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Elsevier

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.

  • Integral and Finite Difference Inequalities and Applications

    • 1st Edition
    • Volume 205
    • B. G. Pachpatte
    • English
    The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.

  • Lectures on the Curry-Howard Isomorphism

    • 1st Edition
    • Volume 149
    • Morten Heine Sørensen + 1 more
    • English
    The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic.Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning

  • Handbook of Algebra

    • 1st Edition
    • Volume 4
    • M. Hazewinkel
    • English
    Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest.In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc.The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published.A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.

  • Advances in Computers

    Web Technology
    • 1st Edition
    • Volume 67
    • Marvin Zelkowitz
    • English
    This volume is number 67 in the series Advances in Computers that began back in 1960. This is the longest continuously published series of books that chronicles the evolution of the computer industry. Each year three volumes are produced presenting approximately 20 chapters that describe the latest technology in the use of computers today. Volume 67, subtitled "Web technology," presents 6 chapters that show the impact that the World Wide Web is having on our society today. The general theme running throughout the volume is the ubiquity of web services. Topics such as wireless access and its problems and reliability of web communications are emphasized. Key features: In-depth surveys and tutorials on software development approaches Well-known authors and researchers in the field Extensive bibliographies with most chapters All chapters focus on Internet and web technology issues Discussion of wireless communication and forensic issues, currently important research areas

  • Relation Algebras

    • 1st Edition
    • Volume 150
    • Roger Duncan Maddux
    • English
    The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has considerable mathematical significance, with applications in various fields: e.g., in computer science---databases, specification theory, AI---and in anthropology, economics, physics, and philosophical logic. This comprehensive treatment of the theory of relation algebras and the calculus of relations is the first devoted to a systematic development of the subject.

  • Mathematical Models of the Cell and Cell Associated Objects

    • 1st Edition
    • Volume 206
    • Viktor V. Ivanov + 1 more
    • English
    This book gives the reader a survey of hundreds results in the field of the cell and cell associated objects modeling. Applications to modeling in the areas of AIDS, cancers and life longevity are investigated in this book.

  • Logic and the Modalities in the Twentieth Century

    • 1st Edition
    • Volume 7
    • Dov M. Gabbay + 1 more
    • English
    Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and artificial intelligence, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas.This volume is number seven in the eleven volume Handbook of the History of Logic. It concentrates on the development of modal logic in the 20th century, one of the most important undertakings in logic’s long history. Written by the leading researchers and scholars in the field, the volume explores the logics of necessity and possibility, knowledge and belief, obligation and permission, time, tense and change, relevance, and more. Both this volume and the Handbook as a whole are definitive reference tools for students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, artificial intelligence, for whom the historical background of his or her work is a salient consideration.

  • Computational and Numerical Challenges in Environmental Modelling

    • 1st Edition
    • Volume 13
    • Zahari Zlatev + 1 more
    • English
    Many large mathematical models, not only models arising and used in environmental studies, are described by systems of partial differential equations. The discretization of the spatial derivatives in such models leads to the solution of very large systems of ordinary differential equations. These systems contain many millions of equations and have to be handled over large time intervals by applying many time-steps (up to several hundred thousand time-steps). Furthermore, many scenarios are as a rule to be run. This explains the fact that the computational tasks in this situation are enormous. Therefore, it is necessary to select fast numerical methods; to develop parallel codes and, what is most important when the problems solved are very large to organize the computational process in a proper way.The last item (which is very often underestimated but, let us re-iterate, which is very important) is the major topic of this book. In fact, the proper organization of the computational process can be viewed as a preparation of templates which can be used with different numerical methods and different parallel devices. The development of such templates is described in the book. It is also demonstrated that many comprehensive environmental studies can successfully be carried out when the computations are correctly organized. Thus, this book will help the reader to understand better that, while (a) it is very important to select fast numerical methods as well as (b) it is very important to develop parallel codes, this will not be sufficient when the problems solved are really very large. In the latter case, it is also crucial to exploit better the computer architecture by organizing properly the computational process.

  • Regression Analysis Study Guide

    • 2nd Edition
    • Rudolf J. Freund + 2 more
    • English

  • Regression Analysis

    • 2nd Edition
    • Rudolf J. Freund + 2 more
    • English
    Regression Analysis provides complete coverage of the classical methods of statistical analysis. It is designed to give students an understanding of the purpose of statistical analyses, to allow the student to determine, at least to some degree, the correct type of statistical analyses to be performed in a given situation, and have some appreciation of what constitutes good experimental design.

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