Glimpses of algebra and geometry
著者
書誌事項
Glimpses of algebra and geometry
（Undergraduate texts in mathematics）（Graduate texts in mathematics）
Springer, c1998
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注記
Includes index
内容説明・目次
内容説明
Seeking to fill a gap between undergraduate and graduate mathematics studies, this text explores the subtle and sometimes puzzling connections between number theory, classical geometry and modern algebra. The text is divided into subtexts of four levels according to the reader's aptitude and should appeal to students who wish to learn modern mathematics, but have few prerequisite courses, and to high-school teachers who always had a keen interest in mathematics but seldom the time to pursue background technicalities. Over 160 computer-generated images, accessible via the Web, facilitate an understanding of mathematical concepts and proofs even further. Thus material from this volume can be taught the traditional way using slides, or interactively in a computer lab or using a PC connected to an LCD-panel.
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 numbers
- complex arithmetic
- stereographic projection
- proof of the fundamental theorem of algebra
- symmetries of regular polygons
- discrete subgroups of Iso(R2)
- moebius geometry
- complex linear fractional transformations
- "out of nothing I created a new universe" (Bolyai)
- Fuchsian groups
- Riemann surfaces
- general surfaces
- the five platonic solids
- detour in topology - Euler Poincare characteristic
- detour in graph theory - Eulerian, Hamilton and the four colour theorem
- the dimension leap
- quaternions
- back to R3
- the fourth dimension
- hints for selected problems.
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