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Combinatorics
| Глоссарий по кибернетике |
That branch of mathematics concerned with the variety of combinations of elements that are possible within given constraints including the number of selections, permutations, arrangements, patterns, and organizations a system is capable of. combinatorics is central to statistics and information theory (->combinatorial explosion).
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Mathematics, английский
- The science which treats of every kind of quantity that can be numbered or measured.
- Математика
- Originally, the science of number and quantity. but with the birth pf numerous more qualitative formalisms, (e.g., logic, propositional calculi, set theory), with the emergence of the unifying idea of a mathematical structure, with the advent of the axiomatic method emphasising inference, proof and the descriptions of complex systems in terms of simple axioms, and, finally, with self-reflective efforts such as meta-mathematics, mathematics has become the autonomous (->autonomy) science of formal constructions. emphasising its formal character and its applicability to all conceivable worlds, mathematics has been likened to a language whose semantics is supplied by other sciences or by particular applications. although all constructions are inventions of the human mind, cannot be found in nature and have no necessary connection with the world outside mathematics, they nevertheless arise in conjunction with solving certain kinds of problems:(1) real world problems, (e.g., geometry evolved in efforts of measuring the earth, game theory grew out of concerns for social conflict resolution, statistics from the need to test hypotheses on large numbers of observations, recursive function theory from the desire for efficient algorithms,) (2) intellectual curiosity and playfulness, (e.g., markov chain theory stems from interest in poetry, probability theory from games of chance, the four-color problem, symmetry and much of topology (see the mobiusband) from`interest in artistic expression), and (3) interest in the powers and limitations of ma thema tics and the mind, (e. g., goedel` s incompleteness theorem from the inherent undecidability or incompleteness of systems, the theory of logical types from disturbing paradoxes, the differential and integral calculi from efforts to transcend the smallest distinctions practically possible). ,however, it is a characteristic of mathematics that the problems giving rise to its constructions are soon forgotten and the constructions develop a life of their own, checked only by such validity criteria as internal consistency, decidability and completeness. empirical data from an existing world do not threaten the products of mathematics. 48 matrix; a many-dimensional arrangement of numbers suitable to various transformations which form the basis of matrix algebra. a one-dimensional matrix is called a scalar. most frequent are two-dimensional, n-by-m, matrices which might contain the coefficients (->parameter) of a set of linear equations or specify a mapping from an n-dimensional to a m-dimensional vector space (->hyperspace).
Combinations, английский
The number of combinations of n things taken k at a time is the number of ways of picking a subset of k of the n things, without replacement, and without regard to the order in which the elements of the subset are picked. the number of such combinations is nck = n!/(k!(n−k)!), where k! (pronounced "k factorial") is k×(k−1)×(k−2)× … × 1. the numbers nck are also called the binomial coefficients. from a set that has n elements one can form a total of 2n subsets of all sizes. for example, from the set {a, b, c}, which has 3 elements, one can form the 23 = 8 subsets {}, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}. because the number of subsets with k elements one can form from a set with n elements is nck, and the total number of subsets of a set is the sum of the numbers of possible subsets of each size, it follows that nc0+nc1+nc2+ … +ncn = 2n. the calculator has a button (ncm) that lets you compute the number of combinations of m things chosen from a set of n things. to use the button, first type the value of n, then push the ncm button, then type the value of m, then press the "=" button.
Constraints, английский
Statistics, английский
- A branch of mathematics that deals with collecting, reviewing, summarizing, and interpreting data or information. statistics are used to determine whether differences between study groups are meaningful.
- Статистика (термин, употребляемый в различных значениях, в практической и научной областях. во-первых, статистика понимается как отрасль практической деятельности, направленной на собирание, обработку, анализ и публикацию массовых данных об общественных явлениях, синоним термина в этом смысле слова — понятие статистического учета; во- вторых, статистика рассматривается как отрасль знания, т. е. специальная научная дисциплина, — статистическая наука — и соответственно этому как учебная дисциплина в высших и средних специальных учебных заведениях; в-третьих, под статистикой пони ¦ мают совокупность сводных итоговых цифровых показателей, собранных для характеристики какой-либо области обществ, явлений или отдельного вопроса, например, статистика рождаемости в ссср в послевоенные годы)
- Official figures which show facts population statistics show that the birth rate is slowing down.
