Glimpses of algebra and geometry
著者
書誌事項
Glimpses of algebra and geometry
（Undergraduate texts in mathematics, . Reading in mathematics）
Springer, c2002
2nd ed
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems
目次
* '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 Transcendential? * Complex Arithmetic * Quadratic, Cubic, and Quartic Equations * Stereographic Projection * Proof of the Fundamental Theorem of Algebra * Symmetries of Regular Polygons * Discrete Subgroups of Iso(R^2) * Moebius 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 Moebius Groups * Detour in Topology: Euler-Poincare Characteristic * Detour in Graph Theory: Euler, Hamilton and the Four Color Theorem * Dimension Leap * Quaternions * Back to R^3! * Invariants * The Icosahedron and the Unsolvable Quintic * The Fourth Dimension * Appendices * Solutions for 100 Selected Problems * Index
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