Little Mathematics Library – Systems of Linear Inequalities

Posted on September 6, 2012 by damitr

In the Little Mathematics Library series we now come to  Systems of
Linear Inequalities by A. S. Solodovnikov.

The book tells about the relation of systems of linear
inequalities to convex polyhedra, gives a description of the
set of all solutions of a system of linear inequalities,
analyses the questions of compatibility and
incompatibility; finally, it gives an insight into linear
programming as one of the topics in the theory of
systems of linear inequalities. The last section but one
gives a proof of duality theorem of lienar programming.
The book is intended for senior pupils and all amateur
mathematicians.

The book was translated the Russian by Vladimir Shokurov and was
first published by Mir in 1979.

PDF | Cover | Bookmarks | OCR | 7.3MB | 130 pp | 600 dpi

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Little Mathematics Library – The Method of Coordinates

Posted on September 6, 2012 by damitr 
The size and aim of the book has forced us to restrict ourselves 
to an account of the basic facts about the method of coordinates
and its simplest applications.

In the Little Mathematics Library series we now come to Method of
Coordinates by A. S. Smogorzhevsky.

The booklet deals with a fundamental method of analytical
geometry and its ability to describe geometrical figures
through equations. This method permits geometrical study
and solution of geometrical problems by algebraic means,
thus making a visual representation of complex spatial
configurations superfluous. Considerable attention has been
devoted to the question of representing geometrical figures
through equations, which is often difficult for those who
being to study the method of coordinates.
Detailed examples have been given to illustrate the
application of the method. The booklet is intended for senior school chidlren and all those interested in mathematics.

The book was translated the Russian by Ram S. Wadhwa and was
first published by Mir in 1980.

PDF | Cover | Bookmarks | OCR | 2.4 MB | 52 pp | 600 dpi

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Little Mathematics Library – Plotting Graphs

Posted on September 6, 2012 by damitr 
The graph of the sine, wave after wave,
Flows along the axis of abscissas...
(FROM STUDENT LORE)


In the Little Mathematics Library series we now come to Plotting
 Graphs by G. E. Shilov. We have already seen another book by Shilov,
namely, Calculus of Rational Functions. The section on graphs in that
book is similar to this booklet.

… we shall be dealing here with graphs of a different kind, with
graphs that must be plotted from given mathematical formulas. A need for such graphs often arises in various fields of knowledge. Thus, in analysing the theoretical course of some physical process, a scientist obtains a formula yielding some magnitude with which he is concerned, for example, the amount of product obtained relative to time. The graph plotted from this formula will provide a clear picture of the future process. Looking at it, the scientist may possibly introduce substantial changes into the scheme of his experiment in order to obtain better results.

In this booklet we shall consider some simple methods of plotting graphs from given formulas.

The book was translated the Russian by S. Sosinsky and was first published by Mir in 1978.

PDF | Cover | Bookmarks | OCR | 1.1 MB | 36 pp | 600 dpi

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Little Mathematics Library – Inequalities

Posted on September 6, 2012 by damitr

In the Little Mathematics Library series we now come to Inequalities by P. P. Korovkin.


In this booklet the author did not pursue the aim of presenting the  basic properties of inequalities and made an attempt only to
familiarize students of senior classes with some particularly
remarkable inequalities playing an important role in various sections of higher mathematics and with their use for finding the greatest and the least values of quantities and for calculating some limits.  The book contains 63 problems, 35 of which are provided with detailed solutions, composing thus its main subject, and 28 others are given in Sections 1.1 and 2.1, 2.3, 2.4 as exercises for individual training. At the end of the book the reader will find the solutions to the given exercises.

The book was translated the Russian by Sergei Vrubel and was  first published by Mir in 1975.

PDF | Cover | Bookmarks | OCR | 3.2 MB | 74 pp | 600 dpi

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Little Mathematics Library – The Fundamental Theorem of Arithmetic

Posted on September 6, 2012 by damitr

In the Little Mathematics Library series we now come to Fundamental Theorem of Arithmetic by L. A. Kaluzhnin.


In this booklet, Prof. Kaluzhnin deals with one of the fundamental propositions of arithmetic of rational whole numbers – the uniqueness of their expansion into prime  multipliers. Having established a conncetion between arithmetic and Gaussian numbers and the question of representing integers as sum of squares, Prof. Kaluzhnin has shown the uniqueness of expansion also holds in the arithmetic of complex (Gaussian) whole numbers.  The author hopes that the booklet will not only be of interest to senior schoolboys but will also be useful for teachers.

The book was translated the Russian by Ram S. Wadhwa and was
first published by Mir in 1979.

PDF | Cover | Bookmarks | OCR | 2.8 MB | 44 pp | 600 dpi

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Little Mathematics Library – Elements of Game Theory

Posted on September 6, 2012 by damitr

In the Little Mathematics Library series we now come to Elements of  Game Theory by Ye. S. Venttsel.