- Статистика
- N статистика linguistic ~ лингвистическая статистика stative a стативный, статичный, относящийся к состоянию чего-л. verb
- Статистика. классификация и интерпретация данных клинического исследования в соответствии с теорией вероятности и проверка гипотез применительно к таким данным.
Information, английский
- Knowledge of a particular event or situation, or knowledge communicated or received concerning a particular fact.
- Информация
- Facts about something have you any information about the treatment of sunburn? the police won’t give us any information about how the accident happened. you haven’t given me enough information about when your symptoms started. that’s a very useful piece or bit of information. (note: no plural: some information; a piece of information.)
- N информация | attr. информационный flow, structure source of ~ источник информации 1 ранее использовался в более широком значении как ‘умозаключе- ние’. 2 получение выводных данных в процессе обработки информации и/или языка и само выводное знание, умозаключение; мыслительная операция, в ходе которой человек выходит за пределы данных в тек- сте сведений и получает новую информацию. 3 аффикс, вставляемый внутрь корня слова при словообразовании или словоизменении.
- In admiralty courts, implies a clause introduced into a citation, intimating that in the event of a party cited not appearing, the court will proceed in his absence.
- Информация; данные; сведения
- Координационный комитет ин4юрмации о проектируемых и возводимых объектах строительства
- Literally that which forms within, but more adequately
- Data that has been recorded, classified, organized, related or interpreted so that meaning is apparent.
- Contextualised data providing answer to a certain question decreasing uncertainty.
- Информация, сведения
Combinatorial, английский
A комбинатор- ный (тж. combinatory); semantic-~ семантико- комбинаторный combinatory a комбинаторный (тж . combinatorial) semantics combining a сочетаемый form comitative a совместный case
Constraint, английский
- Сдерживание (отношение события к последующей работе, из-за которого работа не может быть начата; отношение работы к последующему событию, из-за которого это событие не может совершиться)
- N 1 ограничение (син. restriction); 2 то же, что и cognitive principle functional head c~ уис один из принципов универсальной грамматики, согласно кото- рому фунциональная вершина требует нали- чия определенных признаков у своих ком- плементов 1 рассматриваемые в логике утвердительные выражения. mental ~s умственные ограничения
- The difference between a set and a subset indicating that the variety that exists under one condition is less than the variety that exists under another (after ashby). for an observer, constraints become apparent when he finds that a system can assume fewer states than are logically possible or hypothesised by him. within a cartesian product a constraint is the complement of a relation, the former contains all states excluded by the latter. information is a measure of the constraint imposed by a condition or message.
- A limitation or a restriction.
- Сдерживающий фактор
- Any restriction that occurs to the transverse contraction normally associated with a longitudinal tension, and that hence causes a secondary tension in the transverse direction.
Arrangement, английский
- Расположение; компоновка; устройство
- N упорядочение
- A custom-created layout of photos in an album.
- A predefined combination of grouped and sorted messages in table view.
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Cognitive system, английский
A construct, map or maze involving a collection of interconnected items of knowledge or beliefs held by an individual about himself, or about his physical or social environnment including the cognitive system of others, it guides behavior in the domain of this cognitive system. an individual typically possesses several separate cognitive systems. an ideology is the extreme case of a highly integrated and consistent cognitive supersystem governing all the important ones an individual may have.
Computer science, английский
- The study of the use, design and constructions of (largely digital) computers. computer science heavily relies on mathematical (->mathematics) and engineering insights. in spite of its mathematically sophisticated, academically demanding, and economically profitable appearance, its body of generally acceptable fundamental laws or principles, is small. a more appropriate name for this "state of the art"-like body of knowledge would be computer technology.
- A) the study of process, data and computation. b) a very cool profession. (no bias here. ;-) ).
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