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Conceptual Mathematics, F. William Lawvere



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Автор: F. William Lawvere
Название:  Conceptual Mathematics   (Лоренс Уильям: Концептуальная математика)
Издательство: Cambridge Academ
Классификация:
ISBN: 052171916X
ISBN-13(EAN): 9780521719162
Обложка/Формат: Paperback
Страницы: 408
Вес: 0.784 кг.
Дата издания: 01.09.2009
Язык: English
Издание: 2 rev ed
Иллюстрации: 575 b/w illus. 12 tables 213 exercises
Размер: 170 x 243 x 23
Читательская аудитория: Tertiary education (us: college)
Подзаголовок: A first introduction to categories
Ссылка на Издательство: Link
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Поставляется из: Англии
Описание: In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.
Дополнительное описание: Foreword; Note to the reader; Preview; Part I. The Category of Sets: 1. Sets, maps, composition; Part II. The Algebra of Composition: 2. Isomorphisms; Part III. Categories of Structured Sets: 3. Examples of categories; Part IV. Elementary Universal Mappin




      Старое издание
Conceptual Mathematics

Автор: F. William Lawvere
Название: Conceptual Mathematics
ISBN: 0521894859 ISBN-13(EAN): 9780521894852
Издательство: Cambridge Academ
Цена: 8053 р.
Наличие на складе: Поставка под заказ.
Описание: In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.


Conceptual Mathematics

Автор: F. William Lawvere
Название: Conceptual Mathematics
ISBN: 0521894859 ISBN-13(EAN): 9780521894852
Издательство: Cambridge Academ
Рейтинг:
Цена: 8053 р.
Наличие на складе: Поставка под заказ.

Описание: In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

Mathematics for the Imagination

Автор: Higgins
Название: Mathematics for the Imagination
ISBN: 0198604602 ISBN-13(EAN): 9780198604600
Издательство: Oxford Academ
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Цена: 1672 р.
Наличие на складе: Поставка под заказ.

Описание: Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind.

Proceedings of the Conference on Applied Mathematics and Scientific Computing

Автор: Drmac Zlatko, Marusic Miljenko, Tutek Zvonimir
Название: Proceedings of the Conference on Applied Mathematics and Scientific Computing
ISBN: 1402031963 ISBN-13(EAN): 9781402031960
Издательство: Springer
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Цена: 14629 р.
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Описание: This book brings together contributed papers presenting new results covering different areas of applied mathematics and scientific computing.Firstly, four invited lectures give state-of-the-art presentations in the fields of numerical linear algebra, shape preserving approximation and singular perturbation theory. Then an overview of numerical solutions to skew-Hamiltonian and Hamiltonian eigenvalue problems in system and control theory is given by Benner, Kressner and Mehrmann. The important issue of structure preserving algorithms and structured condition numbers is discussed. Costantini and Sampoli review the basic ideas of the abstract schemes and show that they can be used to solve any problem concerning the construction of spline curves subject to local constraints. Kvasov presents a novel approach in solving the problem of shape preserving spline interpolation. Formulating this problem as a differential multipoint boundary value problem for hyperbolic and biharmonic tension splines he considers its finite difference approximation. Miller and Shishkin consider the Black-Scholes equation that, for some values of the parameters, may be a singularly perturbed problem. They construct a new numerical method, on an appropriately fitted piecewise-uniform mesh, which is parameter-uniformly convergent.

Where Mathematics, Computer Science, Linguistics and Biology Meet

Автор: MartГ­n-Vide Carlos, Mitrana V.
Название: Where Mathematics, Computer Science, Linguistics and Biology Meet
ISBN: 079236693X ISBN-13(EAN): 9780792366935
Издательство: Springer
Цена: 17760 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: There are not many interdisciplinary scientific fields as formal language theory. In this volume, it is presented as the very intersection point between Mathematics, Computer Science, Linguistics and Biology. The book is a collection of papers going deep into classical topics in computer science inspired formal languages, as well as other ones showing new concepts and problems motivated in linguistics and biology. The papers are organized in four sections: Grammars and Grammar Systems, Automata, Languages and Combinatorics, and Models of Molecular Computing. They clearly prove the power, wealth and vitality of the theory nowadays and sketch some trends for its future development. The volume is intended for an audience of computer scientists, computational linguists, theoretical biologists and any other people interested in dealing with the problems and challenges of interdisciplinarity.

