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Rating: 
Summary: Wonderful Book --Wish I had had it to read it in high school
Review: Get it now -- don't wait!As might be expected from the title, Steele's book includes an in depth exploration of the Cauchy Schwarz. It, however, includes so much more -- for example, many, many useful inequalities are set forth in its pages. But even its richness in range and number of inequalities (and equalities) is secondary to Prof. Steele's method of explication. For the real fruit of this book is the techniques and confidence built by the exercises and exposure to the examples. The exercises feed and bolster confidence in approching or deriving familiar and more importantly, never-before-seen inequalities, a confidence which grows with each page and exercise. Techniques that might normally only accrete after years of experience in the course of undergraduate and graduate mathematics courses are set forth one after another. On top of that, this is one of that handful of mathematics books that you can read almost like a novel. It's so readable and rewarding/interesting and engaging that when people have asked me what I have been reading lately, I can answer with a good deal of pride and satisfaction: "a book on the Cauchy Schwarz inequality" -- which I never said about Royden, etc. These techniques are vital for many types of research -- applied mathematics, CS, economics, statistics, (and competitions) to name a few -- in all of these areas finding bounds can play a central role in research. Well worth every penny.
Rating:
Summary: Wonderful Book
Review: I rate this book with FIVE STARS *****
Somehow, the review rating software keeps changing the rating to two stars which is incorrect -- again I must emphasize it is FIVE STARS ****.
Get it now -- don't wait!
As might be expected from the title, Steele's book includes an in depth exploration of the Cauchy Schwarz. It, however, includes so much more -- for example, many, many useful inequalities are set forth in its pages. But even its richness in range and number of inequalities (and equalities) is secondary to Prof. Steele's method of explication. For the real fruit of this book is the techniques and confidence built by the exercises and exposure to the examples. The exercises feed and bolster confidence in approching or deriving familiar and more importantly, never-before-seen inequalities, a confidence which grows with each page and exercise. Techniques that might normally only accrete after years of experience in the course of undergraduate and graduate mathematics courses are set forth one after another. On top of that, this is one of that handful of mathematics books that you can read almost like a novel. It's so readable and rewarding/interesting and engaging that when people have asked me what I have been reading lately, I can answer with a good deal of pride and satisfaction: "a book on the Cauchy Schwarz inequality" -- which I never said about Royden, etc. These techniques are vital for many types of research -- applied mathematics, CS, economics, statistics, (and competitions) to name a few -- in all of these areas finding bounds can play a central role in research. Well worth every penny.
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