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Beschreibung
Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: [...] Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems
Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: [...] Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems
Zusammenfassung
Glimpses of Algebra and Geometry is intended for a "Bridge Course" that facilitates the transition between undergraduate and graduate studies. This new edition includes innumerable improvements throughout the text, including an in-depth treatment of root formulas, a detailed and complete classification of finite Mobius groups a la Klein, and a quick, direct, and modern approach to Felix Klein's "Normalformsatz."
Inhaltsverzeichnis
"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 Transcendental?.- Complex Arithmetic.- Quadratic, Cubic, and Quartic Equations.- Stereographic Projection.- Proof of the Fundamental Theorem of Algebra.- Symmetries of Regular Polygons.- Discrete Subgroups of Iso (R2).- 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-Poincaré Characteristic.- Detour in Graph Theory: Euler, Hamilton, and the Four Color Theorem.- Dimension Leap.- Quaternions.- Back to R3!.- Invariants.- The Icosahedron and the Unsolvable Quintic.- The Fourth Dimension.
Details
| Erscheinungsjahr: | 2002 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Reihe: | Undergraduate Texts in Mathematics |
| Inhalt: |
xxii
450 S. 47 s/w Illustr. 10 farbige Illustr. 450 p. 57 illus. 10 illus. in color. |
| ISBN-13: | 9780387953458 |
| ISBN-10: | 0387953450 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Toth, Gabor |
| Auflage: | 2nd ed. 2002 |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. Undergraduate Texts in Mathematics |
| Maße: | 241 x 183 x 34 mm |
| Von/Mit: | Gabor Toth |
| Erscheinungsdatum: | 02.05.2002 |
| Gewicht: | 1,112 kg |
Zusammenfassung
Glimpses of Algebra and Geometry is intended for a "Bridge Course" that facilitates the transition between undergraduate and graduate studies. This new edition includes innumerable improvements throughout the text, including an in-depth treatment of root formulas, a detailed and complete classification of finite Mobius groups a la Klein, and a quick, direct, and modern approach to Felix Klein's "Normalformsatz."
Inhaltsverzeichnis
"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 Transcendental?.- Complex Arithmetic.- Quadratic, Cubic, and Quartic Equations.- Stereographic Projection.- Proof of the Fundamental Theorem of Algebra.- Symmetries of Regular Polygons.- Discrete Subgroups of Iso (R2).- 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-Poincaré Characteristic.- Detour in Graph Theory: Euler, Hamilton, and the Four Color Theorem.- Dimension Leap.- Quaternions.- Back to R3!.- Invariants.- The Icosahedron and the Unsolvable Quintic.- The Fourth Dimension.
Details
| Erscheinungsjahr: | 2002 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Reihe: | Undergraduate Texts in Mathematics |
| Inhalt: |
xxii
450 S. 47 s/w Illustr. 10 farbige Illustr. 450 p. 57 illus. 10 illus. in color. |
| ISBN-13: | 9780387953458 |
| ISBN-10: | 0387953450 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Toth, Gabor |
| Auflage: | 2nd ed. 2002 |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. Undergraduate Texts in Mathematics |
| Maße: | 241 x 183 x 34 mm |
| Von/Mit: | Gabor Toth |
| Erscheinungsdatum: | 02.05.2002 |
| Gewicht: | 1,112 kg |
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