Basic Mathematics F/college Stud.-text Book

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.