Little Mathematics Library- An Unusual Algebra

The next book on LML series is here. An Unusual Algebra by I.M.Yaglom Translated from the Russian by G. Volosova.




The present book is based on the lecture given by the author to senior pupils in Moscow on the 20th of April of 1966. The distinction between the material of the lecture and that of the book is that the latter includes exercises at the end of each section (the most difficult problems in the exercises are marked by an asterisk). At the end of the book are placed answers and hints to some of the problems. The reader is advised to solve most of the problems, if not all, because only after the problems have been solved can the reader be sure that he understands the subject matter of the book. The book contains some optional material (in particular, Sec. 7 and Appendix which are starred in the table of contents) that can be omitted in the first reading of the book. The corresponding parts of the text of the book are marked by one star at the beginning and by two stars at the end. However, in the second reading of the book it is advisable to study Sec. 7 since it contains some material important for practical applications of the theory of Boolean algebras.
The bibliography given at the end of the book lists some books which can be of use to the readers who want to study the theory of Boolean algebras more thoroughly.
The author is grateful to S. G. Gindikin for valuable advice and to F. I. Kizner for the thoroughness and initiative in editing the book.

Thanks to Gnv64 for uploading this GEM.



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Tales About Metals – Venetsky

We now come to a wonderful book titled Tales About Metals by S. Venetsky. Earlier we had seen the sequel to this book On Rare and Scattered Metals by the same author.



For ages have metals faithfully served humanity in all its endeavours to conquer the elements, unravel the mysteries of Nature and build powerful machines and installations. The world of metals is diverse and absorbing. The history of some of its representatives, notably, copper, iron, lead, mercury, gold, silver and tin dates thousands of years back. Others were discovered within just a few recent decades.

The properties of metals are extremely varied. Mercury will not freeze even at below-zero temperatures, while tungsten will not be consumed by the hottest of flames. Lithium could make a fine swimmer, being half as heavy as water and unable to sink no matter how hard it would try: osmium is a heavy-weight champion among metals and, thrown into water, will hit the bottom faster than a stone. Silver “gladly” conducts electricity, while titanium has an aversion to this “pastime”: its electrical conductivity is only a 300 th part that of silver. We come across iron wherever we turn and holmium is found in such minute quantities in the earth’s crust that it is fabulously expensive: a grain of pure holmium is several hundred times more expensive than gold.

But for all their differences, metals have one thing in common— they all belong to one large family. S. I. Venetsky’s Tales About Metals contains much information on the history of discovery of many metals and on their present and future uses.

It was not the author’s idea to give any systematized account of every metal he tells about. The history of metals abounds in amazing incidents, at times romantic or humorous, at times tragic. And it is mostly this aspect that the author had in mind when he wrote his book.

The book is intended for those who are ever curious, not only youngsters who are just discovering the world of science for themselves, but also those who have probably said goodbye to school and college, but still seize upon every opportunity to learn more about things around them.

The book has many Tales about metals related to their uses and discovery. It is a joy to read these, and I have cherished these Tales since my childhood. The Tales take you to distant times and lands, place the metals in a humanistic framework and expand your imagination. Hope it invokes same feelings in you too. Also the little water paintings that appear in these Tales make the reading much more fun, as a reader you are taken to the fantasy world through these little images.

Some of them can be seen below:







This book was translated from the Russian by N. G. Kittell and was first published by Mir in 1981 and was reprinted in 1988.

This is one of the first books that I had ever got, so has a special meaning for me. There is a Marathi version of this book as well (धातुंच्या नवलकथा), I used to have a hard copy, but it is no longer with me. Also a Hindi translation titled काहानियां धातुओं की for Tales About Metals exists.


Many, many thanks to Guptaji for the scan of this wonderful book.

You can get the book here.


