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The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities (Maa Problem Books Series.)
Binding: Paperback
Author: J. Michael Steele
Manufacturer: Cambridge University Press
Availability: Usually ships in 24 hours
Average Rating: 5.0
Total Customer Reviews: 8
List Price: $34.99
Our Price: $29.91
Sales Rank: 206926
Product Description
Michael Steele describes the fundamental topics in mathematical inequalities and their uses. Using the Cauchy-Schwarz inequality as a guide, Steele presents a fascinating collection of problems related to inequalities and coaches readers through solutions, in a style reminiscent of George Polya, by teaching basic concepts and sharpening problem solving skills at the same time. Undergraduate and beginning graduate students in mathematics, theoretical computer science, statistics, engineering, and economics will find the book appropriate for self-study.
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Users Product Reviews: |
Product Review Summary: Highly recommended This is my first review ever of a technical book. I really love this book, and I highly recommend it. It is simultaneously useful, fun, and thought provoking.
Product Review Summary: Excellent examples of proofs This book's topic, mathematical inequalities, could be considered too esoteric to justify a book for more than a small niche audience of mathematicians. Yet this is an exceptionally well-written book that should appeal not only to those who might need inequalities in their work, but also to any student of mathematics who wants to learn how to discover and present elegant proofs. The only prerequisites are a familiarity with series, sequences, and standard notation in calculus and linear algebra.
In addition to its core content, the book does something that too few books in mathematics do: Provide a solution for every exercise. This makes it a precious resource for independent study.
Product Review Summary: Amazing 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 (try [..]
Have a very very nice reading.
Product Review Summary: Great Book, Entertaining 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 :)
Product Review Summary: A delicious smorgasbord of inequalities 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.
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