Little Mathematics Library – Fascinating Fractions

Posted on September 13, 2012 by damitr 
The theory of continued fractions is vast. This booklet covers 
only its fundamentals, but it contains everything that may be 
useful for a layman interested in mathematics.

One more addition to the Little Mathematics Library series. In this post we see Fascinating Fractions by N. M. Beskin.

This booklet is intended for high-school students interested
in mathematics. It is concerned with approximating real
numbers by rational ones, which is one of the most captivating
topics in arithmetic.

…
Continued fractions represent one of the most perfect
creations of 17-18th century mathematicians: Huygens, Euler,
Lagrange, and Legendre. The properties of these fractions
are really striking.

The following should be borne in mind when reading this
booklet. Topics easily understandable are presented in normal print,
while those more difficult are given in small print. Proofs of some theorems given in small print may be omitted safely. These theorems will necessarily be taken for granted. However, mathematics is not just reading for entertainment. A future mathematician as well as a physicist or an engineer has to acquire skill in dealing with  mathematical constructions and proofs. So take a pencil and a sheet of  paper and study carefully the topics given in small print. You may succeed in simplifying some proofs or finding better ones.

The book was translated from the Russian by V. I. Kisin and was first published by Mir Publishers in 1986.

DJVU | OCR | Bookmarked |  Cover | 827 KB (Zip 823) | 88 pp

All credits to the original uploader, thanks to KS for the link.

You can get the book here. and here

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Problems in Elementary Physics – Bukhovtsev et al.

Posted on September 11, 2012 by damitr

We now come to Problems in Elementary Physics by B. Bukhovtsev, V. Krivchenkov, G. Myakishev, and V. Shalnov.

This collection of 816 problems is based on the textbook “Elementary Physics” edited by Academician G. S. Landsberg. For this reason the content and nature of the problems and their arrangement mainly conform with this textbook. There is no section devoted to “Atomic Physics”, however, since the exercises in Landsberg’s book illustrate the relevant material in sufficient detail. Some problems on this subject have been included in other chapters. The problems, most of which are unique, require a fundamental knowledge of the basic laws of physics, and the ability to apply them in the most diverse conditions. A number of problems in the book have been revised from those used at the annual contests organized by the Physics faculty of the Moscow University. The solutions of all the difficult problems are given in great detail. Solutions are also given for some of the simpler ones. The book is recommended for self-education of senior pupils of general and special secondary and technical schools. Many problems will be useful for first and second year students of higher schools.

The book was translated from the Russian by A. Troitsky and was edited by G. Leib. Mir Publishers published this book first in 1971 and was reprinted again in 1978. The link below is for the 1978 edition.

PDF | OCR | Bookmarked | Pagination | Cover | 27.6 MB (Zip 24.7) | 443 pp | 600 dpi

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Collection of Problems in Theoretical Mechanics – Meshchersky

Posted on September 11, 2012 by damitr 
It should be noted that most of the problems, chosen for this
collection, are not only an illustration of the theoretical 
material, but are well in accord with the materials which serve
as a bridge between theoretical mechanics and intermediate 
sciences.

We now come to another Problem Book in Physics this one is exclusively for theoretical mechanics: Collection of Problems in Theoretical Mechanics by I. V. Meshchersky.

The present edition embraces all basic principles of theoretical
mechanics usually taught during the first two years of studies in
higher and secondary technical schools. The material in this book is presented consistently, i, e., proceeding from the particular to the general. The same method is applied to the order of paragraphs and the arrangement of the text.

…

It should be noted that most of the problems, chosen for this
collection, are not only an illustration of the theoretical material, but are well in accord with the materials which serve as a bridge between theoretical mechanics and intermediate sciences.

The primary objective of the book was to present to the reader
problems of practical value by giving the examples in such fields as the operation of machines and mechanisms, hydrodynamics, resistance of materials, and other branches of science and engineering. All this has made the book widely popular among the Soviet students of technical schools.

…

The material collected in this book will aid students in the
practical application of laws and methods of theoretical mechanics in their engineering practice.

The book was translated from the Russian by N. M. Sinelnikova and edited by A. I. Lurie and the supplementary material: Solutions of Some Typical Problems is written by V. I. Kuznetsov. The other contributors to this edition are S. A. Sorokov (statics), N. N. Naugolnaya and A. S. Kelson (kinematics), A. S. Kelson (dynamics of a particle), M. I. Baty (dynamics of a system), G. J. Djanelidze (analytical statics, dynamics of bodies having variable masses, stability of motion). The book is an abridged version of the 28th edition of the book by Meshchersky published in 1962. This book was published by Higher School Publishing House in the 1968 (as per worldcat record, no date in the book). Dover also published this book in 1965.

PDF | OCR | Bookmarked | Paginated | Cover | 21.9 MB (Zip 19.2 )| 307 pp | 600 dpi

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Problems in Physics – Pinsky

Posted on September 11, 2012 by damitr

We now come to Problems in Physics by A. A. Pinksy. This is the accompanying “Problem Book” to the  two volume set Fundamentals of Physics by A. A. Pinksy and B. M. Yavorvsky (which we might see soon!), who is also the co-author of A Modern Handbook of Physics and Handbook of Physics with A. A. Detlaf.

