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.
- Chapter 1:
- Algebra of points.
- 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.
Last updated 25-May-00.