This study contributes an understanding of the discursive component of a professional development program focused on middle school students? mathematical ideas and presents a methodological approach for investigating teachers? multifaceted knowledge of teaching mathematics. The teachers that formed the studied discursive community participated in planning and facilitating sessions of an after-school mathematics project for middle school students. Two research questions guided this study: (1) What about teachers? knowledge of pedagogy, mathematics, mathematics for teaching, and student?s epistemological understanding is revealed as they reflect on the facilitation of after-school sessions? and (2) What consequential decisions are made...

ISBN: 978-3-8364-8846-4
Издательство: Книга по требованию
Дата выхода: июль 2011

The international community recognizes the need to improve mathematics education. Citizens of the United States and the Russian Federation are concerned with the mathematics literacy of youth. A traditional teaching approach, one-strategy-fits-all, is no longer working. Constructivist and active learning environments have completely changed the view of teaching and learning mathematics. In order to get quality mathematics education, students need to be actively engaged, interested, and motivated in learning. How can we do it? What works in mathematics classrooms and what does not? How can we improve mathematics education? How can we help students succeed in mathematics? Questions like these constantly arise in many schools around the...

ISBN: 978-3-6390-1201-9
Издательство: Книга по требованию
Дата выхода: июль 2011

The work being presented in this thesis is devoted to investigate the different techniques for solving Quadratic Programming Problems (QPP) and Non-Linear Programming Problems (NLPP). We first develop a technique to generalize the traditional simplex method for solving a special type (Quasi-concave) QPP in which the objective function can be factorized. We then investigate three well known methods in Operation Research known as Lagrange's method, Karush-Kuhn-Tucker (KKT) method and Wolf's method for solving QP and NLP problems. Graphical representation of the above three methods are also demonstrated along with their merits and demerits. We implement Lagrange's method for solving any type of NLPP. For this, we develop a computer...

ISBN: 978-3-8383-8390-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values. If these are called a and b, the process can be described by the following master equations: partial_t P(a, t|x, t_0)=-lambda P(a, t|x, t_0)+mu P(b, t|x, t_0) and partial_t P(b, t|x, t_0)=lambda P(a, t|x, t_0)-mu P(b, t|x, t_0). The process is also known under the names Katz process, dichotomous random process. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-3535-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! The telegrapher's equations (or just telegraph equations) are a pair of linear differential equations which describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver Heaviside who in the 1880s developed the transmission line model which is described in this article. The theory applies to high-frequency transmission lines (such as telegraph wires and radio frequency conductors) but is also important for designing high-voltage energy transmission lines. The model demonstrates that the electromagnetic waves can be reflected on the wire, and that wave patterns can appear along the line....

ISBN: 978-6-1305-0649-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In statistical mechanics, the Temperley–Lieb algebra is an algebra from which are built certain transfer matrices, invented by Neville Temperley and Elliott Lieb. It is also related to integrable models, knot theory and the braid group, quantum groups and subfactors of von Neumann algebras.Statistical mechanics (or statistical thermodynamics) is the application of probability theory (which contains mathematical tools for dealing with large populations) to study the thermodynamic behavior of systems of a large number of particles. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be...

ISBN: 978-6-1311-3248-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. It is sometimes also used to refer to tense logic, a particular modal logic-based system of temporal logic introduced by Arthur Prior in the 1960s. Subsequently it has been developed further by computer scientists, notably Amir Pnueli, and logicians. Temporal logic was first studied in depth by Aristotle, whose writings are filled with an early, partially-developed form of first-order temporal modal binary logic. Among classical logic theories, logic which uses the existential quantifier or the universal quantifier is said to be...

ISBN: 978-6-1303-4970-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The various definitions of tensile strength are shown in the following stress-strain graph for low-carbon steel: Stress vs. Strain curve typical of structural steel.Metals including steel have a linear stress-strain relationship up to the yield point, as shown in the figure. In some steels the stress falls after the yield point. This is due to the interaction of carbon atoms and dislocations in the stressed steel. Cold worked and alloy steels do not show this effect. For most metals yield point is not sharply defined. Below the yield strength all deformation is recoverable, and the material will return to its initial shape when the load is removed. This recoverable deformation is known as...

ISBN: 978-6-1303-9833-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (roughly speaking, "multiplication") to be carried out in terms of linear maps (module homomorphisms). The module construction is analogous to the construction of the tensor product of vector spaces, but can be carried out for a pair of modules over a commutative ring resulting in a third module, and also for a pair of a left-module and a right-module over any ring, with result an abelian group. Tensor products are important in areas of abstract algebra, homological algebra, algebraic topology and algebraic geometry. The universal property of the tensor product of vector spaces extends to...

ISBN: 978-6-1303-5014-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, physics and engineering, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials, and in numerous applications in the physical sciences and engineering. As a tensor is a generalization of a scalar (a pure number representing a value, like length) and a vector (a geometrical arrow in space), a tensor field is a generalization of a scalar field or vector field that assign, respectively, a scalar or vector to each point of space. Данное издание не является...

ISBN: 978-6-1303-4997-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the tensor product, denoted by ?, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules. In each case the significance of the symbol is the same: the most general bilinear operation. In some contexts, this product is also referred to as outer product. The term "tensor product" is also used in relation to monoidal categories. The tensor product V ? W of two vector spaces V and W over a field K can be defined by the method of generators and relations. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-5001-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multi-linear concept. Their well-known properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an extension of linear algebra to multilinear algebra. In differential geometry an intrinsic geometric statement may be described by a tensor field on a manifold, and then doesn't need to make reference to coordinates at all. The same is true in general relativity, of tensor fields describing a physical property. The component-free approach is also used heavily in abstract...

