Glimpses of algebra and geometry
Author(s)
Bibliographic Information
Glimpses of algebra and geometry
（Undergraduate texts in mathematics）（Graduate texts in mathematics）
Springer, c1998
Available at / 47 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:512.12/T642070437134
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Note
Includes index
Description and Table of Contents
Description
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.
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 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.
by "Nielsen BookData"