Glimpses of Algebra and Geometry

Table of Contents

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   Book Overview
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   Chapter 1 “A Number Is a Multitude Composed of Units”—Euclid
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   Chapter 2 “... There Are No Irrational Numbers at All”—Kronecker
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   Chapter 3 Rationality, Elliptic Curves, and Fermat’s Last Theorem
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   Chapter 4 Algebraic or Transcendental?
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   Chapter 5 Complex Arithmetic
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   Chapter 6 Quadratic, Cubic, and Quartic Equations
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   Chapter 7 Stereographic Projection
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   Chapter 8 Proof of the Fundamental Theorem of Algebra
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    Chapter 9 Symmetries of Regular Polygons
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    Chapter 10 Discrete Subgroups of Iso (R 2 )
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    Chapter 11 Möbius Geometry
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    Chapter 12 Complex Linear Fractional Transformations
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    Chapter 13 “Out of Nothing I Have Created a New Universe”—Bolyai
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    Chapter 14 Fuchsian Groups
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    Chapter 15 Riemann Surfaces
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    Chapter 16 General Surfaces
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    Chapter 17 The Five Platonic Solids
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    Chapter 18 Finite Möbius Groups
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    Chapter 19 Detour in Topology: Euler-Poincaré Characteristic
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    Chapter 20 Detour in Graph Theory: Euler, Hamilton, and the Four Color Theorem
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    Chapter 21 Dimension Leap
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    Chapter 22 Quaternions
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    Chapter 23 Back to R 3 !
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    Chapter 24 Invariants
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    Chapter 25 The Icosahedron and the Unsolvable Quintic
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    Chapter 26 The Fourth Dimension