I. M. Gelfand

  • Models of the Structural-Functional Organization of Certain Biological Systems

    I. M. Gelfand, V. S. Gurfinkel, S. V. Fomin, and M. L. Tsetlin

    This book was written in 1966 as a memorial tribute to Nikolai Aleksandrovich Bernstein, the eminent Russian pioneer in cybernetics. Representing the work of a number of contributors, it is made up of a collection of papers presenting models of various physiological systems. Together, the papers summarize a great deal of work not conveniently available elsewhere.

    The collection includes only that sort of model for which some real physiological system is the subject; constructions not having well-grounded roots in biology are omitted, and so are those that mathematicians might find simplistic and unlikely to evolve fruitfully. Since from the editors' point of view a model description and physiological experiment are consecutive stages of research, some of these chapters are purely theoretical, while others are of the Department of Theoretical Biology and the Committee on Information Sciences, University of Chicago, has provided not only current information on the topics discussed in the article but also a bibliography of current works and articles.

    Individual papers on the functioning of specific systems discuss the construction of models that correctly describe the functioning system. The postulates employed correspond to the real properties of the elements correspond to the real properties of the elements of the modeled system and to the interrelationship of the elements. The model is then refined to a level at which conclusions can be made that allow experimental verification. The ultimate goal in each case is, of course, to render predictable certain properties of the system not previously obvious and to allow the corresponding model to be utilized in gaining an understanding of the function of the system under investigation.

    Introduction. Mathematical Modeling of Mechanisms of the Central Nervous System • Part I: The Spreading of Excitation in Continuous Media and the Electrical Properties of Branching Structures – An Analysis of the Functional Properties of Dendrites in Relation to Their Structure: The Electrical Behavior of the Myocardium as a System and the Characteristics of the Cellular Membrane of the Heart; The Problem of the Electrical Properties of Syncytia; The Periodic Blocking of Impulses in Excitable Tissues • Part II: The Organization of Certain Parts of the Central Nervous System and the Modeling of Their Operation – Characteristics of the Respiratory Neurons of Different Levels of the Central Nervous System; A Model of a System of Neurons with Periodic Volley Activity Resistant to Random Afferent Influences; Some Special Features of Organization of the Cerebellar Cortex • Part III: The Regulations of Movements – Some Problems in the Analysis of Movements; An Analysis of Physiological Tremor by Means of a General-Purpose Computer; Concerning Tuning before Movement; The Control of Movements of the Joints and Kinesthetic of Respiratory Disturbances of the Erect Posture of Man as an example of the Organization of Interarticular Interaction. Index.

    • Hardcover $30.00
  • Sequences, Combinations, Limits, Volume 3

    I. M. Gelfand, M. L. Gerver, A. A. Kirillov, N. N. Konstantinov, and A. G. Kushnirenko

    A major achievement of Soviet mathematics education is the extensive program of extracurricular activities designed to discover and train future mathematicians and scientists at an early age. In recent years this program has taken on new dimensions. In 1964, the world-renowned mathematician, I. M. Gelfand, organized the Mathematics Correspondence School at Moscow University. Admission is based on highly competitive examinations. By 1968 more than 8,000 gifted secondary school students were enrolled in the MCS and its 29 affiliates located in various parts of the Soviet Union. This number also included students in a special program in which 270 mathematics clubs participate as “collective students.” In 1967, 700 youngsters successfully completed the MCS two-year program, and 690 students graduated in 1968.

    As a result of the activities of the MCS, a series of books in mathematics is currently appearing under the title Library of the Physics-Mathematics School, with Professor Gelfand as the editor. The booklets are designed to give the reader a deeper understanding of mathematics, to acquaint him with new ideas and methods, and to develop in him habits of independent work. These publications contain an abundance of ingenious problems along with solutions, answers, and hints. Solving these imaginative problems often requires thorough analysis and concentrated effort conductive to mathematical creativity.

    These American editions have been prepared by the Survey of Recent East European Mathematical Literature at the University of Chicago under a grant from the National Science Foundation. They should prove to be of great value to mathematics teachers, to college students, and high school students interested in independent study or mathematics group activities.

