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Combinatorics

Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics). Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry,[1] and combinatorics also has many applications in mathematical optimization, computer science, ergodic theory and statistical physics. A mathematician who studies combinatorics is called a combinatorialist or a combinatorist.

http://en.wikipedia.org/wiki/Combinatorics

Related:  Matematica

Applied mathematics Applied mathematics is a branch of mathematics that deals with mathematical methods that find use in science, engineering, business, computer science, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.

Mixin Mixins encourage code reuse and avoid well-known pathologies associated with multiple inheritance.[1] History[edit] Definition and implementation[edit] In Simula, classes are defined in a block in which attributes, methods and class initialization are all defined together; thus all the methods that can be invoked on a class are defined together, and the definition of the class is complete. CLOS and Flavors allow mixin methods to add behavior to existing methods: :before and :after daemons, whoppers and wrappers in Flavors. CLOS added :around methods and the ability to call shadowed methods via CALL-NEXT-METHOD.

The Experiment menu - Google Fusion Tables Help Fusion Tables' Labs offers you a chance to try out the newest visualizations on your data. If you're brave enough to try them, it's important to keep the following things in mind: They may break at any time. Similarly, they may disappear temporarily or permanently. They may not be supported on all browsers, all data sets, as embeddable, or have other limitations. They may work so well that they become a regular feature.

Network theory A small example network with eight vertices and ten edges. It has applications in many disciplines including statistical physics, particle physics, computer science, electrical engineering, biology, economics, operations research, and sociology. Applications of network theory include logistical networks, the World Wide Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc; see List of network theory topics for more examples.

Currying Motivation[edit] Currying is similar to the process of calculating a function of multiple variables for some given values on paper. For example, given the function f(x,y) = y / x: Network Graphs Network Graphs In the 18th century in the town of Königsberg, Germany, a favorite pastime was walking along the Pregel River and strolling over the town's seven bridges (Fig. 1). During this period a natural question arose: Is it possible to take a walk and cross each bridge only once? Before reading further, can you determine the answer? This question was solved by the Swiss mathematician Leonard Euler.

Albert-László Barabási Albert-László Barabási (born March 30, 1967) is a Hungarian-American physicist born in Transylvania, Romania, best known for his work in the research of network theory. He is the former Emil T. Hofmann professor at the University of Notre Dame and current Distinguished Professor and Director of Northeastern University's Center for Complex Network Research (CCNR) and an associate member of the Center of Cancer Systems Biology (CCSB) at the Dana Farber Cancer Institute, Harvard University. He introduced in 1999 the concept of scale-free networks and proposed the Barabási–Albert model to explain their widespread emergence in natural, technological and social systems, from the cellular telephone to the World Wide Web or online communities. Birth and education[edit] Barabási was born to an ethnic Hungarian family of the Székely community in Cârţa, Harghita County, Romania.

Lambda calculus The lowercase lambda, the 11th letter of the Greek alphabet, is used to symbolize the lambda calculus. Because of the importance of the notion of variable binding and substitution, there is not just one system of lambda calculus, and in particular there are typed and untyped variants. Historically, the most important system was the untyped lambda calculus, in which function application has no restrictions (so the notion of the domain of a function is not built into the system). In the Church–Turing Thesis, the untyped lambda calculus is claimed to be capable of computing all effectively calculable functions. The typed lambda calculus is a variety that restricts function application, so that functions can only be applied if they are capable of accepting the given input's "type" of data. Lambda calculus in history of mathematics[edit]

Network Graph - Google Fusion Tables Help Current limitations include: The visualization will only show relationships from the first 100,000 rows in a table. A filter can include rows from 100,001 or beyond in the table, but the graph will still not display them.

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