About This Book 6

The Lightest Metal 7

Space-Age Metal 14

A Fighter Against Fatigue 21

Silver from Clay 28

Son of the Earth 38

“Vitamin V” 47

The “Red Lead” Mystery 54

Iron’s Old Companion 63

A Great Toiler 71

The Charge of the Guns of Peace 83

“Copper Devil” 91

One of the Oldest and Celebrated Metals 100

A “Clothing” for Uranium Rods Ill

The Forty First 118

Iron’s Ally 125

Of a Noble Origin 133

“Hard” but Soft 144

Born “in Torment” 151

Giving Light 157

Behind Three Locks 165

The King of Metals and the Metal of Kings 173

Silver Water 186

The Metal that Destroyed Rome 193

The Fuel of the Twentieth Century 200

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Introduction to Semiconductor Theory – Anselm

In this post we will see Introduction to Semiconductor Theory by A. Anselm.


About the book

This book has been written mainly for the benefit of people engaged in experimental work in the field of semiconductor physics. It will probably prove useful to students specializing in physics. Among the principal subjects treated in this book are crystal lattice vibrations, the laws of electron motion in an ideal and a perturbed periodic fields, the kinetic equation and transport phenomena (electric current).

The reader must be familiar with mathematics, quantum mechanics and physical statistics within the limits specified in the curricula of physical faculties of universities or physical and mathematical faculties of polytechnical colleges. He or she need not have a detailed knowledge of those courses but is expected to be able to find a way through the appropriate sections of textbooks referred to.

The special feature of the book is that those elementary facts are used to derive all the formulae. This, I hope, is done meticulously enough to make the book comprehensible for the above mentioned category of readers.

Some mathematical derivations of a more complex nature and less connected with the main text are presented in the end of the book in Appendices.

The book was translated from the Russian by M. M. Samokhvalov and was first published by Mir Publishers in 1981.

You can get the boo here.


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Selected Problems on Physics – Myasnikov, Osanova

In this post we will see another Problem and Solution book:

Selected Problems on Physics by S. P. Myasnikov, T. N. Osanova

Myasnikov- Osanova-Selected Problems on PhysicsAbout

The main purpose of the book is to help those preparing for entrance examinations to  engineering colleges in revisiing the high-school physics course and in further studies at the college.

The fourth edition of the book came out in 1981.  Amendments to the physics curriculum at the high-school and polytechnic level have been incorporated as well as extra material on other branches of the physics course.  The 6Eth edition was prepared by taking into account the modified style of problems set at the entrance examinations.

Each section begins with a brief description of the basic theory, physical laws, and formulas. This is followed by worked problems and a few descriptive problems. Exercises and questions for revision are givena at the end of each section. The problems are solved according to the unified and optimal approach described in the introduction. By solving the problems, students will acquire a firm theoretical background and knowledge which will help them in their work in whichever sector of the economy they will be employed. The appendices contain tables required for solving problems, SI units of physical quantities. And the rules for approximate calculations.

In addition to the problems composed by the autbors this book also includes a selection  of problems set for the aptitude tests and entrance examination in physics at the N.E. Buaman Higher Technical School and other technical institutios in Moscow.
Intended for students of preparatory courses at engineering colleges, this book can also be used by high-school students, students of intermediate colleges, and those interested in self-education.

The author is indebted to Prof. A.N. Remizov and Asst. Prof. N .V. Tygliyan for their  enormous help in preparing the  manuscript for publication.

The book was translated from the Russian by Natalia Wadhwa and was first published by Mir in 1990.

You can get the book here.

All credits to the original uploader.


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General Methods for Solving Physics Problems – Belikov

In this post we will see another book in the Problems and Solutions book, namely, General Methods for Solving Physics Problems by B. S. Belikov

B. S. Belikov-General methods for solving physics problemsAbout

This book attempts to create systematic use of generalised methods , general methodological principles, and very general concepts in a segment of students instruction of vital importance, the solution of physics problems. The approach is based on the application of the most general concepts of physics to the solution of any problem. I consider the theoretical aspects underlying the general approach to problem solution and methods for solving standard, non-standard, non-specific, and general problems.