Topological and Algebraic Structures in Fuzzy Sets / A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

Автор: Rodabaugh S.E., Klement E.P
Название: Topological and Algebraic Structures in Fuzzy Sets / A Handbook of Recent Developments in the Mathematics of Fuzzy Sets
ISBN: 1402015151 ISBN-13(EAN): 9781402015151
Издательство: Springer
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Цена: 21632 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: Topological and Algebraic Structures in Fuzzy Sets has these unique features: -strategically located at the juncture of fuzzy sets, topology, algebra, lattices, foundations of mathematics; -major studies in uniformities and convergence structures, fundamental examples in lattice-valued topology, modifications and extensions of sobriety, categorical aspects of lattice-valued subsets, logic and foundations of mathematics, t-norms and associated algebraic and ordered structures; -internationally recognized authorities clarify deep mathematical aspects of fuzzy sets, particularly those topological or algebraic in nature; -comprehensive bibliographies and tutorial nature of longer chapters take readers to the frontier of each topic; -extensively referenced introduction unifies volume and guides readers to chapters closest to their interests; -annotated open questions direct future research in the mathematics of fuzzy sets; -suitable as a text for advanced graduate students.

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences / With Complete Bibliography

Автор: Glazek K.
Название: A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences / With Complete Bibliography
ISBN: 1402007175 ISBN-13(EAN): 9781402007170
Издательство: Springer
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Цена: 13584 р.
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Описание: This book presents a guide to the extensive literature on the topic of semirings and includes a complete bibliography. It serves as a complement to the existing monographs and a point of reference to researchers and students on this topic. The literature on semirings has evolved over many years, in a variety of languages, by authors representing different schools of mathematics and working in various related fields. Recently, semiring theory has experienced rapid development, although publications are widely scattered. This survey also covers those newly emerged areas of semiring applications that have not received sufficient treatment in widely accessible monographs, as well as many lesser-known or `forgotten' works. The author has been collecting the bibliographic data for this book since 1985. Over the years, it has proved very useful for specialists. For example, J.S. Golan wrote he owed `... a special debt to Kazimierz Glazek, whose bibliography proved to be an invaluable guide to the bewildering maze of literature on semirings'. U. Hebisch and H.J. Weinert also mentioned his collection of literature had been of great assistance to them. Now updated to include publications up to the beginning of 2002, this work is available to a wide readership. Audience: This volume is the first single reference that can guide the interested scholar or student to the relevant publications in semirings, semifields, algebraic theory of languages and automata, positive matrices and other generalisations, and ordered semigroups and groups.

Internal Logic / Foundations of Mathematics from Kronecker to Hilbert

Автор: Gauthier Y.
Название: Internal Logic / Foundations of Mathematics from Kronecker to Hilbert
ISBN: 1402006896 ISBN-13(EAN): 9781402006890
Издательство: Springer
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Цена: 14629 р.
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Описание: Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer.The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.

