Little Mathematics Library – Induction in Geometry

Posted on January 30, 2012 by damitr

After a break we being with our postings again. To start, we will see a title in the Little Mathematics Library which is a`natural continuation’ of last post, this one is called Induction in Geometry and the authors are L. I. Golovina and I. M. Yaglom.  One of the authors, I. M Yaglom,  has written many excellent books in mathematics, we will maybe try to cover them in the future.

The preface says:

This little book is intended primarily for high school pupils, teachers of mathematics and students in teachers training colleges majoring in physics or mathematics. It deals with various applications of the method of mathematical induction to solving geometric problems and was intended by the authors as a natural continuation of I. S. Sominsky’s booklet  The Method of Mathematical Induction published (in English) by Mir Publishers in1975. Our book contains 38 worked examples and 45 problems accompanied by brief hints. Various aspects of the method of mathematical induction are treated in them in a most instructive way. Some of the examples and problems may be of independent interest as well.

The book was translated from the Russian by Leonid Levant and was first published by Mir in 1979. This was also published in the Topics in Mathematics series in 1963, and was translated by A.W. Goodman and Olga A. Titelbaum.

You can get the book here and here.

The book contains following sections:

Introduction: The Method of Mathematical Induction 7

Sec. 1. Calculation by Induction 12

Sec. 2. Proof by Induction 20

Map Colouring 33

Sec. 3. Construction by Induction 63

Sec. 4. Finding Loci by Induction 73

Sec. 5. Definition by Induction 80

Sec. 6. Induction on the Number of Dimensions 98

1. Calculation bv Induction on the Number of Dimensions 106
2. Proof by Induction on the Number of Dimensions 109
3. Finding Loci by Induction on the Number of Dimensions 126
4. Definition by Induction on the Number of Dimensions 130

References 132

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Little Mathematics Library – The Method of Mathematical Induction

Posted on January 5, 2012 by damitr

In the Little Mathematics Library we now come to the book called The Method of Mathematical Induction by I. S. Sominsky (aka Sominskii).

In the foreword it is said:

The method of mathematical induction, which is the subject of this book, is widely applicable in all departments of mathematics, from the elementary school course up to branches of higher mathematics only lately investigated. It is clear, therefore, that even a school course of mathematics cannot be studied seriously without mastering this method. Ideas of mathematical induction, moreover, have a wide general significance and acquaintance with them also has an importance for those whose interests are far removed from mathematics and its applications.

…

This book is meant for pupils in the higher forms of secondary schools, first year students in universities, teacher training colleges and technical colleges. It would also be useful for discussion in a school mathematical society.

The book was translated from Russian by Martin Greendlinger and was first published by Mir in 1975. Previous to that this booklet was also published in the West under the series of Topics in Mathematics (TiM) and also under Popular Lectures in Mathematics (PLM) Vol. 1. The link below is from the PLM version and was translated by Halina Moss, and was edited by I. N. Sneddon ans was published by Pergamon in 1961.

The essentials of the method and some simple examples of its use are given in Chapter I and in the first section of Chapter II. To study these it is sufficient for the reader to be familiar with the course of mathematics in the seven year school period. The remaining sections of this book are fully accessible to the reader who has mastered the mathematics course of a full secondary school.

All credits to the original uploader.

Update: 11 December 2015 | Added Internet Archive Link

You can get the book here.

Update: 10 October 2021 | Added PLM Link

The book was also published as a part of Popular Lectures in Mathematics series in 1961.

PLM version here.

Contents:

Foreword vii

INTRODUCTION  1

CHAPTER I
The Method of Mathematical Induction 3

CHAPTER II
Examples and Exercises  12

CHAPTER III
The Proof by Induction of Some Theorems of Elementary Algebra 39

CHAPTER IV
Solutions 45

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Little Mathematics Library – Stereographic Projection

Posted on January 4, 2012 by damitr

We now come to another book in the Little Mathematics Library titled Stereographic Projection by B. A. Rosenfeld and N. D. Sergeeva. As the title suggests the book deals with projections on planes.

The present booklet is devoted to proofs of the aforesaid properties of the stereographic projection and to the presentation of some of its applications. The booklet consists of eight sections dealing with different properties of projections. …The booklet is aimed to be used in the senior grades of the high schools and by the first- and second-year students.

The book was translated from the Russian by Vitaly Kisin and was first published by Mir in 1977.  All credits to the original uploader.

The Internet Archive Link

and here

Continue reading →

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Little Mathematics Library – Method of Successive Approximations

Posted on January 3, 2012 by damitr

In the Little Mathematics Library we now come to Method of Successive Approximations by N. Ya. Vilenkin. As the title suggests the book has to do with approximation methods, but what kind of approximations and for what kind of use one may ask?

