Mathematics Its Content Methods And Meaning Vol 1 Pdf

Open Preview

See a Problem?

We'd love your help. Let us know what's wrong with this preview of Mathematics by A.D. Aleksandrov.

Thanks for telling us about the problem.

Friend Reviews

To see what your friends thought of this book, please sign up.

Reader Q&A

To ask other readers questions about Mathematics, please sign up.

Be the first to ask a question about Mathematics

Community Reviews

· 205 ratings · 9 reviews

Start your review of Mathematics: Its Content, Methods and Meaning

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 i 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.

...more

Sep 13, 2017 Gavin Rebeiro rated it it was amazing

This book really embodies the Russian spirit of mathematics. There aren't any artificial barriers drawn between mathematics and the sciences, evident in so much of mathematical writing today. Reading every section has a very wholesome feel to it.

I'd recommend this to anyone with a good grasp of basic algebra, trigonometry, logic (mathematical induction with propositional and predicate deduction with quantifiers will do), and an elementary exposure to calculus - that's the minimal background required if one wants to absorb the most they can out of this book. However, that does not mean more mathematically-experienced readers will not gain anything from reading this book.

A lot of the now-standard treatments of modern analysis, algebra, geometry, and probability are very abstract. Reading this book will show how a lot of modern mathematics came to be. More often than not, problems from the sciences, physics in particular, were the driving factors behind development of mathematics. There is also quite a detailed section on early electronic computing machines.

The many examples and figures used in this book are astounding, considering this book was written in the 1960s. It really puts a lot of modern 'door-stops' to shame.

The only big downside I can think of is that there isn't really a discussion of mathematical logic.

If you want to have a general resource of mathematics this book will do. Couple it with a good book on logic and you will have a solid set of materials that will allow you to dive into more specialised and recent developments without much hassle.

There are many suggestions for the reader in the form of calculations and examples interspersed in the text. This makes it a very active read and as with every other book on mathematics, reading with pen(cil) and paper at hand is a must. The pedagogy displayed really shows the amount of effort put into the writing of this book.

Some might accuse this book of not being rigorous in the earlier sections, but this style of exposition and use of those methods are completely justified as that's how the mathematics was developed historically. The concepts are what's important. The rigour is there in the later sections of the book. A lot of people today are not taught how to go from conceptual ideas to rigorous mathematics. This book demonstrates the process of mathematical development very well. Effort will be repaid in vast excess. You don't see many books written like this one anymore.

If all of the above hasn't convinced you to read this book, I should add that the three-volumes-bound-as-one-edition comes at a very affordable price as it is a Dover publication.

...more

Feb 24, 2019 Ted Morgan rated it it was amazing

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.

May 19, 2014 Sam rated it liked it

- 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 influenc - 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 :-)
...more

Awesome panorama of mathematics at not very high level

Excellent primer on the scope of mathematics as a discipline.

Sep 27, 2018 Jason rated it liked it

Leaking math cheatin'(1) ingredients, portioning devices, lists, warnings, and insinuations. Leaking math cheatin'(1) ingredients, portioning devices, lists, warnings, and insinuations. ...more