Thirty Five Years of Automating Mathematics

Автор: Kamareddine F.D.
Название: Thirty Five Years of Automating Mathematics
ISBN: 1402016565 ISBN-13(EAN): 9781402016561
Издательство: Springer
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Цена: 17241 р.
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Описание: N.G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. In the 1960s he became fascinated by the new computer technology and decided to start the Automath project where he could check, with the help of the computer, the correctness of books on mathematics. Through his work on Automath de Bruijn started a revolution in using the computer for verification, and since, we have seen more and more proof-checking and theorem-proving systems. Automath was written in Algol 60 and implemented on the primitive computers of the sixties. Thirty years on, both technology and theory have evolved a lot leading to impressive new directions in using the computer for manipulating and checking mathematics. This volume is a collection of papers with a personal flavour. It consists of 11 articles which propose interesting variations to or examples of mechanising mathematics and illustrate differ developments in symbolic computation in the past 35 years. The first paper is by de Bruijn himself where he uses his experience of automating mathematics to reason about the human mind. After that a number of intriguing articles have been contributed by amongst others Henk Barendregt, who proposes a mathematical proof language between informal and formalised mathematics which helps make proof assistants more user friendly, and Robert Constable, explaining how Automath's telescopes, books and definitions compare to recent developments in computational type theory made by his Nuprl group. The volume further includes a strong argumentation by Arnon Avron that for automated reasoning, there is an interesting logic, somewhere strictly between first and second order logic, determined essentially by an analysis of transitive closure, yielding induction; and Murdoch Gabbay presenting an interesting generalisation of Fraenkel-Mostowski (FM) set theory within higher-order logic, and applying it to model Milner's p-calculus.

Cryptological Mathematics

Автор: Robert Edward Lewand
Название: Cryptological Mathematics
ISBN: 0883857197 ISBN-13(EAN): 9780883857199
Издательство: Cambridge Academ
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Цена: 3565 р.
Наличие на складе: Поставка под заказ.

Описание: This is an introduction to the mathematics involved in the intriguing field of cryptology, the science of writing and reading secret messages which are designed to be read only by their intended recipients. It is written at an elementary level, suitable for beginning undergraduates, with careful explanations of all the concepts used. The basic branches of mathematics required, including number theory, abstract algebra and probability, are used to show how to encipher and decipher messages, and why this works, giving a practical as well as theoretical basis to the subject. Challenging computer programming exercises are also included. The book is written in an engaging style which will appeal to all, and also includes historical background on some of the founders of the subject. It will be of interest both to students wishing to learn cryptology per se, and also to those searching for practical applications of seemingly abstract mathematics.

The Mathematics of Logic

Автор: Richard W. Kaye
Название: The Mathematics of Logic
ISBN: 052170877X ISBN-13(EAN): 9780521708777
Издательство: Cambridge Academ
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Цена: 3910 р.
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Описание: This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with K?nig's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.

Kolmogorov`s Heritage in Mathematics

Автор: Charpentier Eric, Lesne Annick, Nikolski Nikolai
Название: Kolmogorov`s Heritage in Mathematics
ISBN: 3540363491 ISBN-13(EAN): 9783540363491
Издательство: Springer
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Цена: 10449 р.
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Описание: A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov. Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. His contributions are presented, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the current prospects. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than present detailed proofs, the main ideas are described. A bibliography is provided for those who wish to understand the technical details. One can see that sometimes very simple reasoning (with the right interpretation and tools) can lead in a few lines to very substantial results.The Kolmogorov Legacy in Physics was published by Springer in 2004 (ISBN 978-3-540-20307-0).

Extending the Frontiers of Mathematics / Inquiries into argumentation and proof

Автор: Burger Edward B.
Название: Extending the Frontiers of Mathematics / Inquiries into argumentation and proof
ISBN: 1597570427 ISBN-13(EAN): 9781597570428
Издательство: Springer
Цена: 4175 р.
Наличие на складе: Нет в наличии.

Описание: In the real world of research mathematics, mathematicians do not know in advance if their assertions are true or false. Extending the Frontiers of Mathematics: Inquiries into proof and argumentation requires students to develop a mature process that will serve them throughout their professional careers, either inside or outside of mathematics. Its inquiry-based approach to the foundations of mathematics promotes exploring proofs and other advanced mathematical ideas through these features:- Puzzles and patterns introduce the pedagogy. These precursors to proofs generate creativity and imagination that the author builds on later- Prove and extend or disprove and salvage, a consistent format of the text, provides a framework for approaching problems and creating mathematical proofs- Mathematical challenges are presented which build upon each other, motivate analytical skills, and foster interesting discussion


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