Mathematics for Natural Scientists: Fundamentals and Basics

This book covers a course of mathematics designed primarily for physics and engineering students. It includes all the essential material on mathematical methods, presented in a form accessible to physics students, avoiding precise mathematical jargon and proofs which are comprehensible only to mathematicians. Instead, all proofs are given in a form that is clear and convincing enough for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each section of the book.

Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.

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Calculus For Scientists And Engineers

This book presents the basic concepts of calculus and its relevance to real-world problems, covering the standard topics in their conventional order. By focusing on applications, it allows readers to view mathematics in a practical and relevant setting. Organized into 12 chapters, this book includes numerous interesting, relevant and up-to date applications that are drawn from the fields of business, economics, social and behavioural sciences, life sciences, physical sciences, and other fields of general interest. It also features MATLAB, which is used to solve a number of problems. The book is ideal as a first course in calculus for mathematics and engineering students. It is also useful for students of other sciences who are interested in learning calculus.

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Quantum Reality: Theory and Philosophy

Summary
Probably the most successful scientific theory ever created, quantum theory has profoundly changed our view of the world and extended the limits of our knowledge, impacting both the theoretical interpretation of a tremendous range of phenomena and the practical development of a host of technological breakthroughs. Yet for all its success, quantum theory remains utterly baffling.

Quantum Reality: Theory and Philosophy cuts through much of the confusion to provide readers with an exploration of quantum theory that is as authoritatively comprehensive as it is intriguingly comprehensible. Requiring no more than school level physics and mathematics background, this volume requires only an interest in understanding how quantum theory came to be and the myriad ways it both explains how our universe functions and extends the reach of human knowledge.

Written by well-known physics author and teacher Dr. Jonathan Allday, this highly engaging work:

• Presents a thorough grounding in the theoretical machinery of quantum physics
• Offers a whistle-stop tour through the early part of the 20th century when the founding fathers of quantum theory forever altered the frontiers of human thought
• Provides an example-filled interpretation of the theory, its applications, and its pinnacle in quantum field theory (QFT), so crucial in shaping ideas about the nature of reality
• Separates fact from speculation regarding quantum physics’ ability to provide a starting point for philosophical queries into ultimate understanding and the limits of science

The world beneath the one that we experience with our senses is profoundly mysterious, and while we may never completely unravel that mystery, quantum theory allows us to come closer than ever to understanding where the science leaves off and the mystery begins. Quantum Reality: Theory and Philosophy makes that understanding accessible to anyone possessing a quest for knowledge and a sense of awe.

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Space-time: An Introduction to Einstein's Theory of Gravity

This book, suitable for interested post-16 school pupils or undergraduates looking for a supplement to their course text, develops our modern view of space-time and its implications in the theories of gravity and cosmology. While aspects of this topic are inevitably abstract, the book seeks to ground thinking in observational and experimental evidence where possible. In addition, some of Einstein’s philosophical thoughts are explored and contrasted with our modern views.

Written in an accessible yet rigorous style, Jonathan Allday, a highly accomplished writer, brings his trademark clarity and engagement to these fascinating subjects, which underpin so much of modern physics.

Features:

• Restricted use of advanced mathematics, making the book suitable for post-16 students and undergraduates
• Contains discussions of key modern developments in quantum gravity, and the latest developments in the field, including results from the Laser Interferometer Gravitational-Wave Observatory (LIGO)
• Accompanied by appendices on the CRC Press website featuring detailed mathematical arguments for key derivations.

Author(s) Bio:

Jonathan Allday teaches physics at Woodhouse Grove School where he is also Director of Digital Strategy.

After taking his first degree in physics at Cambridge, he moved to Liverpool University where he gained a PhD in particle physics in 1989. While carrying out his research, he joined with a group of academics and teachers working on an optional syllabus to be incorporated into A-level Physics. This new option was designed to bring students up to date on advances in particle physics and cosmology. An examining board accepted the syllabus in 1993 and now similar components appear on most advanced courses and some aimed at GCSE level.

