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Timeline Of Algorithms
The following timeline of algorithms outlines the development of algorithms (mainly "mathematical recipes") since their inception. Antiquity * Before – writing about "recipes" (on cooking, rituals, agriculture and other themes) * c. 1700–2000 BC – Egyptians develop earliest known algorithms for Ancient Egyptian multiplication, multiplying two numbers * c. 1600 BC – Babylonians develop earliest known algorithms for factorization and finding square roots * c. 300 BC – Euclidean algorithm, Euclid's algorithm * c. 200 BC – the Sieve of Eratosthenes * 263 AD – Gaussian elimination described by Liu Hui Medieval Period * 628 – Chakravala method described by Brahmagupta * c. 820 – Al-Khawarizmi described algorithms for solving linear equations and quadratic equations in his ''The Compendious Book on Calculation by Completion and Balancing, Algebra''; the word ''algorithm'' comes from his name * 825 – Al-Khawarizmi described the algorism, algorithms for using the Hindu� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Equation
In mathematics, a linear equation is an equation that may be put in the form a_1x_1+\ldots+a_nx_n+b=0, where x_1,\ldots,x_n are the variables (or unknowns), and b,a_1,\ldots,a_n are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients a_1, \ldots, a_n are required to not all be zero. Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken. The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true. In the case of just one variable, there is exactly one solution (provided that a_1\ne 0). Often, the term ''linear equation'' refers implicitly to this particular case, in which the variable is sensibly called the ''unknown''. In the case of two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Code Book
''The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography'' is a book by Simon Singh, published in 1999 by Fourth Estate and Doubleday. ''The Code Book'' describes some illustrative highlights in the history of cryptography, drawn from both of its principal branches, codes and ciphers. Thus the book's title should not be misconstrued as suggesting that the book deals only with codes, and not with ciphers; or that the book is in fact a codebook. Contents ''The Code Book'' covers diverse historical topics including the Man in the Iron Mask, Arabic cryptography, Charles Babbage, the mechanisation of cryptography, the Enigma machine, and the decryption of Linear B and other ancient writing systems. Later sections cover the development of public-key cryptography. Some of this material is based on interviews with participants, including persons who worked in secret at GCHQ. The book concludes with a discussion of "Pretty Good Privacy" (PGP), quantum co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simon Singh
Simon Lehna Singh, (born 19 September 1964) is a British popular science author and theoretical and particle physicist. His written works include ''Fermat's Last Theorem'' (in the United States titled ''Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem''), '' The Code Book'' (about cryptography and its history), ''Big Bang'' (about the Big Bang theory and the origins of the universe), '' Trick or Treatment? Alternative Medicine on Trial'' (about complementary and alternative medicine, co-written by Edzard Ernst) and '' The Simpsons and Their Mathematical Secrets'' (about mathematical ideas and theorems hidden in episodes of ''The Simpsons'' and ''Futurama''). In 2012 Singh founded the Good Thinking Society, through which he created the website "Parallel" to help students learn mathematics. Singh has also produced documentaries and works for television to accompany his books, is a trustee of the National Museum of Science and Industry, a patro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cipher
In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "code (cryptography), code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography. Codes generally substitute different length strings of characters in the output, while ciphers generally substitute the same number of characters as are input. A code maps one meaning with another. Words and phrases can be coded as letters or numbers. Codes typically have direct meaning from input to key. Codes primarily function to save time. Ciphers are algorithmic. The given input must follow the cipher's process to be solved. Ciphers are commonly used to encrypt written info ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encryption
In Cryptography law, cryptography, encryption (more specifically, Code, encoding) is the process of transforming information in a way that, ideally, only authorized parties can decode. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Despite its goal, encryption does not itself prevent interference but denies the intelligible content to a would-be interceptor. For technical reasons, an encryption scheme usually uses a pseudo-random encryption Key (cryptography), key generated by an algorithm. It is possible to decrypt the message without possessing the key but, for a well-designed encryption scheme, considerable computational resources and skills are required. An authorized recipient can easily decrypt the message with the key provided by the originator to recipients but not to unauthorized users. Historically, various forms of encryption have been used to aid in cryptography. Early encryption ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Al-Kindi
Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ; ; ) was an Arab Muslim polymath active as a philosopher, mathematician, physician, and music theorist Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. '' The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the " rudiments", that .... Al-Kindi was the first of the Early Islamic philosophy, Islamic peripatetic philosophers, and is hailed as the "father of Arab philosophy". Al-Kindi was born in Kufa and educated in Baghdad. He became a prominent figure in the House of Wisdom, and a number of Abbasid Caliphs appointed him to oversee the translation of Ancient Greece, Greek scientific and philosophical texts into the Arabic language. This contact with "the philosophy of the ancients" (as Hellenistic philosophy was often referred to by Muslim scholars) had a profound effect on him, as he synthes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Analysis
In cryptanalysis, frequency analysis (also known as counting letters) is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers. Frequency analysis is based on the fact that, in any given stretch of written language, certain letters and combinations of letters occur with varying frequencies. Moreover, there is a characteristic distribution of letters that is roughly the same for almost all samples of that language. For instance, given a section of English language, , , and are the most common, while , , and are rare. Likewise, , , , and are the most common pairs of letters (termed ''bigrams'' or ''digraphs''), and , , , and are the most common repeats. The nonsense phrase " ETAOIN SHRDLU" represents the 12 most frequent letters in typical English language text. In some ciphers, such properties of the natural language plaintext are preserved in the ciphertext, and these patterns have the poten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptanalysis
Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation. Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like the British Bombes and Colossus computers at Bletchley Park in World War II, to the mathematically advanced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin
Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area around Rome, Italy. Through the expansion of the Roman Republic, it became the dominant language in the Italian Peninsula and subsequently throughout the Roman Empire. It has greatly influenced many languages, Latin influence in English, including English, having contributed List of Latin words with English derivatives, many words to the English lexicon, particularly after the Christianity in Anglo-Saxon England, Christianization of the Anglo-Saxons and the Norman Conquest. Latin Root (linguistics), roots appear frequently in the technical vocabulary used by fields such as theology, List of Latin and Greek words commonly used in systematic names, the sciences, List of medical roots, suffixes and prefixes, medicine, and List of Latin legal terms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Translations Of The 12th Century
Latin translations of the 12th century were spurred by a major search by European scholars for new learning unavailable in western Europe Renaissance of the 12th century, at the time; their search led them to areas of southern Europe, particularly in Taifa of Toledo, central Spain and Sicily#Arab period (827–1091), Sicily, which recently had come under Christian rule following their reconquest in the late 11th century. These areas had been under Muslim rule for a considerable time, and still had substantial Arabic-speaking populations to support their search. The combination of this accumulated knowledge and the substantial numbers of Arabic-speaking scholars there made these areas intellectually attractive, as well as culturally and politically accessible to Latin scholars. A typical story is that of Gerard of Cremona (c. 1114–87), who is said to have made his way to Toledo, well after its reconquest by Christians in 1085, because he: Many Christian theologians were highly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindu–Arabic Numeral System
The Hindu–Arabic numeral system (also known as the Indo-Arabic numeral system, Hindu numeral system, and Arabic numeral system) is a positional notation, positional Decimal, base-ten numeral system for representing integers; its extension to non-integers is the decimal, decimal numeral system, which is presently the most common numeral system. The system was invented between the 1st and 4th centuries by Indian mathematics, Indian mathematicians. By the 9th century, the system was adopted by Arabic mathematics, Arabic mathematicians who extended it to include fraction (mathematics), fractions. It became more widely known through the writings in Arabic of the Persian mathematician Al-Khwārizmī (''On the Calculation with Hindu Numerals'', ) and Arab mathematician Al-Kindi (''On the Use of the Hindu Numerals'', ). The system had spread to medieval Europe by the High Middle Ages, notably following Fibonacci's 13th century ''Liber Abaci''; until the evolution of the printing pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
