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Graeco-Latin Square
In combinatorics, two Latin squares of the same size (''order'') are said to be ''orthogonal'' if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of mutually orthogonal Latin squares. This concept of orthogonality in combinatorics is strongly related to the concept of blocking in statistics, which ensures that independent variables are truly independent with no hidden confounding correlations. "Orthogonal" is thus synonymous with "independent" in that knowing one variable's value gives no further information about another variable's likely value. An older term for a pair of orthogonal Latin squares is ''Graeco-Latin square'', introduced by Euler. Graeco-Latin squares A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order over two sets and (which may be the same), each consisting of symbols, is an arrangement of cells, ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kathleen Ollerenshaw
Dame Kathleen Mary Ollerenshaw, (''née'' Timpson; 1 October 1912 – 10 August 2014) was a British mathematician and politician who was Lord Mayor of Manchester from 1975 to 1976 and an advisor on educational matters to Margaret Thatcher's government in the 1980s. Early life and education She was born Kathleen Mary Timpson in Withington, Manchester, where she attended Lady Barn House School (1918–26). She was a grandchild of the founder of the Timpson shoe repair business, who had moved to Manchester from Kettering and established the business there by 1870. She became fascinated with mathematics, inspired by the Lady Barn headmistress, Miss Jenkin Jones. While at Lady Barn, she met her future husband, Robert Ollerenshaw. Ollerenshaw became completely deaf at age eight and was taught to lip read. She gravitated toward the study of mathematics as it is not dependent on hearing. She was further inspired by a headmistress at Lady Barn House School who studied mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Computer
A computer is a machine that can be programmed to automatically carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as ''programs'', which enable computers to perform a wide range of tasks. The term computer system may refer to a nominally complete computer that includes the hardware, operating system, software, and peripheral equipment needed and used for full operation; or to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems, including simple special-purpose devices like microwave ovens and remote controls, and factory devices like industrial robots. Computers are at the core of general-purpose devices such as personal computers and mobile devices such as smartphones. Computers power the Internet, which links billions of compute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Remington Rand
Remington Rand, Inc. was an early American business machine manufacturer, originally a typewriter manufacturer and in a later incarnation the manufacturer of the UNIVAC line of mainframe computers. Formed in 1927 following a merger, Remington Rand was a diversified conglomerate making other office equipment, electric shavers, etc. The Remington Rand Building at 315 Park Avenue South in New York City is a 20-floor skyscraper completed in 1911. After 1955, Remington Rand had a long series of mergers and acquisitions that eventually resulted in the formation of Unisys. During World War II, Remington Rand produced M1911 pistols used by the United States Armed Forces. History Remington Rand was formed in 1927 by the merger of the Remington Typewriter Company and Rand Kardex Corporation. One of its earliest factories, the former Herschell–Spillman Motor Company Complex, was listed on the National Register of Historic Places in 2013. ''Note:'' This includes an''Accompanyi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
UNIVAC
UNIVAC (Universal Automatic Computer) was a line of electronic digital stored-program computers starting with the products of the Eckert–Mauchly Computer Corporation. Later the name was applied to a division of the Remington Rand company and successor organizations. The BINAC, built by the Eckert–Mauchly Computer Corporation, was the first general-purpose computer for commercial use, but it was not a success. The last UNIVAC-badged computer was produced in 1986. History and structure J. Presper Eckert and John Mauchly built the ENIAC (Electronic Numerical Integrator and Computer) at the University of Pennsylvania's Moore School of Electrical Engineering between 1943 and 1946. A 1946 patent rights dispute with the university led Eckert and Mauchly to depart the Moore School to form the Electronic Control Company, later renamed Eckert–Mauchly Computer Corporation (EMCC), based in Philadelphia, Pennsylvania. That company first built a computer called BINAC (BINary Automat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AN/USQ-20
The AN/USQ-20, or CP-642 or Naval Tactical Data System (NTDS), was designed as a more reliable replacement for the Seymour Cray-designed AN/USQ-17 with the same instruction set. The first batch of 17 computers were delivered to the Navy starting in early 1961. A version of the AN/USQ-20 for use by the other military services and NASA was designated the UNIVAC 1206. Another version, designated the G-40, replaced the vacuum tube UNIVAC 1104 in the BOMARC Missile Program. In accordance with the Joint Electronics Type Designation System (JETDS), the "''AN/USQ-20''" designation represents the 20th design of an Army-Navy electronic device for general utility special combination equipment. The JETDS system also now is used to name all Department of Defense electronic systems. Technical The machine was the size and shape of an old-fashioned double-door refrigerator, about six feet tall (roughly 1.80 meters). Instructions were represented as 30-bit words in the following forma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raj Chandra Bose
