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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010142055 | QA154.3 T67 2002 | Open Access Book | Book | Searching... |
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Summary
Summary
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
Reviews 1
Choice Review
Of all mathematical concepts, the idea of the Riemann surface holds the best claim to the status of "Rosetta Stone of Mathematics." The study of Riemann surfaces belongs equally to complex analysis, algebraic geometry, field theory, topology, number theory, and representation theory, and this multiplicity of viewpoints makes Riemann surface theory a characteristically graduate level topic. Toth intends his book as a bridge from undergraduate to graduate level mathematics. The book takes the form of a sampler, but the choice of topics conforms to this pattern of the disciplines listed above, and Riemann surfaces themselves form one of the book's climaxes. (Of course, graduate level mathematics in its vastness also offers avenues of study entirely independent of these topics.) In the classroom the book would make a reasonable choice for a so-called capstone course, particularly for an instructor who shared Toth's tastes; in the library one should already find more thorough treatments of all these topics, but Toth offers novelties in sufficient profusion to justify a place on the shelf. Upper-division undergraduates through faculty. D. V. Feldman; University of New Hampshire
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 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) |
| Mobius 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 Mobius 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 |
