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Mathematics: Its Content, Methods and Meaning
". . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book Review
This major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."
Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.
Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference.
"This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science
This major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."
Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.
Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference.
"This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science
1120 pages, Paperback
First published January 1, 1963
286 people are currently reading
2438 people want to read
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Displaying 1 - 11 of 11 reviews
November 19, 2011
Absolutely amazing book. It's a very ambitious book that summarizes a good chunk of undergraduate mathematics. It doesn't give a full-blown overview, but it summarizes the main results of each topic with enough detail that so you know important concepts and where they fit within the discipline of mathematics. This is an ideal book to read after learning single variable calculus. I am just in chapter three and I already feel like this is a must have for anyone interested in mathematics. If this is the quality of most soviet-era books, then there is a treasure trove of technical gems hidden from most of the world. I especially like how a few applications to physics are explained and how theorems are illustrated and proven in a non-pedantic fashion.
This is a must have for anyone's personal technical library. It's one of those books you would give to someone interested in math, pure or applied.
This is a must have for anyone's personal technical library. It's one of those books you would give to someone interested in math, pure or applied.
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August 13, 2017Amazon 2009-02-08. A full three-volume set dropped into the hopper at $12, w00t! Good things come to he who waits.
August 21, 2015
- A nice overview of the many mathematical disciplines, including several I've never had any direct experience with: functional analysis, complex analysis, topology, etc.
- Not sure this was the author's goal, but after reading the chapter on non-Euclidean geometry, I have a much better grasp of "curved spacetime" and general relativity.
- In geometry, we often think about a "space" in the abstract, but real spacetime cannot be abstracted in that way: the existence and location of matter influences the properties of the space.
- The "extra dimensions" often mentioned are used to make computation feasible; these aren't necessarily "real" dimensions...
- I found most of the chapters approachable, though there were some passages I couldn't follow. In most cases, I just skipped it and moved on.
- It's a **long** book; I skimmed some parts and skipped a number of the more involved proofs. My goal was to get a taste for all the topics; I think it's unrealistic to go into depth on everything covered in this book.
- The e-book from Amazon (in English) is poorly produced with numerous scanning errors (including many cases of swapping 'a' for Greek alpha, etc).
- Complex numbers are special--and really cool :-)
- Not sure this was the author's goal, but after reading the chapter on non-Euclidean geometry, I have a much better grasp of "curved spacetime" and general relativity.
- In geometry, we often think about a "space" in the abstract, but real spacetime cannot be abstracted in that way: the existence and location of matter influences the properties of the space.
- The "extra dimensions" often mentioned are used to make computation feasible; these aren't necessarily "real" dimensions...
- I found most of the chapters approachable, though there were some passages I couldn't follow. In most cases, I just skipped it and moved on.
- It's a **long** book; I skimmed some parts and skipped a number of the more involved proofs. My goal was to get a taste for all the topics; I think it's unrealistic to go into depth on everything covered in this book.
- The e-book from Amazon (in English) is poorly produced with numerous scanning errors (including many cases of swapping 'a' for Greek alpha, etc).
- Complex numbers are special--and really cool :-)
June 21, 2023
On the back cover, this book notes that the New York Times Book Review called this book "Nothing less than a major contribution to the scientific culture of this world." That quote was, and remains, true.
Some of the Soviet Union's most famous and accomplished mathematicians wrote complex, nuanced introductions of major areas of mathematical science from mathematical foundations, analysis, geometry (Euclidian and non-Euclidian), ordinary and partial differential equations, computation, algebra, and probability. Much of it is dated, but that age sometimes works to one's advantage to be able to see the development and progression of the mathematical sciences to the modern era. Thoroughly worth the two months I spent working and annotating through the book, and I'm sure another read will show me the parts I didn't grasp the first read through. All of it is shockingly readable, builds from foundations to application, and is an excellent place for beginners or intermediate mathematicians to get a more comprehensive view of the field in general.
Some of the Soviet Union's most famous and accomplished mathematicians wrote complex, nuanced introductions of major areas of mathematical science from mathematical foundations, analysis, geometry (Euclidian and non-Euclidian), ordinary and partial differential equations, computation, algebra, and probability. Much of it is dated, but that age sometimes works to one's advantage to be able to see the development and progression of the mathematical sciences to the modern era. Thoroughly worth the two months I spent working and annotating through the book, and I'm sure another read will show me the parts I didn't grasp the first read through. All of it is shockingly readable, builds from foundations to application, and is an excellent place for beginners or intermediate mathematicians to get a more comprehensive view of the field in general.
February 24, 2019
I have read only the basic part of this work-the first half. I am not gifted for mathematics though I did study it at university. The introductory part of this work is clear and helpful.
November 27, 2021
If you want to take a trip into the land of mathematics from the height of an aerostat (hot air flying baloon), get this. The authors were top tier USSR mathematicians (eg. Kolmogorov, Alexandrov) and each one of them in every chapter show from a high level (without making it a pop-science book, you *will* see a *lot* of math inside) what the corresponding mathematics field is about. It might not have the latest developments in geometry or algebra, but surely it'll give you a good idea of how mathematics looked like up until the '70s. If you want to introduce someone to university mathematics, this is where they should start from.
December 9, 2015
Awesome panorama of mathematics at not very high level
March 18, 2018
Excellent primer on the scope of mathematics as a discipline.
May 14, 2018
Excellent reference. Wide range of topics written in a clean and simple fashion with good examples.
September 27, 2018
Leaking math cheatin'(1) ingredients, portioning devices, lists, warnings, and insinuations.
February 15, 2025
Simplemente una obra maestra. Un camino logico por las matematicas donde todo lo que sabes y mucho de lo que no conoces empieza a cobrar sentido y formar parte de un unico corpus de conocimiento.
Displaying 1 - 11 of 11 reviews