Shortly after this, Jonathan started work on Quarks, Leptons and the Big Bang, published by CRC Press and now in its 3rd edition, which was intended as a rigorous but accessible introduction to these topics. Since then he has also written Apollo in Perspectiveand Quantum Reality, also published by CRC, as well as co-authoring various textbooks for 16+ level, most prominently Advanced Physics from the well-respected OUP series of Advanced Science books. He is also active writing articles for Physics Review which is a journal intended for 16+ physicists.

Outside of teaching physics, Jonathan has a keen interest in cricket and Formula 1, although no ability in either sport. He and his wife Carolyn live in Yorkshire and spend a reasonable amount of time wandering the country following their three children in their sporting endeavours. While his eldest son somehow found his way into Accountancy via Psychology, his middle son is reading Physics at Bristol and his youngest is completing A levels and hoping to read philosophy.

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Complex Analysis, Riemann Surfaces and Integrable Systems

Using basic tools from the first year of university studies, the book leads a reader to the impressive achievements of mathematics of the 21st century

Studying the book, the reader will get acquainted with analytical and harmonic functions, as well as with the main results of the theory of Riemann surfaces. The reader will also get acquainted with the modern use of these results for solving classical problems of practical importance. These applications are based on the theory of integrable systems, which is also discussed in the book

Practical all the statements are given in the book with full proofs

About this Textbook:

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided.

We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications.

After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc.

The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

About the authors:

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided.

We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications.

After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc.

The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

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Algebraic Curves

Leads a reader to far advanced topics widely used in modern research, using basic tools from the first two years of university studies

From the very beginning, the study of algebraic curves is aimed at the construction of their moduli spaces in the final chapters

Supplied with numerous exercises and problems both making the book a convenient base for a university lecture course and allowing the reader to control his/her progress

About this Textbook:

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well.

The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces.

The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion.

Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework

About the authors:

Maxim Kazaryan is a researcher at the Steklov Mathematical Institute RAS. He also works as a professor of mathematics at the NRU Higher School of Economics since 2008 and at the Skolkovo Institute of Science and Technology since 2016.

Sergei Lando is a professor of mathematics at the NRU Higher School of Economics since 2008 and at the Skolkovo Institute of Science and Technology since 2016. He was the first Dean of the Department of Mathematics at the NRU HSE. He also is a Vice-President of the Moscow Mathematical Society.

Victor Prasolov is a permanent teacher of mathematics at the Independent University of Moscow.

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Introduction to the Theory of Schemes

About this Textbook:

This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. 

This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas.

"This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson

About the authors:

Yuri I. Manin is a retired scientific member of the Max Planck Institute for Mathematics in Bonn. He has received various prizes and notable awards, including the Moscow Mathematical Society Award (1963), the Lenin Prize (1967), the Brouwer Gold Medal (1987), the Frederic Esser Nemmers Prize (1994), the Rolf Schock Prize (1999), the King Faisal Prize for Mathematics, the Georg Cantor Medal of the German Mathematical Society (2002) and the Bolyai Prize (2010).

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Geometry, Mechanics, and Dynamics

This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy.

The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.

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Research in History and Philosophy of Mathematics

This volume contains seventeen papers that were presented at the 2015 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held in Washington, D.C. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of general topics in the history and philosophy of mathematics, this meeting also honored the memories of Jacqueline (Jackie) Stedall and Ivor Grattan-Guinness; celebrated the Centennial of the Mathematical Association of America; and considered the importance of mathematical communities in a special session. These themes and many others are explored in these collected papers, which cover subjects such as

1. New evidence that the Latin translation of Euclid’s Elements was based on the Arabic version attributed to al-Ḥajjāj
2. Work done on the arc rampant in the seventeenth century 
3. The history of numerical methods for finding roots of nonlinear equations
4. An original play featuring a dialogue between George Boole and Augustus De Morgan that explores the relationship between them
5. Key issues in the digital preservation of mathematical material for future generations
6. A look at the first twenty-five years of The American Mathematical Monthly in the context of the evolving American mathematical community
7. The growth of Math Circles and the unique ways they are being implemented in the United States

Written by leading scholars in the field, these papers will be accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.

