a structural account of mathematics

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A Structural Account Of Mathematics

Author : Charles S. Chihara
ISBN : 9780199267538
Genre : Philosophy
File Size : 49. 11 MB
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Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chiharapresents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings. A Structural Account of Mathematics will be required reading for anyone working in this field.

Modern Algebra And The Rise Of Mathematical Structures

Author : Leo Corry
ISBN : 9783034879170
Genre : Mathematics
File Size : 20. 37 MB
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This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.

Technical Shop Mathematics

Author : Thomas Achatz
ISBN : 0831130865
Genre : Mathematics
File Size : 29. 54 MB
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Annotation The new third edition has been completely revised and updated by new co-authors to reflect the latest trends in content and pedagogy. Yet they have been careful to retain and build on the strengths which have made this book a success for more 25 years: its straightforward, easy-to-follow writing style and numerous study problems based on typical shop applications. Technical Shop Mathematics is designed for both home-study and classroom use, and also has been widely used as an on-the-job reference by shop professionals.

The Development Of Mathematics

Author : E. T. Bell
ISBN : 9780486152288
Genre : Mathematics
File Size : 21. 20 MB
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Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

Variational Methods For Structural Optimization

Author : Andrej Cherkaev
ISBN : 9781461211884
Genre : Science
File Size : 62. 95 MB
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This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.

Structural Stability And Morphogenesis

Author : Rene Thom
ISBN : 9780429972652
Genre : Mathematics
File Size : 38. 18 MB
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First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.

Structure And Geometry Of Lie Groups

Author : Joachim Hilgert
ISBN : 0387847944
Genre : Mathematics
File Size : 52. 63 MB
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This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.

Realism In Mathematics

Author : Penelope Maddy
ISBN : 9780198240358
Genre : Political Science
File Size : 64. 70 MB
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When engaged in mathematics, most people tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Penelope Maddy delineates and defends a novel versionof mathematical realism that answers the traditional questions and refocuses philosophical attention on the pressing foundational issues of contemporary mathematics.

Structuralism And Structures

Author : Charles Earl Rickart
ISBN : 9810218605
Genre : Mathematics
File Size : 32. 80 MB
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This book is devoted to an analysis of the way that structures must enter into a serious study of any subject, and the term ?structuralism? refers to the general method of approaching a subject from the viewpoint of structure. A proper appreciation of this approach requires a deeper understanding of the concept of structure than is provided by the simple intuitive notion of structures that everyone posseses to some degree. Therefore, a large part of the discussion is devoted directly or indirectly to a study of the nature of structures themselves. A formal definition of a structure, plus some basic general properties and examples, is given early in the discussion. Also, in order to clarify the general notions and to see how they are used, the later chapters are devoted to an examination of how structures enter into some special fields, including linguistics, mental phenomena, mathematics (and its applications), and biology (especially in the theory of evolution). Because the author is a mathematician, certain mathematical ideas have influenced greatly the choice and approach to the material covered. In general, however, the mathematical influence is not on a technical level and is often only implicit. Even the chapter on mathematical structures is nontechnical and is about rather than on mathematics. Only in the last chapter and earlier in three short sections does one find any of the expected ?formal? mathematics. In other words, the great bulk of the material is accessible to someone without a mathematical background.

Mathematical Structures For Computer Science

Author : Judith L. Gersting
ISBN : 071676864X
Genre : Mathematics
File Size : 38. 14 MB
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This edition offers a pedagogically rich and intuitive introduction to discrete mathematics structures. It meets the needs of computer science majors by being both comprehensive and accessible.

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