ISBN: 978-6-1303-4980-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the theory of fields in abstract algebra lacks a direct product: the direct product of two fields, considered as a ring is never itself a field. On the other hand it is often required to 'join' two fields K and L, either in cases where K and L are given as subfields of a larger field M, or when K and L are both field extensions of a smaller field N (for example a prime field). The tensor product of fields is the best available construction on fields with which to discuss all the phenomena arising. As a ring, it is sometimes a field, and often a direct product of fields; it can, though, contain non-zero nilpotents (see radical of a ring). Данное издание не...

ISBN: 978-6-1303-5008-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product. It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most general" algebra containing V, in the sense of the corresponding universal property. The tensor algebra also has a coalgebra structure. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-4985-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, the nth term test for divergence is a simple test for the divergence of an infinite series. Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are...

ISBN: 978-6-1311-5477-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! The word term is from the Latin terminus which literally means "boundary line, limit", from the Proto-Indo-European root *ter- "peg, post, boundary". In general mathematical use, however, the word "term" is not limited to additive terms. Individual factors in an expression representing a product would be multiplicative terms. Indeed, individual elements of any mathematical expression may be referred to as terms. Terms in first order logic constitute another use of the word. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1311-5397-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A ternary, three-valued or trivalent logic (sometimes abbreviated 3VL) is any of several multi-valued logic systems in which there are three truth values indicating true, false and some third value. This is contrasted with the more commonly known bivalent logics (such as boolean logic) which provide only for true and false. Conceptual form and basic ideas were initially created by ?ukasiewicz, Lewis and Sulski. These were then re-formulated by Grigore Moisil in an axiomatic algebraic form, and also extended to n-valued logics in 1945. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-5041-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! A ternary search algorithm is a technique in computer science for finding the minimum or maximum of a function that is either strictly increasing and then strictly decreasing or vice versa. A ternary search determines either that the minimum or maximum cannot be in the first third of the domain or that it cannot be in the last third of the domain, then repeats on the remaining two-thirds. A ternary search is an example of a divide and conquer algorithm (see search algorithm). Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1311-2388-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! There are two closely related error-correcting codes known as ternary Golay codes. The code generally known simply as the ternary Golay code is a perfect ternary linear code; the extended ternary Golay code is a linear code obtained by adding a zero-sum check digit to the code.The ternary Golay code has been constructed by Marcel J. E. Golay. He published it in a very short correspondence in 1949. Independently and slightly earlier the same code had also been developed by the Finnish football pool enthusiast Juhani Virtakallio who published it in 1947. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1311-4105-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Terrell rotation is the name of a mathematical and physical effect. Specifically, Terrell rotation is the distortion that a passing object would appear to undergo, according to the special theory of relativity if it were travelling a significant fraction of the speed of light. This behaviour was described independently by both James Terrell and Roger Penrose in pieces published in 1959. Due to an early dispute about priority and correct attribution, the effect is also sometimes referred to as the Penrose-Terrell effect, the Terrell-Penrose effect, or just as the Terrell effect. Данное издание не является...

ISBN: 978-6-1311-4135-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, a tertiary ideal is an (two-sided) ideal in a (perhaps noncommutative) ring that cannot be expressed as a nontrivial intersection of a right fractional ideal with another ideal. Tertiary ideals generalize primary ideals to the case of noncommutative rings. Although primary decompositions do not exist in general for ideals in noncommutative rings, tertiary decompositions do, at least if the ring is Noetherian. Every primary ideal is tertiary. Tertiary ideals and primary ideals coincide for commutatitve rings. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1311-4154-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In geometry, the tesseract, also called an 8-cell or regular octachoron, is the four-dimensional analog of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8 cubical cells. The tesseract is one of the six convex regular 4-polytopes. A generalization of the cube to dimensions greater than three is called a “hypercube”, “n-cube” or “measure polytope”. The tesseract is the four-dimensional hypercube, or 4-cube. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-5074-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher. Tessellations are seen throughout art history, from ancient architecture to modern art. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-1704-1
Издательство: Книга по требованию
Дата выхода: июль 2011

Testing if a multivariate polynomial given as an arithmetic circuit is identically zero is a fundamental problem in the theory of computation. It has been studied by computer scientists and mathematicians for about thirty years. From early on, there have been efficient randomized algorithms solving the problem. However, designing efficient algorithms that use fewer or no random bits at all has turned into a notorious open problem over the years. By now, it is understood that a deterministic algorithm for general arithmetic circuits would have major consequences in theoretical computer science. To approach this goal, it is worthwhile to understand the randomness complexity of polynomial identity testing in restricted models. In this book,...

ISBN: 978-3-6390-2542-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a total of 24 symmetries including transformations that combine a reflection and a rotation. The group of all symmetries is isomorphic to the group S4 of permutations of four objects, since there is exactly one such symmetry for each permutation of the vertices of the tetrahedron. The set of orientation-preserving symmetries forms a group referred to as the alternating subgroup A4 of S4. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-5122-9
Издательство: Книга по требованию
Дата выхода: июль 2011