Glimpses of Algebra and Geometry
Gabor Toth(Author)
Springer (Publisher)
Published on 1. January 1997
Book
Hardback
XVIII, 308 pages
978-0-387-98213-7 (ISBN)
Article exhausted; check for reprint
Description
Filling a gap between undergraduate and graduate mathematics studies, this is one of the few texts to explore the subtle and sometimes puzzling connections between number theory, classical geometry and modern algebra in a clear and easily understandable style. The text is divided into subtexts of four levels according to the readers aptitude and will 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. Even postgraduate mathematicians will enjoy being able to browse through a number of mathematical disciplines in one sitting. 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.
More details
Series
Language
English
Place of publication
NY
United States
Target group
College/higher education
Professional and scholarly
Illustrations
150
18 farbige Abbildungen, 150 s/w Abbildungen
164 figures, index
Weight
760 gr
ISBN-13
978-0-387-98213-7 (9780387982137)
Schweitzer Classification
Other editions
New editions

Gabor Toth
Glimpses of Algebra and Geometry
Book
05/2002
2nd Edition
Springer
€85.59
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Content
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).- M bius 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 Color Theorem.- The Dimension Leap.- Quaternions.- Back to R3.- The Fourth Dimension.- Appendices.- Hints for Selected Problems.- Index.