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Mathematical Masterpieces

Experience the discovery of mathematics by reading the original work of some of the greatest minds throughout history. Here are the stories of four mathematical adventures, including the Bernoulli numbers as the passage between discrete and continuous phenomena, the search for numerical solutions to equations throughout time, the discovery of curvature and geometric space, and the quest for patterns in prime numbers. Each story is told through the words of the pioneers of mathematical thought. Particular advantages of the historical approach include providing context to mathematical inquiry,  perspective to proposed conceptual solutions, and a glimpse into the direction research has taken. The text is ideal for an undergraduate seminar, independent reading, or a capstone course, and offers a wealth of student exercises with a prerequisite of at most multivariable calculus.

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A History of the Central Limit Theorem

This study aims to embed the history of the central limit theorem within the history of the development of probability theory from its classical to its modern shape, and, more generally, within the corresponding development of mathematics. The history of the central limit theorem is not only expressed in light of "technical" achievement, but is also tied to the intellectual scope of its advancement. The history starts with Laplace's 1810 approximation to distributions of linear combinations of large numbers of independent random variables and its modifications by Poisson, Dirichlet, and Cauchy, and it proceeds up to the discussion of limit theorems in metric spaces by Donsker and Mourier around 1950. This self-contained exposition additionally describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The importance of historical connections between the history of analysis and the history of probability theory is demonstrated in great detail. With a thorough discussion of mathematical concepts and ideas of proofs, the reader will be able to understand the mathematical details in light of contemporary development. Special terminology and notations of probability and statistics are used in a modest way and explained in historical context.

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Mathematical Expeditions

This book contains the stories of five mathematical journeys into new realms, told through the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, while others had more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realization that still greater vistas remained to be explored. The authors tell these stories by guiding the reader through the very words of the mathematicians at the heart of these events, and thereby provide insight into the art of approaching mathematical problems. The book can be used in a variety of ways. The five chapters are completely independent, each with varying levels of mathematical sophistication. The book will be enticing to students, to instructors, and to the intellectually curious reader. By working through some of the original sources and supplemental exercises, which discuss and solve - or attempt to solve - a great problem, this book helps the reader discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.

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Mathematics of the 19th Century

This multi-authored effort, Mathematics of the nineteenth century (to be fol­ lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend, first, to unravel the forces that shape mathe­ matical progress. We examine the interaction of mathematics with the social structure, technology, the natural sciences, and philosophy. Throughan anal­ ysis of mathematical history proper, we hope to delineate the relationships among the various mathematical disciplines and to evaluate mathematical achievements in the light of the current state and future prospects of the science. The difficulties confronting us considerably exceeded those encountered in preparing the three-volume edition.

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Mathematics and Its History

One of the disappointments experienced by most mathematics students is that they never get a course in mathematics. They get courses in calculus, algebra, topology, and so on, but the division of labor in teaching seems to prevent these different topics from being combined into a whole. In fact, some of the most important and natural questions are stifled because they fall on the wrong side of topic boundary lines. Algebraists do not discuss the fundamental theorem of algebra because "that's analysis" and analysts do not discuss Riemann surfaces because "that's topology," for example. Thus if students are to feel they really know mathematics by the time they graduate, there is a need to unify the subject. This book aims to give a unified view of undergraduate mathematics by approaching the subject through its history. Since readers should have had some mathematical experience, certain basics are assumed and the mathe­ matics is not developed as formally as in a standard text. On the other hand, the mathematics is pursued more thoroughly than in most general histories of mathematics, as mathematics is our main goal and history only the means of approaching it. Readers are assumed to know basic calculus, algebra, and geometry, to understand the language of set theory, and to have met some more advanced topics such as group theory, topology, and differential equations.

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A Concrete Introduction to Real Analysis, Second Edition

The Second Edition offers a major re-organization of the book, with the goal of making it much more competitive as a text for students. The revised edition will be appropriate for a one- or two-semester introductory real analysis course. Like the first edition, the primary audience is the large collection of students who will never take a graduate level analysis course. The choice of topics and level of coverage is suitable for future high school teachers, and for students who will become engineers or other professionals needing a sound working knowledge of undergraduate mathematics.

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Introduction to Real Analysis, 7th Edition

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Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science.
After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.
As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.

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Introduction to Real Analysis

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject.

The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more.

Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.

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Measure, Integration & Real Analysis

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics.

Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn.

Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability.

Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.

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Much Ado About Calculus

The calculus has been one ofthe areas of mathematics with a large number of significant applications since its formal development in the seventeenth century. With the recent development of the digital computer, the range of applications of mathematics, including the calculus, has increased greatly and now includes many disciplines that were formerly thought to be non­ quantitative. Some of the more traditional applications have been altered, by the presence of a computer, to an extent such that many problems hitherto felt to be intractable are now solvable. This book has been written as a reaction to events that have altered the applications of the calculus. The use of the computer is made possible at an early point, although the extent to which the computer is used in the course is subject to the decision of the instructor. Some less traditional applications are included in order to provide some insight into the breadth of problems that are now susceptible to mathematical solution. The Stieltjes integral is introduced to provide for easier transition from the stated problem to its mathematical formulation, and also to permit the use of functions like step functions in later courses (such as statistics) with relative ease. The course is designed to include all the background material ordinarily associa­ ted with the first course in the calculus, but it is also designed with the user in mind.

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Mathematics Handbook

This is the fourth edition of the Mathematics handbook for science and engineering (BETA). Compared to the previous editions a number of additions and corrections have been made. The Mathematics handbook covers basic areas of mathematics, numerical analysis, probability and statistics and various applications. The handbook is intended for students and teachers of mathematics, science and engineering and for profession­ als working in these areas. The aim of the handbook is to provide useful informa­ tion in a lucid and accessible form in a moderately large volume. The handbook concentrates on definitions, results, formulas, graphs, figures and tables and emphasizes concepts and methods with applications in technology and science. The Mathematics handbook is organised in 19 chapters starting with basic concepts in discrete mathematics and ending with chapters on probability and statistics and a miscellaneous chapter. Crossreferences and an extensive index help the user to find required information. We have not included numerical tables of functions which are available on most scientific calculators and pocket computers. We have treated one variable and multi variable calculus in different chapters, because students, usu­ ally, meet these areas in different courses. In formulating theorems and results sometimes all assumptions are not explicitely stated.

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Handbook of Mathematics

This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and new paragraphs, new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.

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A Course of Pure Mathematics (Cambridge Mathematical Library)

There are few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigour of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Celebrating 100 years in print with Cambridge, this edition includes a Foreword by T. W. Körner, describing the huge influence the book has had on the teaching and development of mathematics worldwide. Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to.

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Physics A General Course – Savelyev

In this post we will see the three volume Physics – A General Course by I. V. Savelyev.

I have done everything in my power to acquaint students with the basic ideas and methods of physics and to teach them how to think physically. This is why the book is not encyclopedic in its nature. It is mainly devoted to explaining the meaning of physical laws and showing how to apply them consciously. What I have tried to achieve is a deep knowledge of the fundamental principles of physics rather than a shallower acquaintance with a wide range of questions.

While using the book, try not to memorize the material formalistically and mechanically, but logically, i.e. memorize the material by thoroughly understanding it. I have tried to present physics not as a science for “cramming”, not as a certain volume of information to be memorized, but as a clever, logical, and attractive science.

Notwithstanding my desire to reduce the size, I considered it essential to include a number of mathematical sections in the course: on vectors, linear differential equations, the basic concepts of the theory of probability, etc. This was done to impart a “physical” tinge to the relevant concepts and relations. In addition, the mathematical “inclusions” make it possible to go on with the physics even if, as is often the case, the relevant material has not yet been covered in a mathematics course.

The present course is intended above all for higher technical schools with an extended syllabus in physics. The material has been arranged, however, so that the book can be used as a teaching aid for higher technical schools with an ordinary syllabus simply by omitting some section.

The books were translated from the Russian by G. Leib and were first publised in 1980, this copy is the third reprint in 1989.

Volume 1 (Download)

Volume 2 (Download)

Volume 3 (Download)

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Senior Physics 1 – Kikoin, Kikoin

About the book

This book is the second in the series the first one being Junior Physics. There is a second volume in this series which we do not have now. This book covers fundamentals of motion, its laws, forces in nature and conservation laws also. There is a section on Practical work at the end of the book.

The book was translated from the Russian by Natalia Wadhwa. And was first published by Mir in 1987.

