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Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the '' variety of groups''. History Before the nineteenth century, alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rubik's Cube V2
The Rubik's Cube is a 3-D combination puzzle originally invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, and then by Ideal Toy Corp in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. The cube was released internationally in 1980 and became one of the most recognized icons in popular culture. It won the 1980 German Game of the Year special award for Best Puzzle. , 350 million cubes had been sold worldwide, making it the world's bestselling puzzle game and bestselling toy. The Rubik's Cube was inducted into the US National Toy Hall of Fame in 2014. On the original classic Rubik's Cube, each of the six faces was covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. Some later versions of the cube have been updated to use coloured plastic panels instead, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variety (universal Algebra)
In universal algebra, a variety of algebras or equational class is the class of all algebraic structures of a given signature satisfying a given set of identities. For example, the groups form a variety of algebras, as do the abelian groups, the rings, the monoids etc. According to Birkhoff's theorem, a class of algebraic structures of the same signature is a variety if and only if it is closed under the taking of homomorphic images, subalgebras and (direct) products. In the context of category theory, a variety of algebras, together with its homomorphisms, forms a category; these are usually called ''finitary algebraic categories''. A ''covariety'' is the class of all coalgebraic structures of a given signature. Terminology A variety of algebras should not be confused with an algebraic variety, which means a set of solutions to a system of polynomial equations. They are formally quite distinct and their theories have little in common. The term "variety of algeb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Peacock (mathematician)
George Peacock FRS (9 April 1791 – 8 November 1858) was an English mathematician and Anglican cleric. He founded what has been called the British algebra of logic. Early life Peacock was born on 9 April 1791 at Thornton Hall, Denton, near Darlington, County Durham. His father, Thomas Peacock, was a priest of the Church of England, incumbent and for 50 years curate of the parish of Denton, where he also kept a school. In early life Peacock did not show any precocity of genius, and was more remarkable for daring feats of climbing than for any special attachment to study. Initially, he received his elementary education from his father and then at Sedbergh School, and at 17 years of age, he was sent to Richmond School under James Tate, a graduate of Cambridge University. At this school he distinguished himself greatly both in classics and in the rather elementary mathematics then required for entrance at Cambridge. In 1809 he became a student of Trinity College, Cambridge. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
