Isaak Yaglom

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For similar names, see Yahalom.

Isaak Moiseevich Yaglom[1] (Russian: Иссак Моисеевич Яглом) (6 March 1921, Kharkov — 17 April 1988, Moscow)[2] was a Soviet mathematician and author of popular mathematics books.

Yaglom received a Ph.D. from Moscow State University in 1945 as student of Veniamin Kagan.[3] As the author of several books, translated into English, that have become academic standards of reference, he has an international stature. His attention to the necessities of learning (pedagogy) make his books pleasing experiences for students. The seven authors of his Russian obituary recount “…the breadth of his interests was truly extraordinary: he was seriously interested in history and philosophy, passionately loved and had a good knowledge of literature and art, often came forward with reports and lectures on the most diverse topics (for example, on Blok, Akhmatova, and the Dutch painter Escher), actively took part in the work of the cinema club in Yaroslavl and the music club at the House of Composers in Moscow, and was a continual participant of conferences on mathematical linguistics and on semiotics.”[4]

Contents

[edit] University life

Yaglom started his higher education at Moscow State University in 1938. During World War II he volunteered but due to myopia he was deferred from military service. In the evacuation of Moscow he went with his family to Sverdlovsk in the Ukraine. He studied at the Sverdlovsk State University, graduated in 1942, and when the usual Moscow faculty assembled in Sverdlovsk during the war, he took up graduate study. Under the geometer Veniamin Kagan he developed his Ph.D. thesis which he defended in Moscow in 1945. It is reported that this thesis “was devoted to projective metrics on a plane and their connections with different types of complex numbers a + jb (where jj = -1, or jj = +1, or else jj = 0).”[4]

[edit] Institutes and titles

During his career, Yaglom was affiliated with these institutions.[4]

  • Moscow Energy Institute (1946) – lecturer in mathematics
  • Moscow State University (1946 – 49) – lecturer, dept. analysis and differential g.
  • Orekhovo-Zuov Pedagogical Institute (1949-56) - lecturer in mathematics
  • Lenin State Pedagogical Institute (Moscow) (1956-68) - obtained D.Sc. 1965
  • Moscow Evening Metallurgical Institute (1968-74) – professor of mathematics
  • Yaroslavl State University (1974-83) – professor of mathematics
  • Academy of Pedagogical Sciences (1984-88) – technical consultant

[edit] Principle works

Isaac Yaglom wrote over 40 books and many articles. Here are some of the better known ones with their date of appearance in English:

[edit] Complex numbers in geometry (1968)

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.

[edit] Geometric transformations (1962, 68, 73)

These publications of the New Mathematics Library (volumes 8, 21, and 24) from Random House publishing were keenly appreciated by proponents of the New Math in the U.S.A. They represent only a part of Yaglom’s two-volume original published in 1955 and 56.

[edit] A simple non-euclidean geometry and its physical basis (1979)

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". Then he introduces Galilean angle.

The concepts of the dual number and its "imaginary" ε, ε2 = 0, do not appear in the development of Galilean geometry. Nevertheless, Yaglom extensively develops his non-Euclidean geometry including the theory of cycles (pp. 77-9), duality, and the circumcycle and incycle of a triangle (p. 104).

[edit] Probability and information (1983)

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.

[edit] Felix Klein and Sophus Lie (1988)

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.”[5] 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.

[edit] Notes

  1. ^ His last name is sometimes transliterated as "Jaglom", "Iaglom", "IAglom", or "I-Aglom". The double capitalization in the latter cases indicates that IA transliterates a single capital letter Я (Ya).
  2. ^ Russian Jewish Encyclopedia
    About Isaak Moiseevich Yaglom by B. A. Rozenfel'd (Russian)
  3. ^ Isaak Moiseivich Yaglom at the Mathematics Genealogy Project
  4. ^ a b c Boltyanskii, et al.
  5. ^ Chapter 7, pp. 111-24.

[edit] References

  • Boltyanskii, V G; L I Golovina, O A Ladyzhenskaya, Yu I Manin, S P Novikov, B A Rozenfel'd, A M Yaglom. "Isaak Moiseevich Yaglom (obituary)". Russian Mathematical Surveys 44 (1): 225–227. doi:10.1070/RM1989v044n01ABEH002018. 
  • Yaglom, Isaak M. (c1979). A simple non-Euclidean geometry and its physical basis : an elementary account of Galilean geometry and the Galilean principle of relativity, Abe Shenitzer (trans.), New York: Springer-Verlag. ISBN 0387903321.  (translated from the Russian) (bibrec)

[edit] External links