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The Nine Colours of The Rainbow – Steinhaus

About the book (from the front jacket)

Have you ever stopped to think how many colours there are in a rainbow? Seven or, perhaps, nine as the title of the book suggests? It appears, there are many more and still the title is correct. Why so?

The book will tell you what is visible and invisible light, how it helps man to acquaint himself with his environment, investigate it, penetrate into the mysteries of matter and space. You will also find out how man learned to see in the dark, transmit images over long distances and record processes occurring within millionth fractions of a second. The book contains a wealth of other information on the latest achievements in science and technology.

The author, Alexander Steinhaus, is a Soviet specialist in electronics and TV. Many years of industrial experience served as a fertile ground for his literary career on which he embarked with ardour. He has written many sci-fic articles, some stories and a few books, among which are “The Nine Colours of the Rainbow”, “A Factory Without Men”, and others. At present A. Steinhaus is working at a large sci-fic book on television.

The book was translated from the Russian by David Sobolfy and was published by Mir in 1966.

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Fundamentals of Physics – Ivanov

About the book:

The book being of­fered by the author differs from other existing books on the subject in its nontraditional approach to the course of phys­ics. The principle underlying the preparation of this course can be summarized as follows:  “From atom to matter”.

What prompted the author to adopt this approach? In­deed, the creation of new materials with unusual mechani­cal, thermal, electrical, magnetic, and optical properties requires a microscopic approach to the problem and a clear understanding of the practical significance of the approach “from atom to matter”. This means that the scientists and industrial workers engaged in fields like physical materials science, nuclear and semiconductor engineering, laser
…

This book is intended for those who wish to acquire a deeper knowledge of physical phenomena. It can be used by students of physics and mathematical schools, as well as by those who have finished school and are engaged in self- education. A good deal of the material may be useful to teachers delivering lectures on various topics of physics.

…

This is not a textbook, but rather a helpbook that should be used in conjunction with the standard textbooks. Nor is the book intended for a light reading; you have to use a pen and paper, think, analyze, and even compute whenever it is necessary. We shall describe physics here in the way re­ searchers understand it today.

Physics essentially deals with the fundamental laws of nature. The progress being made at present in all branches of natural science is due, as a rule, to the introduction of physical concepts and techniques in them. This is besides the fact that a knowledge of physical sciences is essential for new industrial ventures lying at the root of technical progress. Physics is fast becoming an important element in the modern civilization.

The book was published by Mir in 1989 and was translated from the Russian by R. S. Wadhwa.

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Semiconductors: Testing and Adjusting – Green, Shokalsky

In this post, we will look at the book Semiconductors: Testing and Adjusting by G. Green and A Shokalsky.

About the book:

The book describes the working of many electronic devices and methods of testing them. Since the book was written in the early 70s, some of the technology presented in the book may be outdated.

The book was translated from the Russian by George Roberts and was first published by Mir in 1972.

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Fundamentals of Theoretical Physics – Savelyev

In this post we will see the two volume set titled Fundamentals of Theoretical Physics by I. V. Savelyev. Previously we have seen Physics A General Course by the same author.

The book being offered to the reader is a logical continuation of the author’s three-volume general course of physics. Everything possible has been done to avoid repenting what has been set out in the three-volume course. Particularly. the experiments underlying the advancing of physical ideas are not treated, and some of the results obtained are not discussed.

The book has been conceived as a training aid for students of non- theoretical specialities of higher educational institutions. I had in mind readers who would like to grasp the main ideas and methods of theoretical physics without delving into the details that are of interest only for a specialist. This book will be helpful for physics instructors at higher schools, and also for everyone interested in the subject but having no time to become acquainted with it (or re- store it in his memory) according to fundamental manuals.

The books were translated from the Russian by G. Leib and was first published in 1982.

Fundamentals of Theoretical Physics Vol 1 (Download)

Fundamentals of Theoretical Physics Vol 2 (Download)

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Electricity And Man – Manoilov

About the book:

“… Life on Earth originated and developed in

interaction with electromagnetic fields. Electricity is

inherent in the living in its most complicated form – the

vital activity of man. Scientists have done much in

studying this amazing interaction of electricity and the

animate but much in nature is still concealed, much

must be analyzed and understood. This book will help

to widen the reader’s understanding of the interaction

of electricity and the living organism, although it makes

no claim to exhaust the subject … “

The book was translated from the Russian by George Kittell and was published by Mir in 1978.

