Struik's book provides solid coverage of curve and surface theory from the classical point of view, i.e. the kind of stuff Monge, Serret, Frenet and Gauss did. I agree that the book should be on the shelves of mathematicians. A number of classical topics are simply not in vogue these days, and one can find them discussed at length in Struik, or in the exercises. In this sense the book certainly has a more geometric flavor than a number of contemporary texts.

However, Struik can't be used to understand what is happening today. For these purposes,books by O'Neill and do Carmo would be more appropriate. The discussion of manifolds and coordinate charts, the discussion of connection forms, differential forms, covariant derivatives, exterior derivatives, pullbacks and pushforwards can be found in these texts. This is the language of modern geometry.It leads on naturally to tensors, fibre bundles, de Rham cohomology and so on and so forth.The emphasis in modern geometry is on global phenomena, the interaction between local and global (e.g. Morse theory or De Rham cohomology), and the attempt to do everything in an algebraic setting (projective modules, spectral sequences, categories etc.) For this purpose, Struik is useless, though he does have some coverage of forms (he calls them by their earlier name of 'pfaffians').

The price of the book makes it an attractive purchase.

I simply cannot believe I am the first reviewer of this book!This book should be on the shelf of every mathematician interested in geometry, every computer graphics specialist, everyone interested in solid modelling. For ten bucks, you get a great summary of a wide range of topics in "classical differential geometry" -- the stuff geometers were interested in one hundred years ago. Today it's gauge and string theory -- but the topics discussed in this book are timeless, and many have seen remarkable renaissances in recent years. It is a wonderful little book ... I am using it to teach a basic differential geometry course next year.

If you are searching some book about introduce you in the math World, you can find it in this book.

If you are looking for a book that clearly describes the evolution of mathematics, you don't need to try more, this book is for you.

Struik's book, "A Concise History of Mathematics", is a well documented book with the main contributions, dates, and names of the people involved in the development of mathematics from their ancients origins until the first half of the 20th century.

Struik's style of writing is clear and, how the title of the book says, concise, highlighting the relevant discoveries made in the field and relating them in order to give a better understanding of the subject.

Reading is easy for all people because Struik avoids to use formulas where it is not necessary, focusing more in the works of the great mathematicians and describing them of a comprehensible way.

Another excellent feature of the book is the great bibliography that contains, with a many references to other books not only in English, but in other languages also.

Somebody would hope to find more mathematical demonstrations and more illustrations, but this is not the objective of the book, contents in a single volume of 228 pages are the most important facts of the history of the mathematics, therefore, the relationship between cost and content is excellent.

A Concise History of Mathematics is a classical book, written by a world wide recognized author, of a clear and concise manner.

All people interested in this area of the mathematics must have this book in their shelf.