The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990s. As early as the 1960s, I.M. Gelfand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and ...
Prominent Russian mathematician's concise, well-written exposition considers: n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, introduction to tensors, more. 1961 edition.
'All through both volumes ["Functions & Graphs" and "The Methods of Coordinates"], one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ...very fortunate that an account of this caliber has finally made it to ...
'All through both volumes ["Functions & Graphs and The Methods of Coordinates"] , one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ...very fortunate that an account of this caliber has finally made it to ...
Focusing on theory more than computations, this 3-part text covers sequences, definitions, and methods of induction; combinations; and limits, with introductory problems, definition-related problems, and problems related to computation limits. Answers and hints to the test problems are provided; "road signs" mark passages requiring particular ...
From the Preface (1960): "This book is devoted to an account of one of the branches of functional analysis, the theory of commutative normed rings, and the principal applications of that theory. It is based on [the authors'] paper written...in 1940, hard on the heels of the initial period of the development of this theory..."The book consists of ...
I.M. Gelfand, one of the leading contemporary mathematicians, largely determined the modern view of functional analysis with its numerous relations to other branches of mathematics, including mathematical physics, algebra, topology, differential geometry and analysis. With the publication of these Collected Papers in three volumes Gelfand gives a ...
The unifying theme of this collection of papers by the very creative Russian mathematician I. M. Gelfand and his co-workers is the representation theory of groups and lattices. Two of the papers were inspired by application to theoretical physics; the others are pure mathematics though all the papers will interest mathematicians at quite opposite ...
The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. ...
As early as 1917, Radon derived an explicit formula for the reconstruction of a function on the plane, given its integrals over all lines. In the late 1960s, the first applications of the Radon formula appeared, in radio astronomy and then in electron micrography. The use of the Radon formula for constructing tomograms, made possible by the advent ...
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