    • Paperback $2.95
  • Sequences, Combinations, Limits, Volume 3

    I. M. Gelfand, M. L. Gerver, A. A. Kirillov, N. N. Konstantinov, and A. G. Kushnirenko

    A major achievement of Soviet mathematics education is the extensive program of extracurricular activities designed to discover and train future mathematicians and scientists at an early age. In recent years this program has taken on new dimensions. In 1964, the world-renowned mathematician, I. M. Gelfand, organized the Mathematics Correspondence School at Moscow University. Admission is based on highly competitive examinations. By 1968 more than 8,000 gifted secondary school students were enrolled in the MCS and its 29 affiliates located in various parts of the Soviet Union. This number also included students in a special program in which 270 mathematics clubs participate as “collective students.” In 1967, 700 youngsters successfully completed the MCS two-year program, and 690 students graduated in 1968.

    As a result of the activities of the MCS, a series of books in mathematics is currently appearing under the title Library of the Physics-Mathematics School, with Professor Gelfand as the editor. The booklets are designed to give the reader a deeper understanding of mathematics, to acquaint him with new ideas and methods, and to develop in him habits of independent work. These publications contain an abundance of ingenious problems along with solutions, answers, and hints. Solving these imaginative problems often requires thorough analysis and concentrated effort conductive to mathematical creativity.

    These American editions have been prepared by the Survey of Recent East European Mathematical Literature at the University of Chicago under a grant from the National Science Foundation. They should prove to be of great value to mathematics teachers, to college students, and high school students interested in independent study or mathematics group activities.

    • Hardcover $8.50
  • Functions and Graphs, Volume 2

    I. M. Gelfand, E. G. Glagoleva, and E. E. Shnol

    A major achievement of Soviet mathematics education is the extensive program of extracurricular activities designed to discover and train future mathematicians and scientists at an early age. In recent years this program has taken on new dimensions. In 1964, the world renowned mathematician, I. M. Gelfand, organized the Mathematics Correspondence School at Moscow University. Admission is based on highly competitive examinations. By 1968 more than 8,000 gifted secondary school students were enrolled in the MCS and its 29 affiliates located in various parts of the Soviet Union. This number also included students in a special program in which 270 mathematics clubs participate as “collective students.” In 1967, 700 youngsters successfully completed the MCS two-year program, and 690 students graduated in 1968.

    As a result of the activities of the MCS, a series of books in mathematics is currently appearing under the title Library of the Physics-Mathematics School, with Professor Gelfand as the editor. The booklets are designed to give the reader a deeper understanding of mathematics, to acquaint him with new ideas and methods, and to develop in him habits of independent work. These publications contain an abundance of ingenious problems along with solutions, answers, and hints. Solving these imaginative problems often requires thorough analysis and concentrated effort conductive to mathematical creativity.

    These American editions have been prepared by the Survey of Recent East European Mathematical Literature at the University of Chicago under a grant from the National Science Foundation. They should prove to be of great value to mathematics teachers, to college students, and to high school students interested in independent study or mathematics group activities.

    • Hardcover $7.50
    • Paperback $1.95
  • The Method of Coordinates, Volume 1

    I. M. Gelfand, E. G. Glagoleva, and A. A. Kirillov

    A major achievement of Soviet mathematics education is the extensive program of extracurricular activities designed to discover and train future mathematicians and scientists at an early age. In recent years this program has taken on new dimensions. The world-renowned mathematician, I. M. Gelfand, organized in 1963 the Mathematics Correspondence School at Moscow State University. An indication of the scope of the MCS is the admission in 1966 of 1000 ninth-grade pupils as correspondence students on the basis of highly competitive examinations. The MCS has also established a special program in which 250 mathematics clubs from all over the country participate as “collective students.”

    As a result of the activities of the MCS, a series of books in mathematics is currently appearing under the title Library of the Physics-Mathematics School, with Professor Gelfand as the editor. The booklets are designed to give the reader a deeper understanding of mathematics, to acquaint him with new ideas and methods, and to develop in him habits of independent work. These publications contain an abundance of ingenious problems along with solutions, answers, and hints. Solving these imaginative problems often requires thorough analysis and concentrated effort conductive to mathematical creativity.

    These American editions have been prepared by the Survey of Recent East European mathematical Literature at the University of Chicago under a grant from the National Science Foundation. They should prove to be of great value to mathematics teachers, to college students, and to high school students interested in independent study or mathematics group activities.

    • Hardcover $10.00
    • Paperback $2.45