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Elementary Textbook on Physics Vol 3 – Landsberg

About the book:

Volume 3 covers aspects of wave motion, oscillations, optics and atomic and modern physics. These topics include:

Basic Concepts. Mechanical Vibrations. Acoustic Vibrations. Electric Oscillations. Wave Phenomena. Interference of Waves. Electromagnetic Waves. Light Phenomena: General. Photometry and Lighting Engineering. Basic Laws of Geometrical Optics. Application of Reflection and Refraction of Light to Image Formation. Optical Systems and Errors. Optical Instruments. Interference of Light. Diffraction of Light. Physical Principles of Optical Holography. Polarization of Light. Transverse Nature of Lightwaves. Electromagnetic Spectrum. Velocity of Light. Dispersion of Light and Colours of Bodies. Spectra and Spectral Regularities. Effects of Light. Atomic Structure. Radioactivity. Atomic Nuclei and Nuclear Power. Elementary Particles. New Achievements in Elementary Particle Physics.

About the series (from Front Jacket and Preface):
Elementary Textbook on Physics first appeared in 1948-52 under the editorship of Academician G.S. Landsberg (1890-1957) and immediately became popular with students preparing for entrance examinations in physics. The success of the book was due very much to the fact that each section was written by a specialist. Contributors to the book included the scientists S.E. Khaikin, M.A. Isakovich, M.A. Leontovich, D.I. Sakharov (Vol. 1), S.G. Kalashnikov (Vol. 2), S.M. Rytov, M.M. Sushchinskii (with the participation of I.A. Yakovlev), F.S. Landsberg-Baryshanskaya, and F.L. Shapiro (Vol. 3).

These three volumes form a course on elementary physics that has become very popular in the Soviet Union. Each sectioh was written by an authority in the appropriate field, while the overall unity and editing was supervised by Academician G.S. Landsberg (1890-1957). This textbook has gone through ten Russian editions and a great deal of effort went into the last edition to introduce SI units and change the terminology and notation for the physical units.

A feature of this course is the relatively small number of formulas and mathematical manipulations. Instead, attention was focussed on explaining physical phenomena in such a way as to combine scientific rigour and a form understandable to school children. Another aspect of the text is the technological application of the physical laws.

These features make the text a world-class textbook.

For students preparing to enter universities and colleges to study physics, and for those it high schools specialising in physics.

The book was translated from the Russian by Natalia Wadhwa and was first published by Mir in 1989.

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Elementary Textbook on Physics Vol 2 – Landsberg

About the book:

Volume 2 covers aspects of basic aspects of electricity and magnetism. These topics include:

Electric Charges. Electric Field. Direct Current. Thermal Effect of Current. Electric Current in Electrolytes. Chemical and Thermal Generators. Electric Current in Metals. Electric Current in Gases. Electric Current in Semiconductors. Basic Magnetic Phenomena. Magnetic Field. Magnetic Field of Current. Magnetic Field of the Earth. Forces Acting on Current- Carrying Conductors in Magnetic Field. Electromagnetic Induction. Magnetic Properties of Bodies. Alternating Current. Electric Machines: Generators, Motors and Electromagnets.

About the series (from Front Jacket and Preface):
Elementary Textbook on Physics first appeared in 1948-52 under the editorship of Academician G.S. Landsberg (1890-1957) and immediately became popular with students preparing for entrance examinations in physics. The success of the book was due very much to the fact that each section was written by a specialist. Contributors to the book included the scientists S.E. Khaikin, M.A. Isakovich, M.A. Leontovich, D.I. Sakharov (Vol. 1), S.G. Kalashnikov (Vol. 2), S.M. Rytov, M.M. Sushchinskii (with the participation of I.A. Yakovlev), F.S. Landsberg-Baryshanskaya, and F.L. Shapiro (Vol. 3).