This book offers the reader over 750 problems concerning the same subject matter as is treated in the two volumes of  the “Fundamentals of Physics”. The order of presentation of the theoretical material is also the same.
The availability of a great number of problem books based on the traditional school physics curriculum prompted us to enlarge those sections which are absent from traditional problem books, namely the dynamics of a rotating rigid body, the elements of the theory of relativity and of quantum and statistical physics, of solid-state physics, wave optics, atomic and nuclear physics, etc. Problems dealing with astrophysics illustrate the application of the laws of physics to celestial bodies.
The book contains a few problems requiring elementary
skill in differentiating and integrating, as well as some problems
to be solved with the aid of numerical methods, which
nowadays are being increasingly used.

The book was translated from the Russian by Mark Samokhvalov and was first published by Mir Publishers in 1980.

PDF | OCR | Cover | Pagination | Bookmarked | 342 pp | 600 dpi | 21.5 MB (Zip 19.4)

You can get the book here. and here

Update: Posted Internet Archive Links 03 December 2015, file parameters might be different than listed above.

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A Collection of Questions and Problems in Physics – Sena

Posted on September 11, 2012 by damitr 
I believe that if you have solved or studied the solution of a 
large number of problems, the basics of the physical method of 
thinking have become clearer.

We now come to A Collection of Questions and Problems in Physics by L. A. Sena.

The aim of the present collection of questions and problems is to develop practical skills during study of one of the fundamental sciences, physics. The Collection is intended for the self-instruction of students of technical colleges. The best way to use it is to solve the problems while preparing for term exams.

The Collection contains more than 400 questions and problems covering all the sections of the physics course. All questions and problems have detailed answers and solutions. For this reason the two main sections of the book, Questions and Problems and Answers and Solutions, have identical headings and numbering: each chapter in the first section has a corresponding chapter in the second, and the numbering of answers corresponds to the numbering of problems.

A special feature of the Collection is the drawings and diagrams for most of the questions and answers. The diagrams use a variety of scales: linear, semilog, log-log, and quadratic.

Arrangement of the material in this Collection corresponds to the structure most commonly used in college physics textbooks. One exception is the questions and problems involving the special theory of relativity. These are placed in different chapters, starting from the one dealing with mechanics.

The book was translated from the Russian by Eugene Yankovsky and was first published by Mir Publishers in 1988.

PDF | OCR | Cover | Pagination | Bookmarked | 344 pp | 600 dpi | 23.8 MB (Zip 20.9)

Update 7 May 2018: The Internet Archive link

and here

 

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Update: The book is in print and available here. Price is INR 80.

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Problems in General Physics – Wolkenstein

Posted on September 11, 2012 by damitr 
When solving a problem, first of all establish the physical
laws which it is based on. Then use the formulas expressing
these laws to solve the problem in symbols, and finally 
substitute the numerical data in one system of units.

We now come to another book in the Problem Book series by Valentina Wolkenstein titled Problems in General Physics.

This collection of problems is based on the International System
of Units preferred today in all the fields of’ science, engineering
and economy. Other units can be converted to 51 units with the aid of the relevant tables given in this book.
Each section is preceded by a brief introduction describing the
fundamental laws and formulas which are used to solve the problems. The solutions to the problems and the reference data are appended at the end of the book.

The book was translated from the Russian by A. Troitsky and was edited by G. Leib. The book was first printed by Mir Publishers in 1971, and fourth reprint appeared in 1987. The link below is for the 1987 edition. Incidentally there is a Hindi translation of this book. I do not know if it was translated in other Indian languages. (We have digitised the book as of 2024)

PDF | OCR | Pagination | Cover | Bookmarked | 382 pp | 600 dpi | 27.4 MB (Zip 24.7)|

You can get the book here. and here

Update: 08 December 2015 | Added Internet Archive Link

Update 11 June 2026 | Added Hindi version link

You can get the book in Hindi here. and here

 

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Problems in Physics – Zubov, Shalnov

Posted on September 10, 2012 by damitr

We now come to the much anticipated “Problem Books” series and start with Problems in Physics by V. Zubov and V. Shalnov. This will be a good material for those who are preparing for Olympiads and other competitive exams.

For the most part, this is a collection of modified problems
discussed in extracurricular circles and at tutorials and
Olympiads at the Moscow University.
In selecting and preparing the problems for this collection
the authors attempted to focus the attention of the reader
on those postulates and laws of physics where students make
the most mistakes. Some problems were specially selected
to explain comprehensively the application of the most
important laws – something which students often fail to
grasp properly. A number of problems concern the subjects
usually omitted in secondary school text-book problems.
Some problems are intended for discussion in extracurricular
circles or for independent study by those wishing to
acquaint themselves with material beyond the scope of the
school syllabus.
The most difficult problems and the problems outside
the scope of the secondary school syllabus are provided
with detailed explanations in order to give the student
a better understanding of the general principles of solution.
With this end in view, some sections are also supplemented
with brief information about the most frequent mistakes
and the simplest means of solution.

