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Arithmetical Algebra
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Book Synopsis Arithmetical algebra by : George Peacock
Download or read book Arithmetical algebra written by George Peacock and published by . This book was released on 1842 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Peacock's mathematical work, although not extensive, is significant in the evolution of a concept of abstract algebra. In the textbook, A Treatise on Algebra, he attempted to put the theory of negative and complex numbers on a firm logical basis by dividing the field of algebra into arithmetical algebra and symbolic algebra. In the former the symbols represented positive integers; in the latter the domain of the symbols was extended by his principle of the permanence of equivalent forms. This principle asserts that rules in arithmetical algebra, which hold only when the values of the variables are restricted, remain valid when the restriction is removed. Although it was a step toward abstraction, Peacock's view was limited because he insisted that if the variables were properly chosen, any formula in symbolic algebra would yield a true formula in arithmetical algebra. Thus a noncommunicative algebra would not be possible.
Book Synopsis A Treatise on Algebra: Arithmetical algebra by : George Peacock
Download or read book A Treatise on Algebra: Arithmetical algebra written by George Peacock and published by . This book was released on 1842 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Principles and Practice of Arithmetical Algebra ... Third Edition by : John HIND (M.A.)
Download or read book The Principles and Practice of Arithmetical Algebra ... Third Edition written by John HIND (M.A.) and published by . This book was released on 1855 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pascal's Arithmetical Triangle by : A.W.F. Edwards
Download or read book Pascal's Arithmetical Triangle written by A.W.F. Edwards and published by Courier Dover Publications. This book was released on 2019-06-12 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey explores the history of the arithmetical triangle, from its roots in Pythagorean arithmetic, Hindu combinatorics, and Arabic algebra to its influence on Newton and Leibniz as well as modern-day mathematicians.
Book Synopsis A Study of Mathematical Education Including the Teaching of Arithmetic by : Benchara Branford
Download or read book A Study of Mathematical Education Including the Teaching of Arithmetic written by Benchara Branford and published by . This book was released on 1924 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Popular Mathematics, being the first elements of arithmetic, algebra and geometry in their relations and uses by : Robert Mudie
Download or read book Popular Mathematics, being the first elements of arithmetic, algebra and geometry in their relations and uses written by Robert Mudie and published by . This book was released on 1836 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Arithmetic by : Eric Temple Bell
Download or read book Algebraic Arithmetic written by Eric Temple Bell and published by . This book was released on 1927 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the Bôcher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, elliptic and theta functions, Bernoulli numbers and functions, and the foundations of mathematics.
Book Synopsis Examples in Arithmetic and Algebra by :
Download or read book Examples in Arithmetic and Algebra written by and published by . This book was released on 1834 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Oxford Handbook of Philosophy of Mathematics and Logic by : Stewart Shapiro
Download or read book The Oxford Handbook of Philosophy of Mathematics and Logic written by Stewart Shapiro and published by Oxford University Press. This book was released on 2005-02-10 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.
Book Synopsis The rationale of arithmetical teaching exemplified by : John Blain
Download or read book The rationale of arithmetical teaching exemplified written by John Blain and published by . This book was released on 1857 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Rationale of Arithmetical Teaching, Exemplified in a Full Exposition of the Principles of Numeration and the Four Elementary Rules, Etc by : John BLAIN
Download or read book The Rationale of Arithmetical Teaching, Exemplified in a Full Exposition of the Principles of Numeration and the Four Elementary Rules, Etc written by John BLAIN and published by . This book was released on 1857 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamental Conceptions of Modern Mathematics ... by : Robert Porterfield Richardson
Download or read book Fundamental Conceptions of Modern Mathematics ... written by Robert Porterfield Richardson and published by . This book was released on 1916 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Towards an Arithmetical Logic by : Yvon Gauthier
Download or read book Towards an Arithmetical Logic written by Yvon Gauthier and published by Birkhäuser. This book was released on 2015-09-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an original contribution to the foundations of logic and mathematics and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of logic and mathematics.
Book Synopsis Bringing Out the Algebraic Character of Arithmetic by : Analúcia D. Schliemann
Download or read book Bringing Out the Algebraic Character of Arithmetic written by Analúcia D. Schliemann and published by Routledge. This book was released on 2006-08-29 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it. The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation. The book, suitable as a text in undergraduate or graduate mathematics education courses, includes downloadable resources with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three videopapers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM. Bringing Out the Algebraic Character of Arithmetic is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation.
Book Synopsis Fundamental Conceptions of Modern Mathematics ...: Variables and quantities, with a discussion of the general conception of functional relation. 1916 by : Robert Porterfield Richardson
Download or read book Fundamental Conceptions of Modern Mathematics ...: Variables and quantities, with a discussion of the general conception of functional relation. 1916 written by Robert Porterfield Richardson and published by . This book was released on 1916 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Arithmetical Functions by : Paul J. McCarthy
Download or read book Introduction to Arithmetical Functions written by Paul J. McCarthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of arithmetical functions has always been one of the more active parts of the theory of numbers. The large number of papers in the bibliography, most of which were written in the last forty years, attests to its popularity. Most textbooks on the theory of numbers contain some information on arithmetical functions, usually results which are classical. My purpose is to carry the reader beyond the point at which the textbooks abandon the subject. In each chapter there are some results which can be described as contemporary, and in some chapters this is true of almost all the material. This is an introduction to the subject, not a treatise. It should not be expected that it covers every topic in the theory of arithmetical functions. The bibliography is a list of papers related to the topics that are covered, and it is at least a good approximation to a complete list within the limits I have set for myself. In the case of some of the topics omitted from or slighted in the book, I cite expository papers on those topics.
Book Synopsis Mathematics and Music by : Gerard Assayag
Download or read book Mathematics and Music written by Gerard Assayag and published by Springer Science & Business Media. This book was released on 2002-07-10 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.
