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Richard Dedekind
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Book Synopsis Theory of Algebraic Integers by : Richard Dedekind
Download or read book Theory of Algebraic Integers written by Richard Dedekind and published by Cambridge University Press. This book was released on 1996-09-28 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: A translation of a classic work by one of the truly great figures of mathematics.
Download or read book Richard Dedekind written by Rajesh Thakur and published by Prabhat Prakashan. This book was released on 2021-01-19 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Number Theory by : Peter Gustav Lejeune Dirichlet
Download or read book Lectures on Number Theory written by Peter Gustav Lejeune Dirichlet and published by American Mathematical Soc.. This book was released on 1999 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.
Book Synopsis Essays on the Theory of Numbers by : Richard Dedekind
Download or read book Essays on the Theory of Numbers written by Richard Dedekind and published by Franklin Classics. This book was released on 2018-10-11 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Book Synopsis What are Numbers and what Should They Be? by : Richard Dedekind
Download or read book What are Numbers and what Should They Be? written by Richard Dedekind and published by R I M (Research Institute for Mathematics). This book was released on 1995 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dictionary of Scientific Biography: Richard Dedekind-Firmicus Maternus by : Charles Coulston Gillispie
Download or read book Dictionary of Scientific Biography: Richard Dedekind-Firmicus Maternus written by Charles Coulston Gillispie and published by . This book was released on 1971 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modern Algebra and the Rise of Mathematical Structures by : Leo Corry
Download or read book Modern Algebra and the Rise of Mathematical Structures written by Leo Corry and published by Birkhäuser. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis From Dedekind to Gödel by : Jaakko Hintikka
Download or read book From Dedekind to Gödel written by Jaakko Hintikka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either. Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.
Book Synopsis Contributions to the Founding of the Theory of Transfinite Numbers by : Georg Cantor
Download or read book Contributions to the Founding of the Theory of Transfinite Numbers written by Georg Cantor and published by . This book was released on 1915 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lattices and Ordered Sets by : Steven Roman
Download or read book Lattices and Ordered Sets written by Steven Roman and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.
Book Synopsis Functions and Generality of Logic by : Hourya Benis-Sinaceur
Download or read book Functions and Generality of Logic written by Hourya Benis-Sinaceur and published by Springer. This book was released on 2015-06-24 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive imports from spatio-temporal experience into the deductive presentation of arithmetic, Dedekind had a different goal and used or invented different tools. The chapter highlights basic dissimilarities between Dedekind’s and Frege’s actual ways of doing and thinking. The second chapter reflects on Frege’s notion of a function, in comparison with the notions endorsed by Lagrange and the followers of the program of arithmetization of analysis. It remarks that the foundational programs pursued by Lagrange and Frege are crucially different and based on a different idea of what the foundations of mathematics should be like. However, despite this contrast, the notion of function plays similar roles in the two programs, and this chapter emphasizes the similarities. The third chapter traces the development of thinking about Frege’s program in the foundations of mathematics, and includes comparisons of Frege’s, Russell’s and Ramsey’s views. The chapter discusses earlier papers written by Hintikka, Sandu, Demopoulos and Trueman. Although the chapter’s main focus is on the notion of arbitrary correlation, it starts out by discussing some aspects of the connection between this notion and Dedekind Theorem.
Book Synopsis Foundations of Constructive Mathematics by : M.J. Beeson
Download or read book Foundations of Constructive Mathematics written by M.J. Beeson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.
Download or read book Plato's Ghost written by Jeremy Gray and published by Princeton University Press. This book was released on 2008-09-02 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
Book Synopsis Bernhard Riemann's Gesammelte Mathematische Werke und Wissenschaftlicher Nachlass... by : Bernhard Riemann
Download or read book Bernhard Riemann's Gesammelte Mathematische Werke und Wissenschaftlicher Nachlass... written by Bernhard Riemann and published by Hardpress Publishing. This book was released on 2013-12 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
Book Synopsis Introducing Philosophy of Mathematics by : Michele Friend
Download or read book Introducing Philosophy of Mathematics written by Michele Friend and published by Routledge. This book was released on 2014-12-05 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.
Book Synopsis New Foundations for Physical Geometry by : Tim Maudlin
Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by . This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
