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A computer is a machine for manipulating data according to a list of instructions known as a program.
Computers are extremely versatile. In fact, they are universal information-processing machines. According to the Church–Turing thesis, a computer with a certain minimum threshold capability is in principle capable of performing the tasks of any other computer, from those of a personal digital assistant to a supercomputer, as long as time and memory capacity are not considerations. Therefore, the same computer designs may be adapted for tasks ranging from processing company payrolls to controlling unmanned spaceflights. Due to technological advancement, modern electronic computers are exponentially more capable than those of preceding generations (a phenomenon partially described by Moore's Law).
Computers take numerous physical forms. Early electronic computers were the size of a large room, and such enormous computing facilities still exist for specialized scientific computation — supercomputers — and for the transaction processing requirements of large companies, generally called mainframes. Smaller computers for individual use, called personal computers, and their portable equivalent, the laptop computer, are ubiquitous information-processing and communication tools and are perhaps what most non-experts think of as "a computer". However, the most common form of computer in use today is the embedded computer, small computers used to control another device. Embedded computers control machines from fighter aircraft to digital cameras.
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Computational Algebra :: Algorithms
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Algorithm Design Manual - Number Theoretic Algorithms - A chapter from The Algorithm Design Manual by Steven S. Skiena.
Algorithmic Number Theory - Notes by Al Sethuraman.
Basics of Computational Number Theory - Notes and Javascript illustrations by Robert Campbell.
Computational Number Theory - Lecture notes by Robert Campbell, December 1997.
Computational Projects in Number Theory - Interesting problems, usually requiring extensive verifications or enumerations, to occupy the idle CPU time of workstations and personal computers. Compiled by Tomás Oliveira e Silva.
Future Directions in Algorithmic Number Theory - Some of the conjectures and open problems motivated by the PRIMES is in P papers, compiled at the AIM.
Implementations of Extended LLL - Links and notes by Wilberd van der Kallen.
LLL Page - Maintained by Keith Matthews. Papers, examples, pseudocode.
Some Number Records - Connected with divisibility and factoring.
Suggested Readings in Algorithmic Number Theory - Provided by the organizers of the MSRI Fall 2000 research program.
The LLL Algorithm - Papers on the LLL algorithm and its applications collected by François Koeune.
Meta Description: [ A list of interesting papers on the LLL algorithm and its applications to cryptology. ]
Visible Euclidean Algorithm - Enter two positive integers, and click the button to see the operations of the Euclidean Algorithm.
| MIT 18.085 Computational Science & Engineering I, Fall 2007 | |
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