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Fundamentals of Physics and Chemistry of the Atmosphere
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PI and the AGM: A Study in Analytic Number Theory and Computational Complexity by Jonathan M. Borwein (Repost)
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Algebraic Aspects of Cryptography (Algorithms and Computation in Mathematics) by Neal Koblitz (Repost)
Mathematics Mathematical Foundations of Computer Science 2004 [Repost]
Mathematics Mathematical Logic for Computer Science (3rd edition)
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Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity by Jonathan M. Borwein
Posted on 2011-04-05
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More Presents new research revealing the interplay between classical analysis and modern computation and complexity theory. Two intimately interwoven threads run though the text: the arithmetic-geometric mean (AGM) iteration of Gauss, Lagrange, and Legendre and the calculation of pi[l.c. Greek letter]. These two threads are carried in three directions. The first leads to 19th century analysis, in particular, the transformation theory of elliptic integrals, which necessitates a brief discussion of such topics as elliptic integrals and functions, theta functions, and modular functions. The second takes the reader into the domain of analytic complexity--Just how intrinsically difficult is it to calculate algebraic functions, elementary functions and constants, and the familiar functions of mathematical physics? The answers are surprising, for the familiar methods are often far from optimal. The third direction leads through applications and ancillary material--particularly the rich interconnections between the function theory and the number theory.
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