S.V.Duzhin

Transformation Groups in Algebra, Geometry and Calculus

This is my book, written together with B.D.Chebotarevsky in 1983-86 and published in 1988 under the title "Ot ornamentov do differencialnyh uravnenij" ("From ornaments to differential equations", in Russian) by "Vysheishaya Shkola", Minsk. In 1996-2000, I translated it (with many modifications and improvements) into English. The English text was further translated into Japanese and published in 2000 by Springer Verlag Tokyo under the title "Henkangun Nyuumon". The book provides an introduction into the theory of transformation groups at the level of high-school students and university newcomers. Its chapters about group theory were used a textbook in Higher College of Chemistry in Moscow in 1989-1992.

Full text in Russian: DejaVu file.

Below is chapter-split English translation (version August 2002) and a draft of the Japanese translation due to S.Yukita and M.Nagura dating back to 2000, before it went to the publishers. (You will need Japanese fonts support to view the corresponding pdf files!)

Chapter 0:
Table of contents and Introduction.
Japanese text.
Chapter 1:
Algebra of points.
Japanese text.
Patches for the two pages of Chapter 1: page 25 and page 26.
Chapter 2:
Plane movements.
Japanese text.
Chapter 3:
Transformation groups.
Japanese text.
Chapter 4:
Arbitrary groups.
Japanese text.
Chapter 5:
Orbits and ornaments.
Japanese text.
Chapter 6:
Other types of transformations.
Japanese text.
Chapter 7:
Symmetries of differential equations.
Japanese text.
Appendix:
Answers and solutions.
Japanese text.

Gzipped PostScript file of the whole book in English updated in April 2004.

S.V.Duzhin