The preface of the book reads:

The main purpose of this book is to present various methods of approximate solution of equations. Their practical value is beyond doubt, but still little attention is paid to them either at school or a college and so someone who has passed a college level higher mathematics course usually has difficulty in solving a transcendental equation of the simplest type. Not only engineers need to solve equations, but also technicians, production technologists and people in other professions as well. It is also good for high-school students to become acquainted with the methods of approximate solution of equations. Since most approximate solution methods involve the idea of the derivative we were forced to introduce this concept. We did this intuitively, making use of a geometric interpretation. Hence, a knowledge of secondary school mathematics will be sufficient for anyone wanting to read this book.

The book was translated from the Russian by Mark Samokhvalov and was first published by Mir in 1979. All credits to the original uploader.

The Internet Archive Link

and here

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Little Mathematics Library – Gödel’s Incompleteness Theorem

Posted on January 2, 2012 by damitr

After the last two posts by V. A. Uspenskii (check out his site here) which dealt with Post’s Machine, and Pascal’s Triangle, we now come to another book by him in the Little Mathematics Library series titled Gödel’s Incompleteness Theorem.

The back cover of the book reads:

 Few discoveries have had as much impact on our perception of human thought as Gödel’s proof in 1930 that any logical system such as usual rules of arithmetic, must be inevitably incomplete, i.e., must contain statements which are true but can never be proved. Professor Uspensky’s makes both a precise statement and also a proof of Gödel’s startling theorem understandable to someone without any advanced mathematical training, such as college students or even ambitious high school student. Also, Uspensky introduces a new method of proving the theorem, based on the theory of algorithms which is taking on increasing importance in modern mathematics because of its connection with computers. This book is recommended for students of mathematics, computer science, and philosophy and for scientific layman interested in logical problems of deductive thought.

The book was translated from the Russian by Neal Koblitz and was first published by Mir in 1987.

Thanks to hawa-ka-jhonka who made this book accessible.

The Internet Archive Link

and here

For magnet / torrent links go here.

Continue reading →

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Little Mathematics Library – Pascals Triangle

Posted on January 2, 2012 by damitr

In continuing from the last post on Post’s Machine by V. A. Uspenskii (sometimes Uspensky) we come to another volume by him titled Pascals’s Triangle.

The book opens with an interesting note

The reader who is not familiar with Pascal’s triangle should be warned that it is not a geometric triangle with three angles and three sides. What we call Pascal’s triangle is an important numerical table, with the help of which a number of computation problems may be solved. We shall examine some of these problems and shall incidentally touch upon the question of what “solving a problem” can mean in general.

This exposition requires no preliminary knowledge beyond the limits
of the eighth-grade curriculum, except for the definition of and notation for the zeroth power of a number. That is, one must know that any non-zero number, raised to the zeroth power, is considered (by definition!) to be equal to unity: a0 = 1 for a ≠ 0.

The book was published by Mir in the Little Mathematics Library in 1976. But earlier in the West many books from this series were translated and published by University of Chicago Press under the series Popular Lectures in Mathematics. This particular title was translated from the Russian by David J, Soonke and Timothy McLarnan and was published in 1974.

You can get the book here (PLM version here.)

and here

All credits to the original uploader.

Continue reading →

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Little Mathematics Library – Post’s Machine

Posted on December 28, 2011 by damitr

We start our posts in the Little Mathematics Library series with a book by V. A. Uspensky titled Post’s Machine.

This booklet is intended first of all for school children. The first two chapters are comprehensible even for junior schoolchildren. The book deals with a certain “toy” (“abstract” in scientific terms) computing machine – the so called Post machine – on which calculations involve many important features inherent in the computations on real electronic computers. By means of the simplest examples the students are taught the fundamentals of programming for the Post machine, and the machine, though extremely simple, is found to possess quite high potentialities.The reader is not expected to have any knowledge of mathematics beyond the primary school curriculum.

The book was translated from the Russian by R. Alavina and was first published by Mir in 1983.

All credits to the original uploader.

The Internet Archive Link

and here

Continue reading →

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Let’s Play Geometry

Posted on December 28, 2011 by damitr

[The aim of the book] is to acquaint children in exciting and stimulating way with some of principle concepts of geometry, to teach them how to find bearings in simple geometrical situations and to discern geometrical patterns in the world around them.

In this post we will be looking at a book from which I have many fond memories. This book is titled Lets Play Geometry by L. N. Shevrin and V. G. Zhitomirsky. The book is written in the style of A Book About Stars and Planets which we have seen already.

The back cover of the book says:

Through fascinating stories and rhymes, young readers are introduced to some elementary geometry. The book is made up of adventures which bring in the theory, and some exercises to develop the topics. It is written in a simple and attractive language, and is particularly well-suited to 5-8-year olds

The book is intended for children and to be read to them by an adult. The activities “hands-on” and “minds-on” that are suggested in the book are amazing. I had a copies of this book in English and Marathi, and also know that there is a Hindi translation. I do not know if there are other translations in Indian languages.