These three volumes form a course on elementary physics that has become very popular in the Soviet Union. Each sectioh was written by an authority in the appropriate field, while the overall unity and editing was supervised by Academician G.S. Landsberg (1890-1957). This textbook has gone through ten Russian editions and a great deal of effort went into the last edition to introduce SI units and change the terminology and notation for the physical units.

A feature of this course is the relatively small number of formulas and mathematical manipulations. Instead, attention was focussed on explaining physical phenomena in such a way as to combine scientific rigour and a form understandable to school children. Another aspect of the text is the technological application of the physical laws.

These features make the text a world-class textbook.

For students preparing to enter universities and colleges to study physics, and for those it high schools specialising in physics.

The book was translated from the Russian by Natalia Wadhwa and was first published by Mir in 1988.

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Elementary Textbook on Physics Vol 1 – Landsberg

About the book:

Volume 1 covers aspects of basic mechanics and fluid mechanics (both statics and dynamics), heat and molecular physics. These topics include:

Kinematics. Dynamics. Statics. Work and Energy. Curvilinear Motion. Motion in Noninertial Reference Systems and inertial Forces. Hydrostatics. Aerostatics. Fluid Dynamics. Thermal Expansion of Solids and Liquids. Work. Heat. Law of Energy Conservation. Molecular Theory. Properties of Gases. Properties of Liquids. Properties of Solids. Transition from Solid to Liquid State. Elasticity and Strength. Properties of Vapours. Physics of the Atmosphere. Heat Engines.

About the series (from Front Jacket and Preface):

Elementary Textbook on Physics first appeared in 1948-52 under the editorship of Academician G.S. Landsberg (1890-1957) and immediately became popular with students preparing for entrance examinations in physics. The success of the book was due very much to the fact that each section was written by a specialist. Contributors to the book included the scientists S.E. Khaikin, M.A. Isakovich, M.A. Leontovich, D.I. Sakharov (Vol. 1), S.G. Kalashnikov (Vol. 2), S.M. Rytov, M.M. Sushchinskii (with the participation of I.A. Yakovlev), F.S. Landsberg-Baryshanskaya, and F.L. Shapiro (Vol. 3).

These three volumes form a course on elementary physics that has become very popular in the Soviet Union. Each sectioh was written by an authority in the appropriate field, while the overall unity and editing was supervised by Academician G.S. Landsberg (1890-1957). This textbook has gone through ten Russian editions and a great deal of effort went into the last edition to introduce SI units and change the terminology and notation for the physical units.

A feature of this course is the relatively small number of formulas and mathematical manipulations. Instead, attention was focussed on explaining physical phenomena in such a way as to combine scientific rigour and a form understandable to school children. Another aspect of the text is the technological application of the physical laws.

These features make the text a world-class textbook.

For students preparing to enter universities and colleges to study physics, and for those it high schools specialising in physics.

The book was translated from the Russian by Natalia Wadhwa and was first published by Mir in 1988.

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Elementary Physics: Problems and Solutions – Gurskii

The book is intended for those preparing for university entrance examinations in physics. The contents and sequence of topics are in keeping with the requirements for such examinations. The few sections beyond the entrance examination programme are marked by circles. In view of the introduction of the elements of higher mathematics to the high-school curriculum, some problems have also been illustrated using differential calculus. The author has endeavoured to present the basic principles of school physics in a compact form to help the candidates revise the entire course in the shortest possible time. All sections have been illustrated with problems to give a better understanding of the subject. Each problem and its solution is followed by one or more exercises on the same topic, the exercises corresponding to problems that have been solved in the text are assigned the same number.Those intending to use this book independently are advised to attempt the exercises after going through the theoretical part. The relevant solved problems should be consulted if difficulties are encountered while solving the exercises. After this, the exercise should be tried again, and if there is more than one exercise bearing the same number, another exercise (preferably the last one) should be tackled. In most cases, the last exercises in a series are the most difficult.

The book was translated from Russian by Natalia Wadhwa and was first published in 1987.

