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Computational Number Theory
In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program. Software packages * Magma computer algebra system * SageMath * Number Theory Library * PARI/GP * Fast Library for Number Theory Further reading * Michael E. Pohst (1993): ''Computational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ABC Conjecture
ABC are the first three letters of the Latin script. ABC or abc may also refer to: Arts, entertainment and media Broadcasting * Aliw Broadcasting Corporation, Philippine broadcast company * American Broadcasting Company, a commercial American TV broadcaster ** Disney–ABC Television Group, the former name of the parent organization of ABC * Australian Broadcasting Corporation, one of the national publicly funded broadcasters of Australia ** ABC Television (Australian TV network), the national television network of the Australian Broadcasting Corporation *** ABC TV (Australian TV channel), the flagship TV station of the Australian Broadcasting Corporation *** ABC Canberra (TV station), Canberra, and other ABC TV local stations in state capitals *** ABC Australia (Southeast Asian TV channel), an international pay TV channel * ABC Radio (other), several radio stations * Associated Broadcasting Corporation, the former name of TV5 Network, Inc., a Philippine media com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Number Theory
In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program. Software packages * Magma computer algebra system * SageMath * Number Theory Library * PARI/GP * Fast Library for Number Theory Further reading * Michael E. Pohst (1993): ''Computational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, '' The Daily Princetonian'', and later added book publishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graduate Texts In Mathematics
Graduate Texts in Mathematics (GTM) () is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with variable numbers of pages). The GTM series is easily identified by a white band at the top of the book. The books in this series tend to be written at a more advanced level than the similar Undergraduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level. List of books #''Introduction to Axiomatic Set Theory'', Gaisi Takeuti, Wilson M. Zaring (1982, 2nd ed., ) #''Measure and Category – A Survey of the Analogies between Topological and Measure Spaces'', John C. Oxtoby (1980, 2nd ed., ) #''Topological Vector Spaces'', H. H. Schaefer, M. P. Wolff (1999, 2nd ed., ) #''A Course in Homological Algebra'', Peter Hilton, Urs Stammbach (1997, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fast Library For Number Theory
The Fast Library for Number Theory (FLINT) is a C library for number theory applications. The two major areas of functionality currently implemented in FLINT are polynomial arithmetic over the integers and a quadratic sieve. The library is designed to be compiled with the GNU Multi-Precision Library (GMP) and is released under the GNU General Public License. It is developed by William Hart of the University of Kaiserslautern (formerly University of Warwick) and David Harvey of University of New South Wales (formerly Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...) to address the speed limitations of the PARI and NTL libraries.Page 10 of thProject DescriptionfoUW 2006 COMPMATH Proposalby William Stein Design Philosophy * Asymptotically Fast Algorith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PARI/GP
PARI/GP is a computer algebra system with the main aim of facilitating number theory computations. Versions 2.1.0 and higher are distributed under the GNU General Public License. It runs on most common operating systems. System overview The PARI/GP system is a package that is capable of doing formal computations on recursive types at high speed; it is primarily aimed at number theorists. Its three main strengths are its speed, the possibility of directly using data types that are familiar to mathematicians, and its extensive algebraic number theory module. The PARI/GP system consists of the following standard components: * PARI is a C library, allowing for fast computations, and which can be called from a high-level language application (for instance, written in C, C++, Pascal, Fortran, Perl, or Python). * gp is an easy-to-use interactive command line interface giving access to the PARI functions. It functions as a sophisticated programmable calculator which contains mos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory Library
NTL is a C++ library for doing number theory. NTL supports arbitrary length integer and arbitrary precision floating point arithmetic, finite fields, vectors, matrices, polynomials, lattice basis reduction and basic linear algebra. NTL is free software released under the GNU Lesser General Public License The GNU Lesser General Public License (LGPL) is a free-software license published by the Free Software Foundation (FSF). The license allows developers and companies to use and integrate a software component released under the LGPL into their own ... v2.1.{{Cite web, title=NTL: A Library for doing Number Theory, url=https://shoup.net/ntl/, access-date=2020-06-06, website=shoup.net References External links Official NTL website C++ libraries Free mathematics software 2015 software ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SageMath
SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, group theory, differentiable manifolds, numerical analysis, number theory, calculus, and statistics. The first version of SageMath was released on 24 February 2005 as free and open-source software under the terms of the GNU General Public License version 2, with the initial goals of creating an "open source alternative to Magma, Maple, Mathematica, and MATLAB". The originator and leader of the SageMath project, William Stein, was a mathematician at the University of Washington. SageMath uses a syntax resembling Python's, supporting procedural, functional, and object-oriented constructs. Development Stein realized when designing Sage that there were many open-source mathematics software packages already written in different languages, namely C, C++, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magma Computer Algebra System
Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure magma. It runs on Unix-like operating systems, as well as Windows. Introduction Magma is produced and distributed by thComputational Algebra Groupwithin the Sydney School of Mathematics and Statistics at the University of Sydney. In late 2006, the booDiscovering Mathematics with Magmawas published by Springer as volume 19 of the Algorithms and Computations in Mathematics series. The Magma system is used extensively within pure mathematics. The Computational Algebra Group maintain a list of publications that cite Magma, and as of 2010 there are about 2600 citations, mostly in pure mathematics, but also including papers from areas as diverse as economics and geophysics. History The predecessor of the Magma system was named Cayley (1982–1993), after Arthur Cayley. Magma was officially released in August 1993 (version 1.0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
