Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (Canadian Mathematical Society Series of Monographs and Advan) Review

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Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (Canadian Mathematical Society Series of Monographs and Advan) ReviewThis book fills an important and very neglected place in the mathematics curriculum. We suppose we understand the usual, foundational transcendental functions, like the logarithm, exponential, trig functions, and several others. Still, most of us don't really know practical approaches to computing the values of these functions efficiently. We may punch a calculator button or even look at an old tables book, but we ourselves don't always have good ways to compute the values from scratch. If you consult most numerical analysis books, they will give approaches to other computations and even approaches to computing higher transcendental functions, but these foundational calculations are neglected. So, this book is practically the only careful and complete record in book form of the ways these computations ought to be done.
These topics are often bypassed in the curriculum as offered in most schools---even decent schools. So, there are a lot of students (like me) who will want to consult this book as a way to fill in glaring holes in the existing education. It is, of course, entirely possible to use this as a successful text for its own special topics course. That is seldom done, but it would be reasonable. The writing is clear. The scholarship is excellent. There is no reason to complain about this book. The only people who won't just LOVE this book are those who don't care too much for writing that has lots of technical detail. If you're a "big picture" person and don't enjoy knowing the details that make an area craftsmanlike, then you might not enjoy this book as much as I do. I do love it entirely, and feel grateful it is available. Finally, I understand this isn't a great review. I just couldn't stand to see such a fine book with no reviews on Amazon. I invite you to write a more particular review and replace mine.Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (Canadian Mathematical Society Series of Monographs and Advan) Overview

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