readme.txt

[什么是数学：对思想和方法的基本研究（增订版）]

	

43 of 46 people found the following review helpful:
Timeless., April 15, 2003
Reviewer:	Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
(REAL NAME)   
Einstein writes..."Easily understandable." And Herman Weyl,..."It is a work of high perfection." It is both for
beginners and for scholars. The first edition by Courant and Robbins, has been revised, with love and care, by Ian Stewart.
Of the sciences, math stands out in the way some central ideas and tools are timeless. Key math ideas from our first mathematical experiences, perhaps early in life, often have more permanence this way. While the fads do change in math, there are some landmarks that remain, and which inspire generations. And they are as useful now as they were at their inception, the fundamentals of numbers, of geometry, of calculus and differential equations, and more. Much of it is presented with an eye to applications. The book is a classic and a masterpiece. The co-authors are ambitious (and remarkably sucessful)in trying to cover the essetials within the span of 500 plus pages. You find the facts, presented in clear and engaging prose, and with lots of illustrations. The book has been used by generations of readers, and it still points to the future.





	

19 of 21 people found the following review helpful:
theoretically very good, December 9, 2002
Reviewer:	"kangaru" (Sydney,OZ) - See all my reviews
This is an interesting and wide ranging book. In the main it presents, develops and explains it's ideas very well, although I did not always find it, as one reviewer, a mister Albert Einstein described it, "easily understandable". I have two minor complaints about this book:

1) Print quality
For no apparent reason the text size varies occasionally, and in places the printing is slightly blurred, so that sometimes the subscripts and superscripts on formulae are illegible. Perhaps they skimped on typesetting costs by photoreproducing formulae from the original printing?

2) Incompleteness
If you bought this book because the front cover says "...representation of the fundamental concepts and methods of the whole field of mathematics" (another A.E. quote) you may be disappointed to find this is not the case. Trigonometry, for example, is not discussed, except where it crops up in other topics such as applying calculus to trig functions.

 

  	

8 of 9 people found the following review helpful:
For mature thinking in mathematics, January 31, 2002
Reviewer:	Alok Govil (CA USA) - See all my reviews
(REAL NAME)   
A "closer" look at mathematics: Book ends where all other books on Mathematics start. With this book, you look at all of basic mathematics much more deeply. It does not help you how to solve specific maths problems, it tells you why were those problems were solved the way they were by the mathematicians.

A unique blend of actual mathematics, philosophy, and history of mathematics. It goes well beyond defining 'what' is mathematics; Actual mathematics is there in the book.

Example: You know (-1)(-1)=(+1) but never knew that there's 'more' to it -- That it sounds so right yet it doesn't have to be right! With this book, you look at all of basic mathematics much more deeply.





	

11 of 12 people found the following review helpful:
A classic that will challenge and inspire.. A MUST HAVE!!, September 11, 2001
Reviewer:	Kersi Von Zerububbel "Kersi" (San Diego, CA USA) - See all my reviews
This book will give you a superb introduction to basic mathematics culminating in the CALCULUS. The topics and manner of presentations are excellent. I have the 1978 edition that I still use to much benefit. Things such as numbers, matrices, algebra and trig are introduced in rapid but detailed segments. If you have been away from mathematics for a while you will soon get drawn into the text and the exercises. If you are into math today this will serve as an excellent review and perhaps give you a gem or two. However, if you have been put off by math in the past you may want to approach with caution. For even though the pace is within speed limits the text does expect a good effort to reap the rewards. I recommend this book for anyone interested in the theory behind mathematics. A real jewel for your library and personal enjoyment. Just superb!





	

15 of 20 people found the following review helpful:
classic, August 3, 2001
Reviewer:	Antonio Villarroel "nrvilla" (Montreal) - See all my reviews
I give this book 5 stars because it is a classic. I believe, however, that it is too sketchy to be useful for the beginner as it is advertised. For chapter 1, for example, on number theory, I recommend Hardy's "Introduction to the Theory of Numbers." For the second chapter, on the number systems, I recommend a book like Birkhoff and MacLane's "Modern Algebra." It's difficult to write a survey of mathematics textbook without being sketchy and Courant isn't up to the task. In addition, the bibliography at the end of the book is fairly outdated, although the two books I mentioned above are included there. I also wish Courant would have provided more information on the evolution of mathematical concepts and ideas. This is something Kline does in his "History of Mathematical Thought." I find this information vital in answering the question "what is mathematics?" If you really want to get a good idea of what mathematics is you should start with a general history of mathematics like Kline's book and quickly move on to Greek mathematics. Even a small understanding of Euclid's axiomatic method will help you understand modern day mathematics and why mathemticians do what they do the way they do it. Having said that, I plan on making more use of Courant's book later on in my mathematics career.





