Over the last decade or two, there has been a discernible move to include modeling in the mathematics curricula in schools. This has come as the result of the demand that society is making on educational institutions to provide workers that are capable of relating theoretical knowledge to that of the real world. Successful industries are those that are able to effectively overcome the complexities of real world problems they encounter on a daily basis. This book focuses, to some extent, on research conducted at a secondary school. The book, initially, looks at the various definitions of modeling with examples to illustrate where necessary. More importantly though, this work attempted to build on existing research and tested some of these...

ISBN: 978-3-8383-5258-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Road to Reality is a book on modern physics by the British mathematical physicist Roger Penrose, published in 2004. It covers the basics of the standard model of modern physics, discussing general relativity and quantum mechanics and then expands on the possible unification of these two theories. The book is just over 1100 pages, of which the first 350 are dedicated to mathematics—Penrose's goal was to acquaint inquisitive readers with the mathematical tools needed to understand the remainder of the book in depth. On page 383 physics enters the discussion with the topic of spacetime. From there it moves on to fields in spacetime, deriving the classical electrical and magnetic forces from...

ISBN: 978-6-1311-4551-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Sea Island Mathematical Manual or Haidao suanjing was written by the Chinese mathematican Liu Hui of the Three Kingdoms era (220–280) as an extension of chapter 9 of The Nine Chapters on the Mathematical Art. During the Tang Dynasty, this appendix was taken out from The Nine Chapters on the Mathematical Art as a separate book, titled Haidao suanjing (Sea Island Mathematical Manual), named after problem No 1 "Looking at a sea island". This book contained many practical problems of surveying using geometry. This work provided detailed instructions on how to measure distances and heights with tall surveyor's poles and horizontal bars fixed at right angles to them. Данное...

ISBN: 978-6-1311-4557-5
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Sand Reckoner is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. In order to do this, he had to estimate the size of the universe according to the then-current model, and invent a way to talk about extremely large numbers. The work, also known as Archimedis Syracusani Arenarius & Dimensio Circuli, is about 8 pages long in translation, is addressed to the Syracusan king Gelo II (son of Hiero II) and is probably the most accessible work of Archimedes; in some sense, it is the first research-expository paper. Данное издание не является оригинальным. Книга...

ISBN: 978-6-1305-4141-5
Издательство: Книга по требованию
Дата выхода: июль 2011

Since the first cases of HIV/AIDS disease were recognised in the early 1980s, a large number of mathematical models have been proposed. However, the mobility of people, which has an obvious impact on the spread of the disease, has not been much considered in the modelling studies. This book provides various new results pertaining to the spread of the disease, including epidemic intervention, in mobile populations. The results can serve as a basic framework how to formulate and analyse a more realistic stochastic model for the spread of HIV in mobile heterogeneous populations — classifying all individuals by age, risk, and at the same time considering different modes of the disease transmission. Some strategies such as how to allocate a...

ISBN: 978-3-8383-6290-8
Издательство: Книга по требованию
Дата выхода: июль 2011

In this research, respondents are presented with sequences of heads and tails derived from flipping a fair coin five times and asked to consider their chances of occurrence. A new iteration of the comparative likelihood task, which maintains the ratio of heads to tails in all of the sequences presented, provides unique insight into individuals’ perceptions of randomness and associated probabilities. To develop the aforementioned insight, unconventional interpretations of the sample space, organized according to switches, longest run, and switches and longest run, help situate individuals’ answers and justifications within conventional probability. To accurately render the data compiled, an original theoretical framework, entitled the...

ISBN: 978-3-6391-9694-8
Издательство: Книга по требованию
Дата выхода: июль 2011

We continue our investigations of the scale of a quasi-uniform space, which we had started in an earlier article. We distinguish between the left-sided scale and the two-sided scale of a quasi-uniform space. While the behavior of the two-sided scale of a quasi-uniform space X shows similarities with the usual hyperspace of X equipped with its Hausdorff quasi-uniformity, the left-handed scale generalizes the quasi-uniform multifunction space of X into itself.For instance the two-sided scale of any totally bounded quasi-uniform space X is totally bounded, while total boundedness of the left-sided scale of a quasi-uniform space X implies that X is finite or indiscrete. Either construction of the scale is based on the idea of the prefilter...

ISBN: 978-3-8433-8562-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Story of Maths is the title of a television series outlining aspects of the history of mathematics. The series was a co-production between the Open University and the BBC and aired in October 2008 on BBC Four. The material was written and presented by Oxford professor Marcus du Sautoy. The consultants were the Open University academics Robin Wilson, Professor Jeremy Gray and Dr June Barrow-Green. Kim Duke is credited as series producer. The series comprised four programmes respectively titled: The Language of the Universe; The Genius of the East; The Frontiers of Space; and To Infinity and Beyond. Du Sautoy documents the development of mathematics covering subjects such as the invention of...

