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A Treatise on Bessel Functions and Their Applications to Physics
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Casimir Force, Casimir Operators and the Riemann Hypothesis
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Celestial Encounters
Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34-year-old Henri Poincaré submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three-Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincaré found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos. Starting with the story of Poincaré's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in I...
The Development of Prime Number Theory
1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical ...
The Three-body Problem from Pythagoras to Hawking
This book, written for a general readership, reviews and explains the three-body problem in historical context reaching to latest developments in computational physics and gravitation theory. The three-body problem is one of the oldest problems in science and it is most relevant even in today’s physics and astronomy. The long history of the problem from Pythagoras to Hawking parallels the evolution of ideas about our physical universe, with a particular emphasis on understanding gravity and how it operates between astronomical bodies. The oldest astronomical three-body problem is the question how and when the moon and the sun line up with the earth to produce eclipses. Once the universal g...
Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra
The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.
History of Mathematics
Originally issued in 1893, this popular Fifth Edition (1991) covers the period from antiquity to the close of World War I, with major emphasis on advanced mathematics and, in particular, the advanced mathematics of the nineteenth and early twentieth centuries. In one concise volume this unique book presents an interesting and reliable account of mathematics history for those who cannot devote themselves to an intensive study. The book is a must for personal and departmental libraries alike. Cajori has mastered the art of incorporating an enormous amount of specific detail into a smooth-flowing narrative. The Index—for example—contains not just the 300 to 400 names one would expect to fin...
Number Theory for Computing
Taking readers from elementary number theory, via algorithmic, to applied number theory in computer science, this text introduces basic concepts, results, and methods, before going on to discuss their applications in the design of hardware and software, cryptography, and security. Aimed at undergraduates in computing and information technology, and presupposing only high-school math, this book will also interest mathematics students concerned with applications. XXXXXXX Neuer Text This is an essential introduction to number theory for computer scientists. It treats three areas, elementary-, algorithmic-, and applied number theory in a unified and accessible manner. It introduces basic concepts and methods, and discusses their applications to the design of hardware, software, cryptography, and information security. Aimed at computer scientists, electrical engineers and students the presentation presupposes only an understanding of high-school math.
