High Quality Content by WIKIPEDIA articles! In mathematics, an infrastructure is a group-like structure appearing in global fields.The infrastructure was also described for other global fields, namely for algebraic function field over finite fields. This was done first by A. Stein and H. G. Zimmer in the case of real hyperelliptic function fields. It was extended to certain cubic function fields of unit rank one by R. Scheidler and A. Stein. In 1999, S. Paulus and H.-G. Ruck related the infrastructure of a real quadratic function field to the divisor class group. This connection can be generalized to arbitrary function fields and, combining with R. Schoof's results, to all global fields. Данное издание не является...

ISBN: 978-6-1311-2878-3
Издательство: Книга по требованию
Дата выхода: июль 2011

In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, then any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in (Baer 1940) and are discussed in some detail in the textbook (Lam 1999, §3). Injective modules have been heavily studied, and a variety of additional notions are defined in terms of them: Injective...

ISBN: 978-6-1306-2978-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles!Innumeracy: Mathematical Illiteracy and its Consequences is a 1988 book by mathematician John Allen Paulos (1988 1st ed., 135 p. ; 24 cm. New York : Hill and Wang; ISBN 0809074478) about "innumeracy", a term he embraced to describe the mathematical equivalent of illiteracy — incompetence with numbers rather than words. It was a New York Times bestseller. Paulos speaks mainly of the dangers of mathematical innumeracy; that is, the common misconceptions of the layperson in regards to numbers, exploring the relationship between math and the human mind. Paulos discusses innumeracy with quirky anecdotes, scenarios and facts, encouraging readers in the end to look at their world in a more...

ISBN: 978-6-1311-3792-1
Издательство: Книга по требованию
Дата выхода: июль 2011

Insertion sort is a simple sorting algorithm, a comparison sort in which the sorted array (or list) is built one entry at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages: simple implementation, efficient for (quite) small data sets, adaptive, i.e. efficient for data sets that are already substantially sorted: the time complexity is O(n + d), where d is the number of inversions, more efficient in practice than most other simple quadratic (i.e. O(n2)) algorithms such as selection sort or bubble sort: the average running time is n2/4[citation needed], and the running time is linear in the best case, stable, i.e....

ISBN: 978-6-1307-6786-0
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 978-6-1311-8393-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! En mathematiques, l'integrale curviligne est une integrale ou la fonction a integrer est evaluee sur une courbe. L'integrale curviligne est un des outils de base de l'analyse complexe. Si U est un ouvert du plan complexe, f une fonction continue de U dans C et un arc parametre continument derivable trace de [a,b] dans U on definit l'integrale de f le long de en ecrivant une integrale de variable reelle. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1341-8804-3
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 978-6-1341-8828-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! En mathematiques, on appelle integrale de Lebesgue a la fois une theorie de l'integration d'une fonction selon une mesure quelconque et le cas particulier d'integration d'une fonction definie sur les reels, , munis de la mesure de Lebesgue (ou sur ). Il existe d'autres theories de l'integration. L'integrale de Lebesgue joue un role important en analyse, en theorie des probabilites et dans beaucoup d'autres domaines des mathematiques. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1338-2748-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Integrated mathematics is the term used in the United States to describe the style of mathematics education which integrates many topics or strands of mathematics throughout each year of secondary school. Each math course in secondary school covers topics in algebra, geometry, trigonometry and analysis. Nearly all countries throughout the world, except the United States, follow this type of curriculum. In the United States, topics are usually separated so that one year a student focuses entirely on algebra, the next year entirely on geometry, then another year of algebra and finally an optional fifth year of analysis (calculus). The one exception in the American curriculum would be the fourth...

ISBN: 978-6-1311-3795-2
Издательство: Книга по требованию
Дата выхода: июль 2011

In mathematics, an integral curve is a parametric curve that represents a specific solution to an ordinary differential equation or system of equations. If the differential equation is represented as a vector field or slope field, then the corresponding integral curves are tangent to the field at each point. Integral curves are known by various other names, depending on the nature and interpretation of the differential equation or vector field. In physics, integral curves for an electric field or magnetic field are known as field lines, and integral curves for the velocity field of a fluid are known as flow lines. In dynamical systems, the integral curves for a differential equation that governs a system are referred to as trajectories...

ISBN: 978-6-1311-3658-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, an integrating factor is a function that is chosen to facilitate the solving of a given equation involving differentials. It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus, in this case often multiplying through by an integrating factor allows an inexact differential to be made into an exact differential. This is especially useful in thermodynamics where temperature becomes the integrating factor that makes entropy an exact differential. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1327-9253-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In number theory, integer factorization or prime factorization is the breaking down of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer. When the numbers are very large, no efficient integer factorization algorithm is publicly known; an effort concluded in 2009 by several researchers factored a 232-digit number (RSA-768) utilizing hundreds of machines over a span of 2 years. The presumed difficulty of this problem is at the heart of certain algorithms in cryptography such as RSA. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1326-5080-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, an integral curve is a parametric curve that represents a specific solution to an ordinary differential equation or system of equations. If the differential equation is represented as a vector field or slope field, then the corresponding integral curves are tangent to the field at each point. Integral curves are known by various other names, depending on the nature and interpretation of the differential equation or vector field. In physics, integral curves for an electric field or magnetic field are known as field lines, and integral curves for the velocity field of a fluid are known as flow lines. In dynamical systems, the integral curves for a differential equation that...

