Glimpses of algebra and geometry
By: Gábor Tóth
Edition: 2nd ed.
Series: Undergraduate texts in mathematics
Publisher: Springer
Published: 2011
Place of publication: New York; London
Language: eng
ISBN-13: 9781441929624
Subjects: Geometry; Algebra
Notes: This ed. originally published: 2002.
Table of contents: title: 1. "A number is a multitude composed of units"-Euclid; title: 2." ... There are no irrational numbers at all"-Kronecker; title: 3. Rationality, elliptic curves, and Fermat's last theorem; title: 4. Algebraic or transcendental?; title: 5. Complex arithmetic; title: 6. Quadratic, cubic, and quantic equations; title: 7. Stereographic projection; title: 8. Proof of the fundamental theorem of algebra; title: 9. Symmetries of regular polygons; title: 10. Discrete subgroups of Iso (R²); title: 11. Möbius geometry; title: 12. Complex linear fractional transformations; title: 13. "Out of nothing I have created a new universe"-Bolyai; title: 14. Fuchsian groups; title: 15. Riemann surfaces; title: 16. General surfaces; title: 17. The five platonic solids; title: 18. Finite Möbius groups; title: 19. Detour in topology: Euler-Poincaré characteristic; title: 20. Detour in graph theory: Euler, Hamilton, and the four color theorem; title: 21. Dimension leap; title: 22. Quaternions; title: 23. Back to R³!; title: 24. Invariants; title: 25. The Icosahedron and the unsolvable quintic; title: 26. The fourth dimension; title: Appendixes:; title: A. Sets; title: B. Groups; title: C. Topology; title: D. Smooth maps; title: E. The hypergeometric differential equation and the Schwarzian; title: F. Galois theory.