Isaak Yaglom
Encyclopedia
Isaak Moiseevich Yaglom was a Soviet mathematician
and author
of popular mathematics books, some with his twin
Akiva Yaglom
.
Yaglom received a Ph.D. from Moscow State University
in 1945 as student of Veniamin Kagan
. 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."
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 Urals. 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)."
in the Euclidean and Lobachevski planes, and inversive geometry.
(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).
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. 77-9), 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; the two inversive planes show him practicing comparative inversive ring geometry
.
. 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.
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." 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 forward by Richard Bozulich
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and author
Author
An author is broadly defined as "the person who originates or gives existence to anything" and that authorship determines responsibility for what is created. Narrowly defined, an author is the originator of any written work.-Legal significance:...
of popular mathematics books, some with his twin
Twin
A twin is one of two offspring produced in the same pregnancy. Twins can either be monozygotic , meaning that they develop from one zygote that splits and forms two embryos, or dizygotic because they develop from two separate eggs that are fertilized by two separate sperm.In contrast, a fetus...
Akiva Yaglom
Akiva Yaglom
Akiva Moiseevich Yaglom was a Soviet and Russian physicist, mathematician, statistician, and meteorologist. He was known for his contribution to the statistical theory of turbulence and theory of random processes. Yaglom spent most of his career in Russia working in various institutions, including...
.
Yaglom received a Ph.D. from Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
in 1945 as student of Veniamin Kagan
Veniamin Kagan
Veniamin Fedorovich Kagan was a Russian and Soviet mathematician and expert in geometry. He is the maternal grandfather of mathematician Yakov Sinai.-Biography:...
. 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
Pedagogy
Pedagogy is the study of being a teacher or the process of teaching. The term generally refers to strategies of instruction, or a style of instruction....
) 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
Alexander Blok
Alexander Alexandrovich Blok was a Russian lyrical poet.-Life and career:Blok was born in Saint Petersburg, into a sophisticated and intellectual family. Some of his relatives were literary men, his father being a law professor in Warsaw, and his maternal grandfather the rector of Saint Petersburg...
, Akhmatova, and the Dutch painter Escher
M. C. Escher
Maurits Cornelis Escher , usually referred to as M. C. Escher , was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints...
), 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."
University life
Yaglom started his higher education at Moscow State University in 1938. During World War IIWorld War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
he volunteered but due to myopia
Myopia
Myopia , "shortsightedness" ) is a refractive defect of the eye in which collimated light produces image focus in front of the retina under conditions of accommodation. In simpler terms, myopia is a condition of the eye where the light that comes in does not directly focus on the retina but in...
he was deferred from military service. In the evacuation of Moscow he went with his family to Sverdlovsk
Yekaterinburg
Yekaterinburg is a major city in the central part of Russia, the administrative center of Sverdlovsk Oblast. Situated on the eastern side of the Ural mountain range, it is the main industrial and cultural center of the Urals Federal District with a population of 1,350,136 , making it Russia's...
in the Urals. He studied at the Sverdlovsk State University
Ural State University
The Ural State University is located in the city of Yekaterinburg, Sverdlovsk Oblast, Russian Federation. Founded in 1920, it was an exclusive educational establishment made of several institutes which later became independent universities and schools.In 1936 the university was named after one of...
, 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
Veniamin Kagan
Veniamin Fedorovich Kagan was a Russian and Soviet mathematician and expert in geometry. He is the maternal grandfather of mathematician Yakov Sinai.-Biography:...
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)."
Institutes and titles
During his career, Yaglom was affiliated with these institutions.- Moscow Energy Institute (1946) – lecturer in mathematics
- Moscow State UniversityMoscow State UniversityLomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
(1946 – 49) – lecturer, dept. analysis and differential g. - Orekhovo-Zuevo 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
Principal works
Isaac Yaglom wrote over 40 books and many articles. Some of the better known ones in English with their date of appearance are: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 coordinatesLine coordinates
In geometry, line coordinates are used to specify the position of a line just as point coordinates are used to specify the position of a point.-Lines in the plane:...
in the Euclidean and Lobachevski planes, and inversive geometry.
Geometric Transformations (1962, 1968, 1973, 2009)
The first three books were originally published in English by Random House as part of the series New Mathematical LibrarySchool Mathematics Study Group
The School Mathematics Study Group was an American academic think tank focused on the subject of reform in mathematics education. Directed by Edward G...
(Volumes 8, 21, and 24). They were keenly appreciated by proponents of the New Math
New math
New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S...
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).
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".
The concepts of the dual number
Dual number
In linear algebra, the dual numbers extend the real numbers by adjoining one new element ε with the property ε2 = 0 . The collection of dual numbers forms a particular two-dimensional commutative unital associative algebra over the real numbers. Every dual number has the form z = a + bε with a and...
and its "imaginary" ε, ε2 = 0, do not appear in the development of Galilean geometry. However, Yaglom shows that the common slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
concept in analytic geometry corresponds to the Galilean angle. Yaglom extensively develops his non-Euclidean geometry including the theory of cycles (pp. 77-9), duality
Duality (projective geometry)
A striking feature of projective planes is the "symmetry" of the roles played by points and lines in the definitions and theorems, and duality is the formalization of this metamathematical concept. There are two approaches to the subject of duality, one through language and the other a more...
, 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
Nine-point hyperbola
-Discovery:The nine-point hyperbola was first discovered by E.F. Allen and his work was published in a volume of The American Mathematical Monthly in December, 1941...
. Yaglom also covers the inversive Minkowski plane; the two inversive planes show him practicing comparative inversive ring geometry
Inversive ring geometry
In mathematics, inversive ring geometry is the extension of the concepts of projective line, homogeneous coordinates, projective transformations, and cross-ratio to the context of associative rings, concepts usually built upon rings that happen to be fields....
.
Probability and information (1983)
Co-author: A. M. YaglomAkiva Yaglom
Akiva Moiseevich Yaglom was a Soviet and Russian physicist, mathematician, statistician, and meteorologist. He was known for his contribution to the statistical theory of turbulence and theory of random processes. Yaglom spent most of his career in Russia working in various institutions, including...
. 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.
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." 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
Ishi Press
Ishi Press was the world's leading supplier of go books and equipment in the 1990s, and published Go World magazine.Ishi Press was founded in Japan in 1968 by Richard Bozulich. In 1986, it expanded to an office in Mountain View, California under James Connelley...
as Geometry, Groups and Algebra in the Nineteenth Century. The new edition, designed by Sam Sloan
Sam Sloan
Samuel Howard Sloan , also known as Haji Mohammed Ismail Sloan, is an American chess player and publisher. In 2010, Sloan ran for the Libertarian Party nomination in the 2010 New York gubernatorial election but did not succeed. In 2006, Sloan served on the Executive Board of the United States...
, has a forward by Richard Bozulich
Richard Bozulich
Richard Bozulich is an American author and publisher of go books in English. He co-founded the Ishi Press. He has worked with several Japanese professional players....
.
External links
- About Isaak Moiseevich Yaglom by B. A. Rozenfel'd