What is distance? (Popular Lectures in Mathematics) – Shreider

Posted on November 18, 2021 by The Mitr

In this post, we will see the book What Is Distance? by Yu. A. Shreider. This is part of Popular Lectures in Mathematics series.

About the book

This introduction to the theory of metric spaces carries the student through the motivation, development, and application of an abstract mathematical concept. Yu. A. Shreider begins with a definition of mathematical concepts and then, to motivate his definition of “ metric space,” the author evaluates distance functions and their properties in elementary geometry. After introducing two sets of metric space axioms, he surveys the properties of open balls, sequences, Cauchy sequences, complete metric spaces, and isometries. In the following chapter, the author offers a number of informative examples.

Professor Shreider turns next to applications of the theories, especially the theory of coding and cybernetics. Then returning to theory, the author defines an n-dimensional vector space over real numbers and develops the theory of norms and metrics
on Euclidean n-space. The final chapter considers the possibility of generalizing the concept of metric space.

The book was adapted from the Russian edition by Leslie Cohn and Harvey Edelberg
and was published in 1974.

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You can get the book here.

PS: This is the 500th post on the blog! Thanks for all the support over the years!

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Introduction vii

1. The Definition of Mathematical Concepts 1

2. Distance and Its Properties in Elementary Geometry 5

3. The Definition of a Metric Space and of Distance 11

4. Some Examples of Metric Spaces 18

5. The Space of Information 27

6. Automatic Correction of Errors in Messages 38

7. Metrics and Norms in Multi-dimensional Spaces 47

8. The Smoothing of Errors in Experimental Measurements 60

9. A More General Definition of Distance 65

Posted in books, popular lectures in mathematics, soviet | Tagged definition, distance, elementary distance, experimental measurements, general definition, general distance, geodesics, mathematics, metric spaces, metrics, multi-dimensional spaces, norms, popular lectures in mathematics, soviet, space | 1 Comment

The Legend Of The Stone Cutter by R. Kushnerovich

Posted on November 17, 2021 by The Mitr

In this post, we will see the book The Legend Of The Stone Cutter by R. Kushnerovich.

About the book

“The Legend of the Stonecutter” is a slide film released by Diafilm Studios. The screenplay by R. Kushrenovich has been based on a Tajik fairy tale.

The book was translated from Russian (by whom we don’t know 😦 perhaps author did the translation ) and the amazing illustrations are by A. Vinokurov and L. Shvartsman. The book was published in 1975 by Progress Publishers.

All credits to Guptaji.

You can get the book here (cleaned) and here.

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Posted in books, children's books, children's stories | Tagged children's book, children's literature, childrens book, clouds, elephant, illustrated book, illustrations, picture book, soviet, stone, story book, sun, tajik fairy tale, wind | Leave a comment

In The Van – Samuil Marshak

Posted on November 16, 2021 by The Mitr

In this post, we will see the book In the Van by Sanuil Marshak.

About the book

This little book tells you about a train journey of a wee little dog named Snooks!

The book was translated from Russian by Margaret Wettlin and the drawings by Vladimir Lebedev. The book was published in 1987 (second print) by Raduga Publishers.

All credits to Guptaji.

You can get the book here (cleaned) and here.

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Posted in books, children's books, children's stories, raduga publishers, soviet | Tagged books, children's, children's book, dogs, illustrated books, lady, picture book, snook, story book, trains | Leave a comment

Where The Birch Trees Grow – Victor Banykin

Posted on November 15, 2021 by The Mitr

In this post, we will see the book Where The Birch Trees Grow by Victor Banykin.

About the book

This story book tells the tales of Misha who learns a lot about nature, himself by making new friends while on vacation with his grandparents.

The book was translated from Russian by Tracy Kuehn and the drawings are by Anatoly Borisov. The book was published in 1985 by Raduga Publishers.

All credits to Guptaji.

You can get the book here (cleaned version) and here.

