Background
Stepanov, Serguei Alexandrovich was born on February 24, 1941 in Moscow. Son of Alexander Evstaphievich and Lidia Dmitrievna Stepanov.
(Author S.A. Stepanov thoroughly investigates the current ...)
Author S.A. Stepanov thoroughly investigates the current state of the theory of Diophantine equations and its related methods. Discussions focus on arithmetic, algebraic-geometric, and logical aspects of the problem. Designed for students as well as researchers, the book includes over 250 excercises accompanied by hints, instructions, and references. Written in a clear manner, this text does not require readers to have special knowledge of modern methods of algebraic geometry.
http://www.amazon.com/gp/product/0306110369/?tag=2022091-20
(This is a self-contained introduction to algebraic curves...)
This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink 210, is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.
http://www.amazon.com/gp/product/0306461447/?tag=2022091-20
(This is a self-contained introduction to algebraic curves...)
This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink 210, is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.
http://www.amazon.com/gp/product/1461371678/?tag=2022091-20
mathematics educator researcher
Stepanov, Serguei Alexandrovich was born on February 24, 1941 in Moscow. Son of Alexander Evstaphievich and Lidia Dmitrievna Stepanov.
Doctor of Philosophy, Steklov Math Institute, Moscow, 1970. Doctor of Science, Steklov Math Institute, Moscow, 1977. Master of Science, Moscow State University, 1965.
Assistant professor Institute Chemical Technology, Moscow, 1969-1971. Head math department Moscow Executive Committee Computer Center, 1971-1974. Leading science researcher Steklov Math Institute, Moscow, since 1974.
Professor Moscow State University, since 1980, Bilkent University, Ankara, Turkey, since 1993. Leading science researcher Institute Information Transmission Problems, Russian Academy of Sciences, Moscow, since 2004.
(This is a self-contained introduction to algebraic curves...)
(This is a self-contained introduction to algebraic curves...)
(Author S.A. Stepanov thoroughly investigates the current ...)
Lieutenant Higher Military School, 1958-1960. Member American Mathematics Society, Moscow Mathematics Society, All-Union Society "Znanie" (vice-chairman since 1982).
Married Iraida Nikolayevan Sirotkina, April 22, 1961. 1 child, Helen Sergeevna.