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 1998-2000 I made an English translation (with modifications and improvements) which is posted here. In 2000 the book was translated into Japanese by S.Yukita and M.Nagura and published by Springer Verlag Tokyo. Here you can find the PDF files of the preliminary version of the Japanese text.

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. .

Chapter 0:
Table of contents and Introduction.
Japanese text.
Chapter 1:
Algebra of points.
Japanese text.
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.

Last updated 25-May-00.
S.V.Duzhin