1.
Number theory
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Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called The Queen of Mathematics because of its place in the discipline. Number theorists study prime numbers as well as the properties of objects out of integers or defined as generalizations of the integers. Integers can be considered either in themselves or as solutions to equations, questions in number theory are often best understood through the study of analytical objects that encode properties of the integers, primes or other number-theoretic objects in some fashion. One may also study real numbers in relation to rational numbers, the older term for number theory is arithmetic. By the early century, it had been superseded by number theory. The use of the arithmetic for number theory regained some ground in the second half of the 20th century. In particular, arithmetical is preferred as an adjective to number-theoretic. The first historical find of a nature is a fragment of a table. The triples are too many and too large to have been obtained by brute force, the heading over the first column reads, The takiltum of the diagonal which has been subtracted such that the width. The tables layout suggests that it was constructed by means of what amounts, in language, to the identity 2 +1 =2. If some other method was used, the triples were first constructed and then reordered by c / a, presumably for use as a table. It is not known what these applications may have been, or whether there could have any, Babylonian astronomy, for example. It has been suggested instead that the table was a source of examples for school problems. While Babylonian number theory—or what survives of Babylonian mathematics that can be called thus—consists of this single, striking fragment, late Neoplatonic sources state that Pythagoras learned mathematics from the Babylonians. Much earlier sources state that Thales and Pythagoras traveled and studied in Egypt, Euclid IX 21—34 is very probably Pythagorean, it is very simple material, but it is all that is needed to prove that 2 is irrational. Pythagorean mystics gave great importance to the odd and the even, the discovery that 2 is irrational is credited to the early Pythagoreans. This forced a distinction between numbers, on the one hand, and lengths and proportions, on the other hand, the Pythagorean tradition spoke also of so-called polygonal or figurate numbers
2.
Cryptography
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Cryptography or cryptology is the practice and study of techniques for secure communication in the presence of third parties called adversaries. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, Applications of cryptography include ATM cards, computer passwords, and electronic commerce. Cryptography prior to the age was effectively synonymous with encryption. The originator of an encrypted message shared the decoding technique needed to recover the information only with intended recipients. The cryptography literature often uses Alice for the sender, Bob for the intended recipient and it is theoretically possible to break such a system, but it is infeasible to do so by any known practical means. The growth of technology has raised a number of legal issues in the information age. Cryptographys potential for use as a tool for espionage and sedition has led governments to classify it as a weapon and to limit or even prohibit its use. In some jurisdictions where the use of cryptography is legal, laws permit investigators to compel the disclosure of encryption keys for documents relevant to an investigation, Cryptography also plays a major role in digital rights management and copyright infringement of digital media. Until modern times, cryptography referred almost exclusively to encryption, which is the process of converting ordinary information into unintelligible text, decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A cipher is a pair of algorithms that create the encryption, the detailed operation of a cipher is controlled both by the algorithm and in each instance by a key. The key is a secret, usually a short string of characters, historically, ciphers were often used directly for encryption or decryption without additional procedures such as authentication or integrity checks. There are two kinds of cryptosystems, symmetric and asymmetric, in symmetric systems the same key is used to encrypt and decrypt a message. Data manipulation in symmetric systems is faster than asymmetric systems as they generally use shorter key lengths, asymmetric systems use a public key to encrypt a message and a private key to decrypt it. Use of asymmetric systems enhances the security of communication, examples of asymmetric systems include RSA, and ECC. Symmetric models include the commonly used AES which replaced the older DES, in colloquial use, the term code is often used to mean any method of encryption or concealment of meaning. However, in cryptography, code has a specific meaning. It means the replacement of a unit of plaintext with a code word, English is more flexible than several other languages in which cryptology is always used in the second sense above. RFC2828 advises that steganography is sometimes included in cryptology, the study of characteristics of languages that have some application in cryptography or cryptology is called cryptolinguistics
3.
