed. - New York: Springer, c2002. - xxii, 450 p. : ill. ; 25 cm. - (Undergraduate texts in mathematics) .
1. "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.
0387953450
Geometry
Algebra
512.12 / GAB/G
Glimpses of algebra and geometry/ Gabor Toth - 2nd ed. - New York: Springer, c2002. - xxii, 450 p. : ill. ; 25 cm. - (Undergraduate texts in mathematics) .
1. "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.
0387953450
Geometry
Algebra
512.12 / GAB/G