|
| The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities (Maa Problem Books Series.) | 
| Author: J. Michael Steele
Publisher: Cambridge University Press
Category: Book
List Price: $33.99
Buy New: $26.99
You Save: $7.00 (21%)
New (16) from $26.99
Avg. Customer Rating:  6 reviews
Sales Rank: 146769
Media: Paperback
Number Of Items: 1
Pages: 316
Shipping Weight (lbs): 0.9
Dimensions (in): 8.7 x 5.9 x 0.6
ISBN: 052154677X
Dewey Decimal Number: 512.97
EAN: 9780521546775
ASIN: 052154677X
Publication Date: April 26, 2004
Availability: Usually ships in 1-2 business days
Condition: BRAND NEW CRISP AND CLEAN COPY.
|
| Customer Reviews:
| Showing reviews 1-5 of 6 | | NEXT » |
Amazing June 26, 2008
1 out of 1 found this review helpful
Really, you should own it.
It's such a beautiful book. The text, the content, the structure, the exercises, the solutions, the tricks and insight, and it's soft and handy.
What a book. It's modern, rigorous, gives you references to more advanced texts, and teaches you a lot! A pleasure.
If you're interested in inequalities you should really buy it, but even you if don't want to, it's available on the internet (peer-to-peer or torrents..)
Have a very very nice reading.
Great Book, Entertaining December 25, 2007
2 out of 3 found this review helpful
Prof. Steele has done a great job in providing an "entertaining" (if I may say) book on inequalities. Along with Cauchy-Schwarz inequality the book provides very "lively and problem oriented" (adjectives from the first page of the book) chapters that are insightful and enjoyable. For example, the way you are introduced to Cauchy-Schwarz inequality involves attempting it as a "problem" - first looking at cases n=1 and n=2 trying to use induction. After that you get into fancy approach using quadratic expression. Such an approach throughout the book makes this book really enjoyable. Solutions provided make it ideal for self learning as well as a book to entertain yourself when you get bored :)
A delicious smorgasbord of inequalities June 24, 2006
22 out of 22 found this review helpful
Professor Steele has done a wonderful job in developing the theory behind the Cauchy-Schwarz inequality. He starts off with the basic theory and then through the course of the book he teases out the limitless ways the inequality can be used. There is a breathtaking sweep of applications. What is interesting and valuable about his approach is that as he develops the building blocks he explains why or why not a particular approach might not work. I think there is quite a bit of Polya's inspiration in his approach. For instance, he gives Polya's proof of the Carleman inequality which, on it face, is almost outrageously unbelievable ( where does the "e" come from?) but by that stage you worked through the challenge problems and the other material and it is possible to see why the "e" makes sense.
The challenge problems are excellent and his solutions sometimes skip over some important steps which a teacher could get students to fill in so that they can demonstrate that they understand the material.
There is a lot to learn from this book and it should be read by everyone who is seriously interested in mathematics. The classic Hardy-Littlewood-Polya book on inequalities is a quite different beast but the two together provide the serious reader with a depth of understanding that is hard to surpass.
at the core of mathematics March 19, 2006
14 out of 14 found this review helpful
this book deals in a friendly fashion with inequalities (and therefore) with the elementary use of convexity and integrals.
Famous inequalities bear the name of famous mathematicians, e.g: Tchebychev, Hilbert, Cauchy, Hardy, Rademacher...This is one way to understand their significance in maths. This book is about those ones and others such as 3/2 < a/(b+c) + b/(c+a) + c/(a+b) and the many ways to tackle with the fact of proving and using them. Study of this book should be seen as a good and rewarding path towards improving one's mathematical skills .
Erudite and stimulating problem book in inequalities September 11, 2005
40 out of 40 found this review helpful
The classic work in this field is Hardy, Littlewood, and Polya's "Inequalities", but as much as I admire these authors for their other works, I have never gotten much out of their inequality book. Steele's book is different: extremely clear, erudite, and thorough, it almost makes everything obvious. The subject of inequalities is something of a hodge-podge, and Steele isn't able to change that, but he helps tie it together with lots of forward and backward references and with returns to problems after we have learned new methods. A good example is Carleman's inequality (easily the most startling result in the book); Steele provides three different proofs spread out through the book, plus a continuous analog.
Despite the title, the book is not primarily about the Cauchy-Schwarz inequality, although it (and the Arithmetic-Geometric Mean inequality and Jensen's inequality) do recur throughout the book.
The book is structured as a problem book. The body consists of a number of "challenges", each followed by an exploration of how to solve it. Each chapter ends with a copious selection of exercises; they are not as hard as the challenges, but they are hard enough and they will build your mastery of the material. All exercises are worked out in full in the back of the book.
|
|
|
Wildlife, nature and the Environment
Sponsored Links
Learn how to get your own Amazon Book shop | |
