
Pi and the AGM
A Study in Analytic Number Theory and Computational Complexity
Wiley (Publisher)
Published on 27. July 1998
Book
Paperback/Softback
432 pages
978-0-471-31515-5 (ISBN)
Description
Critical Acclaim for Pi and the AGM:
"Fortunately we have the Borwein's beautiful book . . . explores inthe first five chapters the glorious world so dear to Ramanujan . .. would be a marvelous text book for a graduate course."--Bulletinof the American Mathematical Society
"What am I to say about this quilt of a book? One is reminded ofDebussy who, on being asked by his harmony teacher to explain whatrules he was following as he improvised at the piano, replied, "Monplaisir." The authors are cultured mathematicians. They haveselected what has amused and intrigued them in the hope that itwill do the same for us. Frankly, I cannot think of a moreprovocative and generous recipe for writing a book . . . (it) iscleanly, even beautifully written, and attractively printed andcomposed. The book is unique. I cannot think of any other book inprint which contains more than a smidgen of the material theseauthors have included.--SIAM Review
"If this subject begins to sound more interesting than it did inthe last newspaper article on 130 million digits of Pi, I havepartly succeeded. To succeed completely I will have gotten youinterested enough to read the delightful and important book by theBorweins."--American Mathematical Monthly
"The authors are to be commended for their careful presentation ofmuch of the content of Ramanujan's famous paper, 'Modular Equationsand Approximations to Pi'. This material has not heretoforeappeared in book form. However, more importantly, Ramanujanprovided no proofs for many of the claims that he made, and so theauthors provided many of the missing details . . . The Borweins,indeed have helped us find the right roads."--Mathematics ofComputation
"Fortunately we have the Borwein's beautiful book . . . explores inthe first five chapters the glorious world so dear to Ramanujan . .. would be a marvelous text book for a graduate course."--Bulletinof the American Mathematical Society
"What am I to say about this quilt of a book? One is reminded ofDebussy who, on being asked by his harmony teacher to explain whatrules he was following as he improvised at the piano, replied, "Monplaisir." The authors are cultured mathematicians. They haveselected what has amused and intrigued them in the hope that itwill do the same for us. Frankly, I cannot think of a moreprovocative and generous recipe for writing a book . . . (it) iscleanly, even beautifully written, and attractively printed andcomposed. The book is unique. I cannot think of any other book inprint which contains more than a smidgen of the material theseauthors have included.--SIAM Review
"If this subject begins to sound more interesting than it did inthe last newspaper article on 130 million digits of Pi, I havepartly succeeded. To succeed completely I will have gotten youinterested enough to read the delightful and important book by theBorweins."--American Mathematical Monthly
"The authors are to be commended for their careful presentation ofmuch of the content of Ramanujan's famous paper, 'Modular Equationsand Approximations to Pi'. This material has not heretoforeappeared in book form. However, more importantly, Ramanujanprovided no proofs for many of the claims that he made, and so theauthors provided many of the missing details . . . The Borweins,indeed have helped us find the right roads."--Mathematics ofComputation
More details
Edition
Revised edition
Language
English
Place of publication
United States
Publishing group
John Wiley & Sons Inc
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Cloth over boards
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 23 mm
Weight
658 gr
ISBN-13
978-0-471-31515-5 (9780471315155)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Jonathan M. Borwein | Peter Borwein
Pi and the Arithmetic Geometric Mean
Study in Analytic Number Theory and Computational Complexity
Book
01/1987
Wiley
€111.55
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Persons
Jonathan Michael Borwein was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia. Peter B. Borwein is the author of Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, published by Wiley.
Author
Simon Fraser University, Burnaby, Canada
Simon Fraser University, Burnaby, Canada
Content
Complete Elliptic Integrals and the Arithmetic-Geometric MeanIteration.
Theta Functions and the Arithmetic-Geometric Mean Iteration.
Jacobi's Triple-Product and Some Number TheoreticApplications.
Higher Order Transformations.
Modular Equations and Algebraic Approximations to pi.
The Complexity of Algebraic Functions.
Algorithms for the Elementary Functions.
General Means and Iterations.
Some Additional Applications.
Other Approaches to the Elementary Functions.
Pi.
Bibliography.
Symbol List.
Index.
Theta Functions and the Arithmetic-Geometric Mean Iteration.
Jacobi's Triple-Product and Some Number TheoreticApplications.
Higher Order Transformations.
Modular Equations and Algebraic Approximations to pi.
The Complexity of Algebraic Functions.
Algorithms for the Elementary Functions.
General Means and Iterations.
Some Additional Applications.
Other Approaches to the Elementary Functions.
Pi.
Bibliography.
Symbol List.
Index.