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MISHA’S VACATION

THE KAPUSTKIN BROTHERS 5

GRANDFATHER YEGOR AND GRANDMOTHER MARYA 9

LAKE VEDLOZERO 10

THE FISH 13

HELP! HELP! 14

TRICKY NINCHU 16

ON THE ISLAND 20

THE SEARCH FOR DAISY 21

BEST FRIENDS 24

GRANNY FISA

THE GREEN PIKE 25

GRANNY FISA 28

SUTTON’S TRICKS 32

CROW SWINGS 36

Posted in books, children's books, children's stories, raduga publishers, soviet | Tagged children's book, grandma, grandpa, illustrated book, picture book, raduga publishers, soviet, story book, vacation | Leave a comment

The Method Of Trigonometric Sums In The Theory Of Numbers – Vinogradov

Posted on November 14, 2021 by The Mitr

In this post, we will see the book The Method Of Trigonometric Sums In The Theory Of Numbers by I. M. Vinogradov.

About the book

Since 1934 the analytic theory of numbers has been largely transformed by the work of Vinogradov. This work, which has led to remarkable new results, is characterized by its supreme ingenuity and great power.

Vinogradov has expounded his method and its applications in a series of papers and in two monographs, which appeared in 1937 and 1947. The present book is a translation of the second of these monographs, which incorporated the improvements effected by the author during the intervening ten years.

The text has been carefully revised and to some extent rewritten. The more difficult arguments have been set out in greater detail.

Notes have been added, in which we mention the more important changes made and comment on the subject-matter; we hope these will be of assistance or of interest to the reader.

The book was translated from Russian by K. F. Roth and Anne Davenport and was published in 1954.

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You can get the book here.

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Preface by the Translators V
Notation ix

Introduction 1

Note on Vinogradov’s Method by the Translators 19

I. General Lemmas 21

Notes 42

II. The Investigation of the Singular Series in Waring’s Problem 45

Notes 54

III. The Contribution of the Basic Intervals in Waring’s Problem 55

Notes 61

IV. An Estimate for G(n) in Waring’s Problem 62

Notes 69

V. Approximation by the Fractional Parts of the Values of a Polynomial 71

Notes 81

VI. Estimates for Weyl Sums 82

Notes 113

VII. The Asymptotic Formula in Waring’s Problem 117

Notes 123

VIII. The Distribution of the Fractional Parts of the Values of a Polynomial 124

Notes 127

IX. Estimates for the Simplest Trigonometrical Sums with Primes 128

Notes 162

X. Goldbach’s Problem 163

Notes 175

XI. The Distribution of the Fractional Parts of the Values of the Function 𝛼𝓅 177

Notes 180

Posted in mathematics, soviet | Tagged goldbach's problem, mathematics, polynomials, prime numbers, theory of numbers, trigonometric series, Trigonometrical Sums, waring's problem, Weyl Sums | 1 Comment

How They Live – Charushin

Posted on November 13, 2021 by The Mitr

In this post, we will see the book How They Live by Y. Charushin.

About the book

This little picture book describes how various animals live in their natural habitats. The animals described include hares, wolves, lions, tigers, elephants, zebras, bears, squirrels, and camels.

The book was translated from Russian by Irina Zheleznova and was published in 1979 by Progress Publishers (Third printing). The fantastic drawings are by the author. There is a Bengali version also.

Credits to the original uploaders.

You can get the book here (cleaned) and here.

Link to the Bengali version here and here.

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Posted in books, children's books, children's stories, picture books, progress publishers, soviet | Tagged animals, bengali, camel, childrens book, drawings, elephant, hare, illustrated book, lion, picture book, progress publishers, soviet, squirrel, tiger, wolf, wolves, zebra | Leave a comment

The Brave Ant – Makarova

Posted on November 12, 2021 by The Mitr

In this post, we will see the book The Brave Ant by Tatiana Makarova.

About the book

The book describes a story of ant and his family whose home is swept away by water.

The book was translated from Russian by Fainna Glagoleva. The fantastic drawings are by Gennadi Pavlishin. The book was published in in 1976 by Progress Publishers.