The book was translated from the Russian by Alexander Repyev and was first published by Mir in 1985. Thanks for Gordon to bring this copy to my notice and all credits to gnv64 for the book.

You can get the book here and here.

Update: Added Internet Archive Link | 04 December 2015

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Science for Everyone – Taking Stock

Posted on December 23, 2011 by damitr

The last post In the World of Binary Stars, completed the titles of Science for Everyone series that were accessible. When the original post was made with the listings we had listed 37 titles, out of which many are posted already. In this post I will make a stock of what has been accomplished and what remains to be done. Any inputs of how and where to get to the remaining books in this series would be greatly appreciated. This effort would not have been possible without all the people who have given their help, advise and support, mental, physical or otherwise. All credits to the respective, original uploaders! Thanks to all!!

The listing below is done year wise. The books that are with us are presented with links and the books that are not and are in red text and we need to get them.

Only 4 to go!

Update: Science for Everyone all files in one place here.

Password: http://www.mirtitles.org

Thanks to Desperaomar for these links.

Update Jan 2020: We have added four more titles. Only one Earth, Sweet Earth remains now.

 

Aptitude Test Problems in Physics S. S. Krotov [Ed.] 1990

Differential Equations in Applications V. V. Amel’kinn 1990

Discussions on Refraction of Light L. V. Tarasov, A. N. Tarasova 1984

Earth, Sweet Earth Ekaterina Radkevich 1990

Electrons and Crystals Th. Wolkenstein 1985

Elementary Kinematics of Elementary Particles G. I. Kopylov 1983

Encounters with Physicists and Physics I.K. Kikoin. 1989

Ethology What animals do and Why Igor Akimushkin 1988 (Link added 08-10-2013)

Flying Trains G. Zelkin 1986

How We See What We See V. Demidov 1986

In The World of Binary Stars V. N. Lipunov 1989

Learning About Chemistry G. B. Shul’pin. 1989 (Link added 20-10-2013)

Luminescence in Public Health N. N Barashkov 1988

Me or Not Me R. V. Petrov 1987

Modern Geology N.A. Yasamanov 1990

Mystery of Minerology B.I. Srebrodolsky 1989

Origin and Chemical Evolution of the Earth G.V. Voitkevich 1988

(Got the hard copy to be scanned)

Origin and Development of Life on Earth G.V. Voitkevich 1988

Our Planet – The Earth A.V. Byalko. 1987

Physics and Geometry of Disorder: Percolation Theory A. L. Efros 1986

Physics In Your Kitchen Lab I. K. Kikoin (Ed.) 1985

Problems in Plane Geometry I. F. Sharygin 1986

Problems in Solid Geometry I. F. Sharygin 1986

Puppets Without Strings V.I. Varshavsky, D.A. Pospelov 1988

(Got the hard copy to be scanned)

Physical Paradoxes and Sophisms V. N. Lange 1987

Satellite and Typhoon : Eye to Eye S.N. Baibakov and A.I. Martynov 1987

Semiconductors Made Simple A. M. Polyakov 1985

Silhouettes of Chemistry D. N. Trifonov, L. G. Vlasov 1987

Storming The Fortress of Fusion G. S. Voronov 1988

Traces of Bygone Biospheres A. V. Lapo 1987

Temperature Ya. A. Smorodisnky 1984

The Grand Biological Clock V.M. Dilman 1989

The Greatest Speed S.R. Filonovich 1986

The Nature of Magnetism M.I. Kaganov, V.M. Tsukernik 1985

This Fascinating Astronomy V. N. Komarov 1985

The Progeny of Volcanoes P.N. Erofeev 1986

Yes, No or Maybe Ya. I Khurgin 1985

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Science for Everyone – In The World of Binary Stars

Posted on December 23, 2011 by damitr

In the Science for Everyone series we now go to a journey In The World of Binary Stars by V. M. Lipunov. This book discusses many things about the binary stars and the exotic things that they can lead to. White dwarfs, neutron stars, black holes, X-ray pulsars you name it and this book has it. In all it gives you a very substantial overview of the field of binary stars. A must read for all the astro-enthusiasts: Clear Skies!

The back cover of the book says following:

Binary stars contain some of the most exotic objects in the sky. This is an exciting account about binary stars and the way black holes, white dwarfs, and neutron stars can evolve in them. It is, moreover, a short history of the ideas and discoveries that led to our current understanding of this fascinating heavenly object the binary.

This book was translated from the Russian by Alexander A. Kandaurov and was first published by Mir in 1989. Thanks to hawa-ka-jhonka for making this book accessible.

Update: Jan 2020

The Internet Archive Link

and here

 

Continue reading →

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