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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • A Mathematical Treatment of Economic Cooperation and Competition Among Nations, with Nigeria, USA, UK, China, and the Middle East Examples

      • 1st Edition
      • Volume 203
      • September 30, 2005
      • Ethelbert N. Chukwu
      • English
      • Paperback
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      • eBook
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      The book presents a careful mathematical study of Economic Cooperation and Competition among Nations. It appropriates the principles of Supply and Demand and of Rational Expectations to build the dynamic model of the Gross Domestic Products of two groups of nations which are linked up together. The first group consists of Nigeria, the US, the UK and China. The second group is made up of Egypt, the US, Jordan and Israel. The link connecting the four nations of each group is mirrored in the net export function which is broadened to include trade, debts and the inflow or the outflow of wealth from the competing and cooperating nations. This realistic models of the four interacting GDP's, a hereditary differential game of pursuit are validated with historical data from International Financial Statistic Year Book. The Mathematical model is then studied for controllability: from a current initial GDPs a better state can be attained using government and private strategies which are carefully identified. We use regression and differential equation methods to test whether the four countries are competing or cooperating. The consequences of competition or cooperation are explored. Cooperation can be realized and the growth of wealth assured because the system is controllable and we can increase the growth of GDP and then increase the coefficient of cooperation. The outcome may be unbounded growth of wealth for all concerned – the triumph of cooperation. With analogous simple examples the book shows that sufficiently cooperating systems grow unbounded and competing ones are either bounded at best, or become extinct in finite time. If competition is small, i.e., limited, or regulated the GDP's need not be extinct even after a long time. This results are in contrast with popular opinion which advocate competition over cooperation. The detailed policy implication of the cooperation analysis at one time or the other were advocated by Pope John Paul II, President Clinton and President Bush. The mathematical message is clear: the strategy of cooperation is the best way in an Interconnected World: Cooperation triumphs over competition. The same type of analysis allows the book to argue through modeling that prosperity, internal peace and harmony can flourish in Nigeria among the old three regions and the newer six geopolitical regions. The same is true for the four powerful states in the Middle East.Thus the author’s refreshing approach is the "scientific" treatment of cooperation and competition models of the gross-domestic product of two groups of nations – Nigeria, the USA, the UK, and China, and the USA, Egypt, Jordan and Israel. Attempts are made to provide "scientific" answers to broad national policies. It allows predictions of growth to be made with some degree of accuracy for up to 4 years. MATLAB and Maple programs in accompanied CD are provided. The author's individual nations economic models are cited. The dynamics are ordinary and hereditary games of pursuit also cited from the original earlier writings of the author are models of the economic state of each nation – a vector of six things – the gross domestic product (GDP) (y), interest rate R; employment (or unemployment) (L), value of capital stock (k), prices p(t), and therefore inflation and cumulative balance of payment (E). Each economic state is isolated except the impact of export function on aggregate demand.The main difference between this earlier contributions and this book is the link and its apparent policy implications and consequences.Key features:* Study of Cooperation and Competition among Nations with real life examples from the World Bank, the IMF data of Nigeria, the US; the UK, China, Egypt, Jordan and Israel.* Complete MATLAB or MAPLE program with data output and graphs, and possible realistic prediction of economic growth.* Including a comprehensive CD presenting each program in an easy and accessible way.* Realistic Model – comparison of real data and diagram of output. Duplicatable results.* With the CD and IMF data and generic programs, other groups of nations' economies can be studied as well as the economy of all UN members as a group.

    • The Finite Element Method for Fluid Dynamics

      • 6th Edition
      • November 24, 2005
      • O. C. Zienkiewicz + 2 more
      • English
      • Hardback
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      • Paperback
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      Dealing with general problems in fluid mechanics, convection diffusion, compressible and incompressible laminar and turbulent flow, shallow water flows and waves, this is the leading text and reference for engineers working with fluid dynamics in fields including aerospace engineering, vehicle design, thermal engineering and many other engineering applications. The new edition is a complete fluids text and reference in its own right. Along with its companion volumes it forms part of the indispensable Finite Element Method series.New material in this edition includes sub-grid scale modelling; artificial compressibility; full new chapters on turbulent flows, free surface flows and porous medium flows; expanded shallow water flows plus long, medium and short waves; and advances in parallel computing.