Raj Chandra Bose (or Basu) (19 June 1901 – 31 October 1987) was an Indian American mathematician and statistician best known for his work in design theory, finite geometry and the theory of error-correcting codes in which the class of BCH codes is partly named after him. He also invented the notions of partial geometry, association scheme, and strongly regular graph and started a systematic study of difference sets to construct symmetric block designs. He was notable for his work along with S. S. Shrikhande and E. T. Parker in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that for no ''n'' do there exist two mutually orthogonal Latin squares of order 4''n'' + 2. Early life Bose was born in Hoshangabad, India into a Bengali family; he was the first of five children. His father was a physician and life was good until 1918 when his mother died in the influenza pandemic. His father died of a stroke the following year. Despite difficult ci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof By Exhaustion
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. This is a method of direct proof. A proof by exhaustion typically contains two stages: # A proof that the set of cases is exhaustive; i.e., that each instance of the statement to be proved matches the conditions of (at least) one of the cases. # A proof of each of the cases. The prevalence of digital computers has greatly increased the convenience of using the method of exhaustion (e.g., the first computer-assisted proof of four color theorem in 1976), though such approaches can also be challenged on the basis of mathematical elegance. Expert systems can be used to arrive at answers to many of the questions posed to them. In theory, the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaston Tarry
Gaston Tarry (27 September 1843 – 21 June 1913) was a French mathematician. Born in Villefranche de Rouergue, Aveyron, he studied mathematics at high school before joining the civil service in Algeria. He pursued mathematics as an amateur. In 1901 Tarry confirmed Leonhard Euler's conjecture that no 6×6 Graeco-Latin square was possible (the 36 officers problem). See also *List of amateur mathematicians This is a list of amateur mathematicians—people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics. *Ahmes (scribe) *Ashutosh Mukh ... * Prouhet-Tarry-Escott problem * Tarry point * Tetramagic square References External links * * * People from Villefranche-de-Rouergue 1843 births 1913 deaths Combinatorialists 19th-century French mathematicians 20th-century French mathematicians {{France-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book '' Disquisitiones Arithmeticae'', published in 1801. A familiar example of modular arithmetic is the hour hand on a 12-hour clock. If the hour hand points to 7 now, then 8 hours later it will point to 3. Ordinary addition would result in , but 15 reads as 3 on the clock face. This is because the hour hand makes one rotation every 12 hours and the hour number starts over when the hour hand passes 12. We say that 15 is ''congruent'' to 3 modulo 12, written 15 ≡ 3 (mod 12), so that 7 + 8 ≡ 3 (mod 12). Similarly, if one starts at 12 and waits 8 hours, the hour hand will be at 8. If one instead waited twice as long, 16 hours, the hour hand would be on 4. This ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singly And Doubly Even
In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not. The former names are traditional ones, derived from ancient Greek mathematics; the latter have become common in recent decades. These names reflect a basic concept in number theory, the 2-order of an integer: how many times the integer can be divided by 2. Specifically, the 2-order of a nonzero integer ''n'' is the maximum integer value ''k'' such that ''n''/2''k'' is an integer. This is equivalent to the multiplicity of 2 in the prime factorization. *A singly even number can be divided by 2 only once; it is even but its quotient by 2 is odd. *A doubly even number is an integer that is divisible more than once by 2; it is even and its quotient by 2 is also even. The separate consideration of oddly and evenly even numbers is useful in many parts of mathematics, especially in number theory, combinatoric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific American November 1959 Graeco Latin Square
Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which study the physical world, and the social sciences, which study individuals and societies. While referred to as the formal sciences, the study of logic, mathematics, and theoretical computer science are typically regarded as separate because they rely on deductive reasoning instead of the scientific method as their main methodology. Meanwhile, applied sciences are disciplines that use scientific knowledge for practical purposes, such as engineering and medicine. The history of science spans the majority of the historical record, with the earliest identifiable predecessors to modern science dating to the Bronze Age in Ancient Egypt, Egypt and Mesopotamia (). Their contributions to mathematics, astronomy, and medicine entered and shaped the Gree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