The book was translated from the Russian by A. N. Troitsky and the translation was edited
by J. B. Williams. Mir Publishers published this book first time in 1974 with a second reprint in 1985. The link below is for the second print.

PDF | OCR | Pagination | Bookmarked | 301 pp | 600 dpi | 19.3 MB (17.4 Zipped)

You can get the book here. and here

Update: 08 December 2015 | Added Internet Archive Link

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Little Mathematics Library – Taking Stock

Posted on September 6, 2012 by damitr

We take stock of what we have and what remains to be had in the Little Mathematics Library series. There is only 1 (updated 25 Oct 21) 4 5 (+ 1 in bad condition) titles remaining, they are marked in red, so if you have any of these please let us know.

Update: 11 May 2024, as of now all the books listed here are available!!

Or if you know of any book that is missing please let us know.

Of course anything like this would not have been possible if, there were not all others  who preceded us in goodwill and thought. These are people whom we don’t know and maybe won’t ever know, it is due to them that most of titles are with us.

Dedicated to Smiley and team. We all owe it to you!

Update: Thanks to Biju all the files can be found at one place (4shared), here.

Or a single link for all the files here. (52.3 MB)

Password for these files:

www.mirtitles.org

Algebraic Equations of Arbitrary Degrees – A. G. Kurosh

An Unusual Algebra – I. M. Yaglom (Have copy, to be scanned.)

Areas and Logarithms – A. I. Markushevich

Calculus of Rational Functions – G. E. Shilov

Complex Numbers and Conformal Mappings – A. I. Markushevich

Differentiation Explained – V. G. Boltyansky

Dividing A Line Segment in Given Ratio – N. M. Beskin

Elements of Game Theory – Ye. Venttsel

Fascinating Fractions – N. M. Beskin (Thanks to KS for link, we have it now)

Geometrical Constructions With Compasses Only – A. Kostovskii

(Thanks to Saugata for pointing this, we do have the PLM version, will soon release.)

Update: PLM version released, still need to get LML version. 

Link updated with LML version, thanks to 4evercla6 (26 October 2021)

Gödel’s Incompleteness Theorem – V. A. Uspensky

Images of Geometric Solids – N. M. Beskin

Induction in Geometry – L. I. Golovina, I. M. Yaglom

Inequalities – P. P. Korovkin

Lobachevskian Geometry – A. S. Smogorzhevsky

Method of Successive Approximations – N. Ya. Vilenkin

Pascal’s Triangle – V. A. Uspensky

Plotting Graphs – G. E. Shilov

Post’s Machine –  V. A. Uspensky

Proof In Geometry – A. I. Fetisov

Recursion Sequences – A. I. Markushevich

Remarkable Curves – A. I. Markushevich 

Solving Equation In Integers – A. O. Gelfond

Stereographic Projection – A. I. Markushevich, B. A. Rosenfeld, N. D. Sergeeva

Systems of Linear Equations – L. A. Skornyakov 

(Update 25 October 2021)

Systems of Linear Inequalities – A. S. Solodovnikov

The Euler Characteristic – Yu. A. Shaskin

(Update 11 May 2024, Thanks to Anonymous commentator on the blog, we have this last piece of the series)

The Fundamental Theorem of Arithmetic – L. A. Kaluzhnin

The Kinematical Method in Geometrical Problems – Yu. I. Lyubich, L. A. Shor

(Update 26 October 2021)

The Method of Coordinates – A. S. Smogorzhevsky

The Method of Mathematical Induction – I. S. Somisnky

The Monte Carlo Method – I. M. Sobol

The Shortest Lines – L. A. Lyusternik 

(Update 27 October 2021)

 

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Little Mathematics Library – Solving Equations In Integers

Posted on September 6, 2012 by damitr

In the Little Mathematics Library series we now come to Solving
 Equations In Integers by A. O.  Gelfond also sometimes written as
Gelfand.

The book is devoted to one of the most interesting branches of
number theory, the solution of equations in integers. The solution in integers of algebraic equations in more than one unknown with integral coefficients is a most difficult problem in the theory of numbers. The theoretical importance of equations with integral coefficients is quite great as they are closely connected with many problems of number theory. Moreover, these equations are sometimes encountered in physics and so they are also important in practice. The elements of the theory of equations with integral coefficients as presented in this book are suitable for broadening the mathematical outlook of high-school students and students of pedagogical institutes. Some of the main results in the theory of the solution of equations in integers have been given and proofs of the theorems involved are supplied when they are sufficiently simple.

The book was translated the Russian by O. B. Sheinin and was
first published by Mir in 1981.

PDF | Cover | Bookmarks | OCR | 3.2 MB | 60 pp | 600 dpi

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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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