ISBN: 978-6-1303-5218-9
Издательство: Книга по требованию
Дата выхода: июль 2011

The stability of many physical systems depends on spectral properties of ordinary differential operators posed on the entire line. For numerical purposes, one restricts the all-line spectral problem to a finite interval spectral problem. The question of how the two problems are related then arises. In this work, we study principal (or generalized) eigenvalue problems for ordinary differential equations on the infinite line and bounded, but large, intervals by writing them as matrix problems. Matrix formulations allow us to prove that eigenvalue problems on finite intervals are perturbations of the all-line eigenvalue problem if the boundary conditions satisfy a determinant condition. Using this condition, we also prove the convergence of...

ISBN: 978-3-6391-6590-6
Издательство: Книга по требованию
Дата выхода: июль 2011

This work mainly builds on the Variance Gamma (VG) model for financial assets over time of Madan Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-3-6392-0872-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Value of Science is a book by the French mathematician, physicist, and philosopher Henri Poincare. It was published in 1905. The book deals with questions in the philosophy of science and adds detail to the topics addressed by Poincare's previous book, Science and Hypothesis (1902).The first part of the book deals exclusively with the mathematical sciences, and particularly, the relationship between intuition and logic in mathematics. This historic intuition is therefore mathematical intuition. For Poincare, it is a result of the principle of least effort, that is, of a link to scientific convention based on experimentation. Convention, thus given a context, permits one to consider...

ISBN: 978-6-1311-4614-5
Издательство: Книга по требованию
Дата выхода: июль 2011

The purpose of this book is to generalize to the torsion-theoretic setting various concepts and results from the theory of rings and modules. In particular we work in the areas of chain conditions on modules, injectivity and CS (extending) modules. At the outset we acquaint the reader with the main ideas used in torsion theory. We then obtain results that fall into three more or less interrelated areas. In the first area we introduce a torsion-theoretic analogue of Max modules and generalize an important characterization of Noetherian rings by Shock. The second area deals with various flavors of relative injectivity. We generalize well-known results by Fuchs, Azumaya, Faith, Albu and Nastasescu and Cailleau. In the third area we...

ISBN: 978-3-6391-5782-6
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Karl Theodor Vahlen (1869 in Vienna, Austria – 1945 in Prague) was an Austrian-German mathematician who was an ardent supporter of the Nazi Party. Vahlen studied in Berlin from 1889 and received his doctorate there in 1893. From 1883, Vahlen was a Privatdozent in mathematics at the Konigsberg Albertina University. In 1904, he began teaching at the University of Greifswald, and in 1911 he became an ordinarius professor there. Vahlen had joined the Nazi Party (NSDAP) in 1922. From 1924, he was the first Pomeranian district leader of the NSDAP. In 1924, Vahlen incited a crowd at the University against the Weimar Republic, which resulted in taking down flags of the Republic. The University placed...

ISBN: 978-6-1304-5127-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Theodore John Kaczynski ( born May 22, 1942), also known as the Unabomber (University and Airline Bomber), is an American mathematician and social critic, who carried out a campaign of deadly mail bombings. He was born in Chicago, Illinois, where, as an intellectual child prodigy, he excelled academically from an early age. Kaczynski received an undergraduate degree from Harvard University and earned a PhD in mathematics from the University of Michigan. He became an assistant professor at the University of California, Berkeley at age 25 but resigned two years later. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1313-0195-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Theophile Ernest de Donder (1872 – 1957) was a Belgian mathematician and physicist famous for his 1923 work in developing correlations between the Newtonian concept of chemical affinity and the Gibbsian concept of free energy. He was professor between 1911 and 1942, at the Universite Libre de Bruxelles. Initially he continued the work of Henri Poincare and Elie Cartan. As from 1914 he was influenced by the work of Albert Einstein and was an enthusiastic proponent of the theory of relativity. He gained significant reputation in 1923, when he developed his definition of chemical affinity. He pointed out a connection between the chemical affinity and the Gibbs free energy. Данное...

ISBN: 978-6-1305-1044-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! En mathematiques et plus precisement en theorie des groupes, la theorie des representations d'un groupe fini est un cas particulier de representation des groupes. Il traite du cas ou le groupe etudie est d'ordre fini. L'objectif de cette theorie est l'etude des morphismes d'un groupe fini vers GL(V) le groupe general lineaire des automorphismes d'un espace vectoriel V de dimension finie. Cet article traite de l'aspect mathematiques, un article de synthese existe : Representations d'un groupe fini. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1318-8940-0
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. This article collects the main theorems and definitions in linear algebra. A vector space( or linear space) V over a number field F consists of a set on which two operations (called addition and scalar multiplication, respectively) are defined so, that for each pair of elements x, y, in V there is a unique element x + y in V, and for each element a in F and each element x in V there is a unique element ax in V, such that the following conditions hold. P.S. coefficient of the differential equation,differentiability of complex function,vector space of functionsdifferential operator, auxiliary polynomial, to the...