This book treats in a popular manner the elements of game theory and some methods for solving matrix games. It contains almost no proofs and illustrates the basic principles with examples. To be able to read the book, an acquaintance with the elements of probability theory and calculus is enough. The book is intended to disseminate the ideas of game theory which have practical economic or military applications.

The book was translated the Russian by Vladimir Shokurov and was  first published by Mir in 1980.

PDF | Cover | Bookmarks | OCR | 3.8 MB | 76 pp | 600 dpi

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Little Mathematics Library – Dividing A Line Segment in Given Ratio

Posted on September 6, 2012 by damitr 
There is no branch of mathematics such that one could have the right
to say: "I have complete knowledge of this". The most elementary
problem has hidden in it unexpected connections with other problems,
and this process of going deeper and deeper into a problem has no end.


In the Little Mathematics Library series we now come to Dividing A
Segment In A Given Ratio by N. M. Beskin.

The booklet describes various theories to which a deep study of the problem of dividing a line segment in a given ratio  leads. Considering this elementary and those related to it, the  reader will make a short travel over some branches of mathematics come into contact with affine and projective geometry and the theory of groups, though in most cases without mentioning those names.  The book is intended for pupils of the senior forms; in its main parts it can be easily grasped by pupils of the seventh and eighth forms.

The book was translated from the Russian by V. Zhitomirsky and was
first published by Mir in 1975.

PDF | Cover | Bookmarks | OCR | 4.4 MB | 76 pp | 600 dpi

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Little Mathematics Library – Complex Numbers and Conformal Mappings

Posted on September 6, 2012 by damitr 
The book, containing a wealth of illustrative material,
acquaints the reader with complex numbers and operations 
on them and also with conformal mappings, that is mappings
which preserve the angles (they are employed in cartography, 
mechanics, physics).

After seeing two books Areas and Logarithms | Remarkable Curves we now come to Complex Numbers and Conformal Mappings by A. I. Markushevich in the  Little Mathematics Library. We will in the future see more books from him.

The book acquaints the reader with complex numbers and
functions of a complex argument (including Zhukovsky’s function as applied to the construction of a wing section). The material is presented in a geometric form. Complex numbers are considered as directed line segments and functions as mappings. To prepare the reader to such an understanding of complex numbers, we begin with a geometric interpretation of real numbers and operations on them. The book is based on a lecture delivered by the author to high-school students. To read the book, the reader need not be acquainted with complex numbers.

It is intended for all those who are
interested in mathematics and primarily for high-school
students, it can also be of use for self-education. For proper
comprehension of the content of the book the reader must posses
high-school knowledge of mathematics.

The book was translated from the Russian by Irene Aleksanova and was first published by Mir in 1982. This book was also part of the Public Lectures in Mathematics – Volume 8 (PLM) which was published in 1960’s. Link below is for the Mir version.

PDF | OCR | Cover | Bookmarked | 4.4 MB | 68 pp | 600 dpi

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Little Mathematics Library – Calculus of Rational Functions – Shilov

Posted on September 5, 2012 by damitr 
If, however, we restrict ourselves to a comparatively
narrow class of rational functions and utilize the 
illustrative language of graphs, we can present the 
concepts of derivative and integral in a few pages, 
sufficiently accurately and at the same time pithily.

We now come to Calculus of Rational Functions by G. E. Shilov in the  Little Mathematics Library.

The pamphlet “Calculus of Rational Functons” discusses
graphs of functions and the differential and integral calculi
as applied to the simplest class of functions, viz. the rational
functions of one variable. It is intended for pupils of senior
forms and first year students of colleges and universities.

The book was translated from the Russian by V. I. Kisin and was first published by Mir in 1976 with a second reprint in 1982.

PDF | OCR | Cover | Bookmarked | 3.9 MB | 62 pp | 600 dpi

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Little Mathematics Library – Areas and Logarithms

Posted on September 5, 2012 by damitr

We now come to Areas and Logarithms by A. I. Markushevich in the  Little Mathematics Library. We have already seen his remarkable book titled Remarkable Curves .

This book offers a geometric theory of logarithms, in
which (natural) logarithms are represented as areas of
various geometrical shapes. All the properties of
logarithms, as well as their methods of calculation, are
then determined from the properties of the areas. The
book introduces most simple concepts and properties of
integral calculus, without resort to concept of derivative.
The book is intended for all lovers of mathematics,
particularly school children.

The book was translated from the Russian by I. Aleksanova and was first published by Mir in 1981 with a second reprint in 1987. This book was also part of the Topics in Mathematics (TiM) and was published by D. C. Heath in 1963, This edition was translated from the first Russian version by Ronald S. Toczek and Reuben Sandler. Link is for the Mir 1987 edition, though the TiM edition is also available.

PDF | OCR | Cover | Bookmarked | 3.5 MB | 76 pp | 600 dpi

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