Glimpses of Algebra and Geometry
The purpose of Glimpses of Algebra and Geometry is to fill a gap between undergraduate and graduate mathematics studies. It is one of the few undergraduate texts to explore the subtle and sometimes puzzling connections between Number Theory, Classical Geometry and Modern Algebra in a clear and easil...
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| Format: | Electronic eBook |
| Language: | English |
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New York, NY :
Springer New York,
2002.
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| Edition: | Second Edition. |
| Series: | Undergraduate Texts in Mathematics, Readings in Mathematics,
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| Online Access: | Full Text via HEAL-Link |
Table of Contents:
- “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.