All credits to Guptaji.

You can get the book here (cleaned version) and here.

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Posted in books, children's books, children's stories, progress publishers, soviet | Tagged animal drawings, ant story, ants, birds, children's book, fantasy, forest, illustrated book, insects, soviet stories, story book | 4 Comments

Red Hill – Bianki

Posted on November 11, 2021 by The Mitr

In this post, we will see the book Red Hill by Vitaly Bianki.

About the book

The book tells us the story of two sparrows Chirp and Chirpie. Chirp is always fighting with other birds. Will Chirp and Chirpie be able to get help from other birds to defend their nest from a cat attack? To find out read the book!

The book was translated from Russian by Olga Shartse. The drawings are by Yevgeny Charushin. The book was published in 1975 by Progress.

All credits to Guptaji.

You can get the book here and here.

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Posted in books, children's books, children's stories, progress publishers, soviet | Tagged animals, birds, cat, children's book, chirp, illustrated book, nest, progress publishers, soviet, sparrows, story book | Leave a comment

Builders Without Tools – Bianki

Posted on November 10, 2021 by The Mitr

In this post, we will see the book Builders Without Tools by Vitaly Bianki.

About the book

This little book describes how different birds like magpies, night-jars, willow tits, swallows, thrush, woodpecker and eagle build their amazing nests without using any tools.

The book was translated from Russian by Tom Botting and was illustrated by V. Fedotov. The book was published in 1980 by Malysh.

All credits to Guptaji.

You can get the book here (cleaned version) and here.

Write to us: mirtitles@gmail.com

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Posted in books, children's books, children's stories, malysh publishers | Tagged bird watching, birds, children's book, illustrated book, nests, popular science, soviet | Leave a comment

Why Tuppy Doesn’t Chase Birds – Charushin

Posted on November 9, 2021 by The Mitr

In this post, we will see the book Why Tuppy Doesn’t Chase Birds by Y. Charushin.

About the book

In this book you will know about a little mischievous cat named Tuppy and her adventures. Read the book to know why this little cat does not chase any birds!

The book was translated from Russian by Fainna Glagoleva and illustrated by the author. The book was published in 1976 by Progress Publishers. Note: title pages are missing.

All credits to Guptaji.

You can get the book here (cleaned version) an here.

Write to us: mirtitles@gmail.com

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Contents

Posted in books, children's books, children's stories, picture books, progress publishers, soviet | Tagged birds, cat, children's book, illustrated book, purring, soviet, stories, tuppy the cat | Leave a comment

About the book

PS: This is the 500th post on the blog! Thanks for all the support over the years!

Contents

Introduction vii

1. The Definition of Mathematical Concepts 1

2. Distance and Its Properties in Elementary Geometry 5

3. The Definition of a Metric Space and of Distance 11

4. Some Examples of Metric Spaces 18

5. The Space of Information 27

6. Automatic Correction of Errors in Messages 38

7. Metrics and Norms in Multi-dimensional Spaces 47

8. The Smoothing of Errors in Experimental Measurements 60

9. A More General Definition of Distance 65

About the book

About the book

About the book

Contents

MISHA’S VACATION

GRANNY FISA

About the book

Contents

I. General Lemmas 21

II. The Investigation of the Singular Series in Waring’s Problem 45

III. The Contribution of the Basic Intervals in Waring’s Problem 55

IV. An Estimate for G(n) in Waring’s Problem 62

V. Approximation by the Fractional Parts of the Values of a Polynomial 71

VI. Estimates for Weyl Sums 82

VII. The Asymptotic Formula in Waring’s Problem 117

VIII. The Distribution of the Fractional Parts of the Values of a Polynomial 124

IX. Estimates for the Simplest Trigonometrical Sums with Primes 128

X. Goldbach’s Problem 163

XI. The Distribution of the Fractional Parts of the Values of the Function 𝛼𝓅 177

About the book

About the book

About the book

About the book

About the book

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