The book was translated from the Russian by Eugene Yankovsky and was first published by Mir in 1989.

You can get the book here.

All credits to the original uploader.


The book has three parts

Part 1: The Theoretical Bases of the General Approach to Solving Any Physics Problem

Chapter 1: The System of Fundamental Concepts of Physics

1 Some General Concepts of Physics

2 Idealization of a Physics Problem

3 Classification of Physics Problems

Chapter 2: Some General Methods for Solving Physics Problems

4 Stages in Solving a Formulated Problem

5 Method of Analysing the Physical Content of a Problem

6 General-Particular Methods. The DI Method

7 The Simplification and Complication Method. The Estimate Method

8 The Problem Statement Method

9 Another Classification of Formulated Problems

Part 2: Solution of Standard Problems

Chapter 3: The motion of a particle

10 Particle Kinematics

11 Particle Dynamics

12 Mechanical Oscillations

13 Conservation Laws

Chapter 4: The motion of a rigid body

14 Rigid Body Dynamics

15 Conservation Laws in rigid body Dynamics

Chapter 5: The Gravitational Field

16 The Basic Problem of Gravitational Theory

17 The Gravitational Field Generated by a system of particles

18 The Gravitational Field Generated by an arbitrary Mass Distribution

Chapter 6: The Electric Field

19 The Electrostatic Field in Vacuum

20 The Electrostatic Field in Insulators

21 Conductors in Electrostatic Field

22 Direct Current

Chapter 7: The Magnetic Field

23 The Magnetic Field in a Vacuum

24 The Magnetic Field in Matter

Chapter 8: The Electromagnetic Field

25 Electromagnetic Induction and Self-Induction

26 Electromagnetic Oscillations

Chapter 9: Electromagnetic Waves

27 Interference of Light

28 Diffraction of Light

Chapter 10: Thermodynamics

29 The First Law of Thermodynamics

30 The Second Law of Theormodynamics

Chapter 11: Kinetic Theory

31 The Maxwell-Boltzmann Distribution

32 The Boltzmann Distribution

Part 3: Solution of Nonstandard, Nonspecified and Arbitrary problems

Chapter 12: Non-standard and Original Problems

33 Non-standard Problems

34 Original Problems

Chapter 13: Nonspecified, Research and Arbitrary Problems

35 Nonspecified Problems

36 Research Problems

37 Arbitrary Problems



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Mathematics Can Be Fun – Yakov Perelman

This one was long pending: Mathematics Can Be Fun by Yakov Perelman


To read and enjoy this book it will suffice to possess a modest knowledge of mathematics, i.e. a knowledge of the rules of arithmetic and elementary geometry. Very few problems require the ability of forming and solving equations, and the simplest at that. The table of contents, as you may see, is quite diversified: the subjects range from a motley collection of conundrums and mathematical stunts to useful practical problems on counting and measuring. The author has done everything to make his book as fresh as possible, avoiding repetition of all that has already appeared in his other works (Tricks and Amusements, Interesting Problems, etc.). The reader will find a hundred or so brain- teasers that have not been included in earlier books. Chapter 6- “Number Giants” -is adapted from one of the authors earlier pamphlets, with four new stories added.

You can get the book here.

Arabic version here.

All credits to the original uploaders.



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Generalized Functions in Mathematical Physics – Vladimirov

In this post we will see the book Generalized Functions in Mathematical Physics by V. S. Vladimirov.

vladimirov-coverAbout the book:

… modern mathematical physics makes extensive use of the latest attainments of  mathematics, one of which is the theory of generalized functions. The present monograph is devoted to a brief exposition of the fundamentals of that theory and of  certain of its applications to mathematical physics.

The present monograph is an expanded version of a course of lectures that the author has been delivering to students, post-graduates, and associates of the Moscow Physics and Technology Institute and the Steklov Mathematical Institute.

The book was translated from the Russian by George Yankovsky and was published Mir Publishers in 1979.

You can get the book here.


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