    • Handbook of Differential Equations: Ordinary Differential Equations

      • 1st Edition
      • Volume 2
      • September 2, 2005
      • A. Canada + 2 more
      • English
      • Hardback
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      • eBook
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      This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, writtenby leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience.

    • Topological Algebras with Involution

      • 1st Edition
      • Volume 200
      • July 26, 2005
      • M. Fragoulopoulou
      • English
      • Paperback
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      • Hardback
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      • eBook
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      This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common.Key features:- Lucid presentation- Smooth in reading- Informative- Illustrated by examples- Familiarizes the reader with the non-normed *-world- Encourages the hesitant- Welcomes new comers.

    • Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications

      • 1st Edition
      • Volume 199
      • January 20, 2005
      • Badri Dvalishvili
      • English
      • Hardback
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      • Paperback
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      This monograph is the first and an initial introduction to the theory of bitopological spaces and its applications. In particular, different families of subsets of bitopological spaces are introduced and various relations between two topologies are analyzed on one and the same set; the theory of dimension of bitopological spaces and the theory of Baire bitopological spaces are constructed, and various classes of mappings of bitopological spaces are studied. The previously known results as well the results obtained in this monograph are applied in analysis, potential theory, general topology, and theory of ordered topological spaces. Moreover, a high level of modern knowledge of bitopological spaces theory has made it possible to introduce and study algebra of new type, the corresponding representation of which brings one to the special class of bitopological spaces. It is beyond any doubt that in the nearest future the areas of essential applications will be the theories of linear topological spaces and topological groups, algebraic and differential topologies, the homotopy theory, not to mention other fundamental areas of modern mathematics such as geometry, mathematical logic, the probability theory and many other areas, including those of applied nature. Key Features:- First monograph is "Generalized Lattices"

    • Data Mining and Data Visualization

      • 1st Edition
      • Volume 24
      • May 2, 2005
      • English
      • Hardback
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      • eBook
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      Data Mining and Data Visualization focuses on dealing with large-scale data, a field commonly referred to as data mining. The book is divided into three sections. The first deals with an introduction to statistical aspects of data mining and machine learning and includes applications to text analysis, computer intrusion detection, and hiding of information in digital files. The second section focuses on a variety of statistical methodologies that have proven to be effective in data mining applications. These include clustering, classification, multivariate density estimation, tree-based methods, pattern recognition, outlier detection, genetic algorithms, and dimensionality reduction. The third section focuses on data visualization and covers issues of visualization of high-dimensional data, novel graphical techniques with a focus on human factors, interactive graphics, and data visualization using virtual reality. This book represents a thorough cross section of internationally renowned thinkers who are inventing methods for dealing with a new data paradigm.

    • Introductory Statistics

      • 2nd Edition
      • March 18, 2005
      • Sheldon M. Ross
      • English
      • Hardback
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    • Mathematical Methods For Physicists International Student Edition

      • 6th Edition
      • June 3, 2005
      • George B. Arfken + 1 more
      • English
      • Hardback
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      • eBook
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      This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.

    • The Nuts and Bolts of Proofs

      • 3rd Edition
      • August 1, 2005
      • Antonella Cupillari
      • English
      • Paperback
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      The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.

    • Statistics in Medicine

      • 2nd Edition
      • August 4, 2005
      • Robert H. Riffenburgh
      • English
      • Hardback
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      Medicine deals with treatments that work often but not always, so treatment success must be based on probability. Statistical methods lift medical research from the anecdotal to measured levels of probability. This book presents the common statistical methods used in 90% of medical research, along with the underlying basics, in two parts: a textbook section for use by students in health care training programs, e.g., medical schools or residency training, and a reference section for use by practicing clinicians in reading medical literature and performing their own research. The book does not require a significant level of mathematical knowledge and couches the methods in multiple examples drawn from clinical medicine, giving it applicable context.

Related subjects

Mathematics and applied mathematics

Statistics and probability