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.
- Chapter 1:
- Algebra of points.
Patches for the two pages of Chapter 1: page 25 and page 26.
- Chapter 2:
- Plane movements.
- Chapter 3:
- Transformation groups.
- Chapter 4:
- Arbitrary groups.
- Chapter 5:
- Orbits and ornaments.
- Chapter 6:
- Other types of transformations.
- Chapter 7:
- Symmetries of differential equations.
- Answers and solutions.
Gzipped PostScript file of the whole book
in English updated in April 2004.