The Princeton Companion to Mathematics,   ISBN:9780691118802

Customer Rating: 

This book is a great companion with which to navigate higher mathematics. It allows you to quickly intuit the stunning abstract concepts of higher mathematics, that you often cannot easily see when following the traditional approach of deriving concepts rigorously, from a well-defined foundation. This companion guide gives you a top-down perspective to complement the necessary rigorous bottom-up perspective that you get elsewhere. Mathematical encyclopedias and wikipedia topics don't do this as effectively, so I heartily recommend this book.

Customer Rating: 

The Princeton Companion to mathematics is certainly one of the most important texts ever written in the very large field of the one concerning introduction to mathematics.

It is not an illusion to believe that even the most complex concepts of mathematics , for example algebraic topology or analytic number theory , are accessible by anybody who has at the most, acquired the elementary mathematical knowledge taught in high school.

Actually, it is the fact that all the papers collected in the book are written by the most influential mathematicians in the world that makes it possible.
The utterly clear writing style of the authors also give a very attractive and agreable aspect to the book.

The Companion is not only a collection of detailed introductions to concepts , but also a very useful tool (particularily because a very large part of the book is used to the study of the cultural aspect of mathematics , through biographies and sometimes very deep epistemological analysis of various concepts).

The work is then way more important than a simple overview of the global today's knowledge (as an random encyloapedia or a random work of vulgarisation) , but rather a work on general mathematics and everything related to it (applied mathematics , philosophy etc...).

Of course , I warmly recommand the PCM to anybody interested into mathematics , or more generally in "hard sciences" .

For my part , I enjoyed a passionating and unique odyssea into the universe of mathematics , and it really helped me when studying .

It is after all , the best companion you can always rely on.


Enjoy





A simple look to the panel of the contributors should convince .

Customer Rating: 

I'm not a specialist in the field and I find this grand overview of contemporary mathematics fascinating. The topics range from accessible to intricate and sometimes obscure for the non-specialist. Nonetheless the authors - themselves specialists in the respective fields - manage to engage the reader through a balance between detail and anecdote, cross references, and historical prospective. The book list of topic is vast and comprehensive, although the coverage, by nature, not exhaustive (further readings are always suggested in bibliographic notes). I was pleasantly surprised by finding essays on the mathematics of music, chemistry, biology and economics, as well as biographic notes on the major mathematicians of history.
Overall it makes an outstanding addition to the library of anyone interested in mathematics and its history.

Customer Rating: 

It's an outstanding standing addition to the the field of mathematics. It should be of great interest to professional and amateur mathematicians,scholars, or anyone who is interested in mathematics. Individual chapters are written by world renowned experts in the field. If you want to learn of some of the various topics, famous problems, conjectures, new developments, history of mathematics, and about famouus mathematicians, etc. this is The Source to look at.

Customer Rating: 

I love math, and love testing out mathematical ideas and concepts using computers. The book has already given me hours of enjoyment. I pick up on a topic, explore it a bit, write a script and test it out. I'm not a mathematician by training (my background is engineering) but I do have a strong inclination to math. This book together with Numerical Recepies are my favourite two math books.

Ideas and concepts are presented in an an excellent manner. Some of the topics are over my head but I believe in setting the bar a little high and letting people try an reach it.

And when I don't want to scribble equations and expressions on paper, or program, I turn to the history and biographies of the great mathematicians and their impact on math and science.