ISBN: 978-6-1311-4667-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! En mathematiques, le theoreme des fonctions implicites est un resultat de geometrie differentielle. Certaines courbes sont definies par une equation cartesienne, c'est-a-dire la forme f(x, y) = 0, ou x et y decrivent les nombres reels. Le theoreme indique que si la fonction f est suffisamment reguliere au voisinage d'un point de la courbe, il existe une fonction ?, telle que localement, la courbe et le graphe de la fonction ? sont confondus. Plus precisement, si (x0, y0) verifie l'equation, si f est continument differentiable et que sa derivee partielle en (x0, y0) n'est pas nulle, alors il existe un voisinage de (x0, y0) sur lequel la zone s'identifie au graphe de ?. Данное...

ISBN: 978-6-1316-3795-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! En mathematiques, le theoreme des facteurs invariants porte sur les modules de type fini sur les anneaux principaux. Les facteurs invariants sont des obstructions a l'inversibilite des matrices qui n'apparaissent pas dans la theorie des espaces vectoriels. Leur calcul a de nombreuses applications : par exemple trouver la classe d'isomorphie d'un groupe abelien de type fini a partir d'une presentation de celui-ci. Dans un cadre precis, le theoreme des facteurs invariants se particularise en theoremes de reduction d'endomorphisme. Il permet alors notamment de calculer les invariants de similitude d'un endomorphisme sur un espace vectoriel. Le resultat du theoreme des facteurs invariants est aussi...

ISBN: 978-6-1316-3791-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Theory of Constraints (TOC) is an overall management philosophy introduced by Dr. Eliyahu M. Goldratt in his 1984 book titled The Goal, that is geared to help organizations continually achieve their goal. The title comes from the contention that any manageable system is limited in achieving more of its goal by a very small number of constraints, and that there is always at least one constraint. The TOC process seeks to identify the constraint and restructure the rest of the organization around it, through the use of the Five Focusing Steps. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-1208-4
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! En theorie des nombres, le theoreme des nombres premiers est un resultat concernant la densite asymptotique des nombres premiers. Le theoreme des nombres premiers a ete conjecture par Gauss en 1792 alors qu'il avait seulement 15 ans et par Adrien-Marie Legendre en 1798, puis demontre independamment par Jacques Hadamard et de la Vallee Poussin en 1896 a l'aide de methodes d'analyse complexe, en particulier la fonction ? de Riemann. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1316-2802-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! En mathematiques, le theoreme de d'Alembert-Gauss est parfois appele le theoreme de d'Alembert ou encore le theoreme fondamental de l'algebre. Il indique que tout polynome non constant, a coefficients dans les nombres complexes, admet au moins une racine. En consequence, tout polynome a coefficients entiers, rationnels ou encore reels admet au moins une racine complexe, car ces nombres sont aussi des complexes. Une fois ce resultat etabli, il devient simple de montrer que sur mathbb C, le corps des nombres complexes, tout polynome P est scinde, c'est-a-dire qu'il se decompose de maniere unique en produit d'une constante et d'autant de polynomes unitaires du premier degre que le degre de P....

ISBN: 978-6-1316-3755-1
Издательство: Книга по требованию
Дата выхода: июль 2011

By now Algebra (based on set theoretic notions) and Topology have established their dominance over almost all the disciplines in pure mathematics. Both of these subjects have become so vast that they need their detailed discussion separately. However, an attempt has been made here to present the basic and core topics of these subjects together. The book comprises of three main parts:(i) Algebraic systems: Sets and Functions, Groups, Rings, Fields, Integral domains and Linear (or Vector) spaces; (ii) Metric spaces, and (iii) Topological spaces. The first chapter starts with Sets and Functions. It includes the main features of the Set Theory needed in our subsequent discussions. The next three chapters dwell upon different kinds of...

ISBN: 978-3-8383-9943-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the theorem of the cube is a condition for a line bundle of a product of three complete varieties to be trivial. It was a principle discovered, in the context of linear equivalence, by the Italian school of algebraic geometry. The specific result was proved under this name, in the early 1950s, in the course of his fundamental work on abstract algebraic geometry by Andre Weil; a discussion of the history has been given by Kleiman (2005). A treatment by means of sheaf cohomology, and description in terms of the Picard functor, was given by Mumford (2008). The theorem states that for any complete varieties U, V and W, and given points u, v and w on them, any invertible sheaf L...

ISBN: 978-6-1311-4630-5
Издательство: Книга по требованию
Дата выхода: июль 2011

In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. The individual sentences of a theory are called its theorems. When defining theories for foundational purposes, additional care must be taken and normal set-theoretic language may not be appropriate. The construction of a theory begins by specifying a definite non-empty conceptual class mathcal{E}, the elements of which are called statements. These initial statements are often called the primitive elements or elementary statements of the theory, to distinguish them from other statements which may be derived from them. A theory mathcal{T} is a conceptual class consisting of certain of these elementary statements. The elementary...

ISBN: 978-6-1303-0592-5
Издательство: Книга по требованию
Дата выхода: июль 2011