Isaak Yaglom

Translated by Eric J. F. Primrose, published by Academic Press (N.Y.). The trinity of complex number planes is laid out and exploited. Topics include line coordinates in the Euclidean and Lobachevski planes, and inversive geometry.

The first three books were originally published in English by Random House as part of the series New Mathematical Library (Volumes 8, 21, and 24). They were keenly appreciated by proponents of the New Math in the U.S.A., but represented only a part of Yaglom's two-volume original published in Russian in 1955 and 56. More recently the final portion of Yaglom's work was translated into English and published by the Mathematical Association of America. All four volumes are now available from the MAA in the series Anneli Lax New Mathematical Library (Volumes 8, 21, 24, and 44).

Subtitle: An elementary account of Galilean geometry and the Galilean principle of relativity. Translated by Abe Shenitzer, published by Springer-Verlag. In his prefix, the translator says the book is "a fascinating story which flows from one geometry to another, from geometry to algebra, and from geometry to kinematics, and in so doing crosses artificial boundaries separating one area of mathematics from another and mathematics from physics." The author's own prefix speaks of "the important connection between Klein's Erlanger Program and the principles of relativity."

The approach taken is elementary; simple manipulations by shear mapping lead on page 68 to the conclusion that "the difference between the Galilean geometry of points and the Galilean geometry of lines is just a matter of terminology".

The concepts of the dual number and its "imaginary" ε, ε² = 0, do not appear in the development of Galilean geometry. However, Yaglom shows that the common slope concept in analytic geometry corresponds to the Galilean angle. Yaglom extensively develops his non-Euclidean geometry including the theory of cycles (pp. 77–79), duality, and the circumcycle and incycle of a triangle (p. 104).

Yaglom continues with his Galilean study to the inversive Galilean plane by including a special line at infinity and showing the topology with a stereographic projection. The Conclusion of the book delves into the Minkowskian geometry of hyperbolas in the plane, including the nine-point hyperbola. Yaglom also covers the inversive Minkowski plane.

Co-author: A. M. Yaglom. Russian editions in 1956, 59 and 72. Translated by V. K. Jain, published by D. Reidel and the Hindustan Publishing Corporation, India. The channel capacity work of Claude Shannon is developed from first principles in four chapters: probability, entropy and information, information calculation to solve logical problems, and applications to information transmission. The final chapter is well-developed including code efficiency, Huffman codes, natural language and biological information channels, influence of noise, and error detection and correction.

Co-author: A. M. Yaglom. Two volumes. Russian edition in 1954. First English edition 1964-1967

Subtitle: The evolution of the idea of symmetry in the 19th century. In his chapter on "Felix Klein and his Erlangen Program", Yaglom says that "finding a general description of all geometric systems [was] considered by mathematicians the central question of the day."[6] The subtitle more accurately describes the book than the main title, since a great number of mathematicians are credited in this account of the modern tools and methods of symmetry.

In 2009 the book was republished by Ishi Press as Geometry, Groups and Algebra in the Nineteenth Century. The new edition, designed by Sam Sloan, has a foreword by Richard Bozulich.