Gabor Toth, "Glimpses of Algebra and Geometry"
2002 | pages: 466 | ISBN: 0387953450 | PDF | 4,3 mb
2002 | pages: 466 | ISBN: 0387953450 | PDF | 4,3 mb
The purpose of Glimpses of Algebra and Geometry is to fill a gap between undergraduate and graduate mathematics studies. It is one of the few undergraduate texts to explore the subtle and sometimes puzzling connections between number theory, classical geometry and modern algebra in a clear and easily understandable style. Over 160 computer-generated images, accessible to readers via the World Wide Web, facilitate an understanding of mathematical concepts and proofs even further.
From the reviews of the second edition:
"Toth’s ‘Glimpses’ offer selected material that connect algebra and geometry … . This second edition is a revised and substantially expanded version, so for example it includes a detailed treatment of the solution of the cubic and quartic, as well as a long new chapter on Klein’s famous work on the quintic and the icosahedron." (Günter M. Ziegler, Zentralblatt MATH, Vol. 1027, 2004)
"The book is intended – and really manages it – to fill undergraduates with enthusiasm to reach the graduate level. … the author presents various topics of number theory, geometry and algebra and at the same time shows their connection resp. interplay, thus making the study lively and fascinating for the reader. … information on advanced websites and films show how carefully the author has done his job. So this second edition hopefully will not be the last one." (G. Kowol, Monatshefte für Mathematik, Vol. 141 (2), 2004)
"The text covers a wide range of topics and gives a taste of advanced material in number theory, geometry and algebra, particularly where these fields overlap. … there are plenty of references for the interested reader who wishes to pursue a particular topic in greater depth. … the accessibility of the format and the flow of the material combine to create an entertaining and informative work. I recommend the text as a good read for mathematicians of all specialities. " (Stephen Lucas, The Australian Mathematical Society Gazette, Vol. 30 (4), 2003)
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