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Problems in Theoretical Physics – Grechko, Sugakov, Tomasevich, Fedorchenko

About the book:

From the Front Jacket

This book is a collection of problems covering mechanics, electrodynamics, nonrelativistic quantum mechanics, !statistical physics and thermodynamics. Each Section opens with a brief outline of the main laws and relationships used to solve the problems. Also information about the needed mathematical apparatus is included. Along with answers there are guides to solving the more complicated problems. SI units are used throughout the book. Problems in Theoretical Physics is intended for physics majors at universities and other institutions of higher learning. Some of the problems are specifically for students majoring in theoretical physics. Certain ones can be used in the physics and mathematics departments of teachers colleges.

From the Preface

The text draws largely on the Course of Theoretical Physics by L. D. Landau and E. M. Lifshitz, but also makes use of other textbooks and handbooks recommended for the university course in theoretical physics. Some of the problems have been taken from published problem books listed at the end of this book, but many are original. The student will be able to solve the problems if he has a good knowledge of the fundamentals of theoretical physics, which are briefly outlined in each section of this book.

The book was translated from the Russian by Eugene Yankovsky and was published by Mir in 1977.

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Essays About the Universe – Vorontsov-Vel’yaminov

This book by a prominent Soviet astronomer and imaginative interpreter of the history and latest knowledge of astronomy, an age-old science that has come through two shattering decades of exciting discovery and research, can be dubbed a popular encyclopaedia of astronomy. It is a vivid and fascinating account of almost all the celestial bodies with which astronomy is concerned: planets, comets, meteors, the Sun and stars, gaseous and dust nebulae, quasars, black hole., etc. The tome is lavishly illustrated throughout with a mixture of photographs and specially commissioned artwork in full colour. The book will appeal to the general reader with no astronomical and mathematical background, fascinated by the wonders of the Space Age.

The book has two major sections, the first deals with Solid matter, that is the planets (minor and major), comets and meteors. The second part deals with the gaseous state which includes stars, nebulae, galaxies, interstellar matter. Mathematics is avoided as much as possible with the main emphasis on explaining the physical meaning of the concepts and their implications to the reader. The book covers an impressively wide range of topics in astronomy starting from the basics to topics of cutting-edge research.

The book was translated from the Russian by Alexander Repyev and was published by Mir 1985.
Note: The book is large in size (~ 190 MB). It took some time to scan it, as I had to scan individual pages because of their large size almost A4 in size. Unfortunately, before the optimisation of the images could be completed, I lost all the raw images to a disk crash. Hence I have uploaded the pdf that could be salvaged. You might notice some inconsistencies in the pages here and there. There are some amazing full-page illustrations, one of my favourites is one explaining the meteor path for different observers.

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Albert Einstein’s Philosophical views and the Theory of Relativity – Gribanov

This book presents the first integral treatment of the philosophical views of Albert Einstein and their influence on the origin and inter­pretation of the theory of relati­vity. It brings out the specific features of the philosophical com­ prehension of the theory of relativity m the world and Soviet literature, and analyses the influence of the new relativistic physical ideas in enriching and developing the tradi­tional philosophical categories of matter, space, time, and motion.

The book was first published by Progress Publishers in 1987 and was translated from the Russian by H. Campbell Creighton. The book was designed by Vyacheslav Serebryakov.

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The Forces of Nature – Grigoryev, Myakishev

About the book:

This book is a popular description of the unity of the forces of nature for the general reader.
At present, all interactions between bodies in nature are thought to be ultimately due to the interaction of elementary particles and involve only four types of forces: universal gravitation, or gravitational forces, electromagnetic forces, nuclear forces and the so- called weak interactions.
This book describes the principal properties of these four types of force and their “sphere of action”, that is, the part they play in diverse natural processes that range from galaxies to the atomic nucleus and the mutual transformations of elementary particles. It includes the latest achievements of physics and gives a picture of the unresolved problems that confront science today.

About the authors:

The authors of this book are Candidates of Physico-mathematical sciences Vladimir Grigoryev and Gennady Myakishev. In 1948 they graduated from the Physics Department of Moscow University and completed their graduate studies in 1951. At present both are Associate Professors of the Moscow University Physics Department.
V. Grigoryev has published over twenty papers on problems of quantum field theory and has been particularly interested in particle formation via high- energy collisions. G. Myakishev has written a number of works on electronics and problems of the methodology of science, several elementary numerous textbooks on physics and articles for popular-science magazines.

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