ISBN: 978-6-1326-5523-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. In more recent times, the meaning has been broadened to include a view of invariant (or equivariant) transformations from the space of functions on one geometrical space to the space of functions on another geometrical space. Such transformations often take the form of integral transforms such as the Radon transform and its generalizations. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-6788-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Mathematical notation aside, the motivation behind integral transforms is easy to understand. There are many classes of problems that are difficult to solve—or at least quite unwieldy algebraically—in their original representations. An integral transform "maps" an equation from its original "domain" (e.g., functions where time is the independent variable are said to be in the time domain) into another domain. Manipulating and solving the equation in the target domain is, ideally, much easier than manipulation and solution in the original domain. The solution is then mapped back to the original domain with the inverse of the integral transform. Integral transforms work because they are based...

ISBN: 978-6-1327-2903-3
Издательство: Книга по требованию
Дата выхода: июль 2011

The integers (from the Latin integer, literally "untouched", hence "whole": the word entire comes from the same origin, but via French[1]) are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers (?1, ?2, ?3, ...). Viewed as subset of the real numbers, they are numbers that can be written without a fractional or decimal component, and fall within the set {... ?2, ?1, 0, 1, 2, ...}. For example, 65, 7, and ?756 are integers; 1.6 and 1 1/2 are not integers. The set of all integers is often denoted by a boldface Z (or blackboard bold mathbb{Z}, Unicode U+2124 ?), which stands for Zahlen. ?The integers (with addition as operation) form the smallest group containing the...

ISBN: 978-6-1306-2839-0
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! One who constructs a syntactical system usually has in mind from the outset some interpretation of this system. While this intended interpretation can have no explicit indication in the syntactical rules - since these rules must be strictly formal - the author's intention respecting interpretation naturally affects his choice of the formation and transformation rules of the syntactical system. For example, he chooses primitive signs in such a way that certain concepts can be expressed: He chooses sentential formulas in such a way that their counterparts in the intended interpretation can appear as meaningful declarative sentences; his choice of primitive sentences must meet the requirement that...

ISBN: 978-6-1311-8731-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In logic, an intensional statement-form is a statement-form with at least one instance such that substituting co-extensive expressions into it does not always preserve logical value. An intensional statement is a statement that is an instance of an intensional statement-form. Here co-extensive expressions are expressions with the same extension. (A statement-form is simply a form obtained by putting blanks into a sentence where one or more expressions with extensions occur—for instance, "The quick brown ___ jumped over the lazy ___'s back." An instance of the form is a statement obtained by filling the blanks in.) Данное издание не является оригинальным....

ISBN: 978-6-1311-8119-1
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In logic and mathematics, an intensional definition gives the meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined. For example, an intensional definition of "bachelor" is "unmarried man." Being an unmarried man is an essential property of something referred to as a bachelor. It is a necessary condition: one cannot be a bachelor without being an unmarried man. It is also a sufficient condition: any unmarried man is a bachelor. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-8122-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the intersection (denoted as ) of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Although it was invented at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a...

ISBN: 978-6-1311-2885-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Interactive Mathematics Program (IMP) is a four-year, problem-based mathematics curriculum for high schools, designed to meet the needs of both college-bound and non-college-bound students. It was one of several curricula funded by the National Science Foundation and designed around the 1989 National Council of Teachers of Mathematics (NCTM) standards. The curriculum replaces the traditional Algebra I-Geometry-Algebra II/Trigonometry-Precalculus sequence. The IMP books were authored by Dan Fendel and Diane Resek, professors of mathematics at San Francisco State University, and by Lynne Alper and Sherry Fraser. Данное издание не является оригинальным....

ISBN: 978-6-1311-3822-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In model theory, interpretation of a structure M in another structure N is a technical notion that approximates the idea of representing M inside N. For example every reduct or definitional expansion of a structure N has an interpretation in N. Many model-theoretic properties are preserved under interpretability. For example if the theory of N is stable and M is interpretable in N, then the theory of M is also stable. An interpretation of M in N with parameters is a pair where n is a natural number and f is a surjective map from a subset of Nn onto M such that the f-preimage of every set X Mk definable in M by a first-order formula without parameters is definable by a first-order formula with...

ISBN: 978-6-1338-7410-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In descriptive statistics, the interquartile range (IQR), also called the midspread or middle fifty, is a measure of statistical dispersion, being equal to the difference between the third and first quartiles. Unlike (total) range, the interquartile range is a robust statistic, having a breakdown point of 25%, and is thus often preferred to the total range. The IQR is used to build box plots, simple graphical representations of a probability distribution. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1317-5253-7
Издательство: Книга по требованию
Дата выхода: июль 2011

In mathematics, the study of interchange of limiting operations is one of the major concerns of mathematical analysis. in that two given limiting operations, say L and M, cannot be assumed to give the same result when applied in either order.An algebraist would say that the operations do not commute. The approach taken in analysis is somewhat different. Conclusions that assume limiting operations do 'commute' are called formal. The analyst tries to delineate conditions under which such conclusions are valid; in other words mathematical rigour is established by the specification of some set of sufficient conditions for the formal analysis to hold good. It is relatively rare for such sufficient conditions to be also necessary, so that a...

ISBN: 978-6-1311-1303-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematical logic, interpretability is a relation between formal theories that expresses the possibility of interpreting or translating one into the other. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1338-5060-6
Издательство: Книга по требованию
Дата выхода: июль 2011