	

9 of 10 people found the following review helpful:
Inspirational, September 14, 2000
Reviewer:	William E. Klitgaard "wklitgaard" (Cranbury, NJ USA) - See all my reviews
Like other reviewers, I first read this book between high school and college, and my experience was the same - wonder, challenge, appreciation. It seems to start off innocently enough, but it quickly moves into complexity and density. Sort of like going for a jog with a Kenyan who decides to "pick up the pace" about a mile out. You may never be the same again.





	

20 of 20 people found the following review helpful:
A Masterpiece, June 23, 2000
Reviewer:	Ary Armando Perez Jr. (Brazil) - See all my reviews
If you start to read "What is Mathematics?" in order to find a direct answer to the title's issue, forget it! I would like to adapt a piece of "My Brain is Open", by Bruce Schechter, in the following way: "Asking a mathematician to explain exactly what is mathematics is a little like asking a poet what a poem is, or a musician what jazz is. Asked this last question, Louis Armstrong replied, `Man, if you gotta ask, you'll never know.'" On the other hand, if you start to read just to go deeper and deeper in the beautiful, and sometimes magic, structure of Math than I say: Go ahead! Because this book is a perennial source of pleasure. Of course it demands a lot of work to solve some of its problems (at least for me!), but as Courant says, you cannot learn music only by listening! I have reproduced almost all the calculations of this book and I know that it demands a lot of effort, but it is one of the few books I know where each small piece of calculation has its own reward! This book is my definition of perfect guide to Math style! Try it!





	

32 of 32 people found the following review helpful:
Inspiring, October 23, 1999
Reviewer: A reader
Although I was always good in math in high school, I never really appreciated it. One summer I found this book in a dusty little corner of a bookshelf and I started reading it. I still remember how for the first time, I was inspired by the subject while reading this book. I couldn't stop reading it, until I finished it. At the time, I didn't really know Calculus or any advanced subject and I had never read any math books other than the high school textbooks. This book literally changed my life. I might have forgotten who my first love was, but I remember very well this book after 25 years!





	

26 of 29 people found the following review helpful:
Masterpiece of mathematical exposition, May 21, 1999
Reviewer:	Giuseppe A. Paleologo "gappy" (Riverdale, NY United States) - See all my reviews
(REAL NAME)   
I read this book while in high school, before enrolling in college. I was captured by the beauty of the subject. Every concept seemed alive: a triumph of imagination, intuition and intelligence. I chose Physics and Mathematics thanks to this book. Without exaggeration, this book had a big influence in my life. Still today it has no equals, and is an enjoyable yet challenging reading for any reader armed with a good hig-school-level math knowledge, and some curiosity.





	

23 of 24 people found the following review helpful:
Excellent overview of the subject and some of its techniques, May 17, 1999
Reviewer: A reader
Covers a lot of different branches of mathematics in depth but does not require a significant mathematical backround. This is good for beginners; you can even learn the basics of calculus, and in a much better way than those "calculus made simple" types of books. I particularly liked the sections on algebraic number fields, geometric constructions, Louisville's construction of transendental numbers, a "probabilistic proof" of the Prime Number Theorem, and the whole section on functions and the Calculus. Actually, the whole book was great. Get it.





	

8 of 9 people found the following review helpful:
A great book for learning AND recreation, March 6, 1999
Reviewer: A reader
I love math. I eat, drink, and sleep math. But nonetheless I sometimes find it dry. But not in this book. It covers just about every major topic in mathematics (and even dabbles into topology and fractals) and does all this in a way that's very interesting, never dry. I found it impossible to put down.





	

2 of 5 people found the following review helpful:
The best book on mathematics which I ever read!, November 26, 1998
Reviewer: A reader
This is a "must read" for every student of mathematics, engineering and the sciences. You will not fail to learn something.

 

13 of 18 people found the following review helpful:
You'll also learn lots of solid mathematics., July 24, 1998
Reviewer: A reader
So Einstein thought this book "easily understandable" ? Well, if you are a beginner at calculus you will not find it "easily understandable", for that would mean you didn't learn a single new thing! Calculus is perhaps the most profound and far-reaching discovery of the millenium, and is certainly not trivial. However, this magical book is the best possible introduction. It is written so that your perplexities will always be accompanied by so beautiful results or promises of results, that you will be more than ready to do the necessary efforts. These come, for instance, in the form of exercises and in the details of the demonstrations, which are all there. There is no cheating. Well, the book is not only about calculus. There are many previous chapters on theory of numbers, geometry, algebra, topology. But I think it culminates with calculus, and the preceding chapters serve as steps of a staircase leading to it. The new edition has the collaboratio! n of Ian Stewart, an inspired writer.





	

7 of 9 people found the following review helpful:
Good book for a math amateur, July 15, 1998
Reviewer: A reader
I am a college student, majoring in math, but not very far along in my major sequence. I found that this book gave me an understandable perspective on what might lie ahead in my studies. I highly recommend this book for anyone who thinks they might be interested in learning more about Mathematics! It inspired me!