Opteron
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Opteron is AMDs x86 server and workstation processor line, and was the first processor which supported the AMD64 instruction set architecture. It was released on April 22,2003 with the SledgeHammer core and was intended to compete in the server and workstation markets, processors based on the AMD K10 microarchitecture were announced on September 10,2007 featuring a new quad-core configuration. The most-recently released Opteron CPUs are the Piledriver-based Opteron 4300 and 6300 series processors, codenamed Seoul, in January 2016, the first ARMv8-A based Opteron SoC was released. The second capability, by itself, is noteworthy, as major RISC architectures have been 64-bit for many years. The Opteron processor possesses an integrated memory controller supporting DDR SDRAM and this both reduces the latency penalty for accessing the main RAM and eliminates the need for a separate northbridge chip. In multi-processor systems, the CPUs communicate using the Direct Connect Architecture over high-speed HyperTransport links, each CPU can access the main memory of another processor, transparent to the programmer. The Opteron approach to multi-processing is not the same as symmetric multiprocessing, instead of having one bank of memory for all CPUs. Thus the Opteron is a Non-Uniform Memory Access architecture, the Opteron CPU directly supports up to an 8-way configuration, which can be found in mid-level servers. Enterprise-level servers use additional routing chips to support more than 8 CPUs per box, in particular, the Opterons integrated memory controller allows the CPU to access local RAM very quickly. In contrast, multiprocessor Xeon system CPUs share only two buses for both processor-processor and processor-memory communication. As the number of CPUs increases in a typical Xeon system, Intel is migrating to a memory architecture similar to the Opterons for the Intel Core i7 family of processors and their Xeon derivatives. In April 2005, AMD introduced its first multi-core Opterons, at the time, AMDs use of the term multi-core in practice meant dual-core, each physical Opteron chip contained two processor cores. This effectively doubled the performance available to each motherboard processor socket. One socket could then deliver the performance of two processors, two sockets could deliver the performance of four processors, and so on, because motherboard costs increase dramatically as the number of CPU sockets increase, multicore CPUs enable a multiprocessing system to be built at lower cost. AMDs model number scheme has changed somewhat in light of its new multicore lineup, at the time of its introduction, AMDs fastest multicore Opteron was the model 875, with two cores running at 2.2 GHz each. AMDs fastest single-core Opteron at this time was the model 252, for multithreaded applications, or many single threaded applications, the model 875 would be much faster than the model 252. Second-generation Opterons are offered in three series, the 1000 Series, the 2000 Series, and the 8000 Series, the 1000 Series uses the AM2 socket. The 2000 Series and 8000 Series use Socket F. AMD announced its third-generation quad-core Opteron chips on September 10,2007 with hardware vendors announcing servers in the following month, based on a core design codenamed Barcelona, new power and thermal management techniques were planned for the chips
4.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
5.
Prime number
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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a number is called a composite number. For example,5 is prime because 1 and 5 are its only positive integer factors, the property of being prime is called primality. A simple but slow method of verifying the primality of a number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n, algorithms much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits, there are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, many questions regarding prime numbers remain open, such as Goldbachs conjecture, and the twin prime conjecture. Such questions spurred the development of branches of number theory. Prime numbers give rise to various generalizations in other domains, mainly algebra, such as prime elements. A natural number is called a number if it has exactly two positive divisors,1 and the number itself. Natural numbers greater than 1 that are not prime are called composite, among the numbers 1 to 6, the numbers 2,3, and 5 are the prime numbers, while 1,4, and 6 are not prime. 1 is excluded as a number, for reasons explained below. 2 is a number, since the only natural numbers dividing it are 1 and 2. Next,3 is prime, too,1 and 3 do divide 3 without remainder, however,4 is composite, since 2 is another number dividing 4 without remainder,4 =2 ·2. 5 is again prime, none of the numbers 2,3, next,6 is divisible by 2 or 3, since 6 =2 ·3. The image at the right illustrates that 12 is not prime,12 =3 ·4, no even number greater than 2 is prime because by definition, any such number n has at least three distinct divisors, namely 1,2, and n