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.
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:
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:
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.
Download or read book Universal Arithmetick Or A Treatise of Arithmetical Composition and Resolution written by Isaac Newton and published by . This book was released on 1720 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Treatise on 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.
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: "An impressive culmination of meticulous research into original sources, this definitive study constitutes the first full-length history of the Arithmetic Triangle." — Mathematics of Computation Pascal's Arithmetical Triangle was named for the seventeenth-century French philosopher/mathematician Blaise Pascal, though he did not invent it. A never-ending equilateral triangle of numbers that follow the rule of adding the two numbers above to get the number below, it appears much earlier in the literature of Hindu and Arabic mathematics and continues to fascinate Western mathematicians. Two sides are comprised of "all 1s," and because the triangle is infinite, there is no "bottom side." This book by A. W. F. Edwards, Professor of Biometry at the University of Cambridge, explores Pascal's Arithmetical Triangle and the way it has been studied, enjoyed, and used by mathematicians throughout history. "A fascinating book...giving new insights into the early history of probability theory and combinatorics and incidentally providing much stimulating material for teachers of mathematics." — G. A. Bernard, International Statistical Institute Review "Scrupulously researched . . . carries the reader along in a rewarding manner. It is a scientific who-dun-it and one must admire the author for the scholarly yet unpedantic manner in which he disperses some of the mists of antiquity." — A. W. Kemp, Biometrics "Recommended not only to historians and mathematicians, but also to students seeking to put some life into the dry treatment of these topics to which they have doubtless been subjected." — Ivor Grattan-Guinness, Annals of Science
Download or read book Arithmetic and Algebra in Their Principles and Application written by Barnard Smith and published by . This book was released on 1857 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A treatise on algebra by George Peacock written by and published by . This book was released on 1842 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 193 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.
Download or read book An Introduction to the Elements of Algebra written by Leonhard Euler and published by . This book was released on 1821 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Science written by John Michels (Journalist) and published by . This book was released on 1899 with total page 1022 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1911-13 contain the Proceedings of the Helminothological Society of Washington, ISSN 0018-0120, 1st-15th meeting.
Download or read book A Cyclop dia of the Physical Sciences written by John Pringle Nichol and published by . This book was released on 1857 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polynomial Completeness in Algebraic Systems written by Kalle Kaarli and published by CRC Press. This book was released on 2000-07-21 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theory, mathematical logic, and computer science. It is not surprising then that focusing on specific properties of Boolean algebras has lead to new directions in universal algebra. In the first unified study of polynomial completeness, Polynomial Completeness in Algebraic Systems focuses on and systematically extends another specific property of Boolean algebras: the property of affine completeness. The authors present full proof that all affine complete varieties are congruence distributive and that they are finitely generated if and only if they can be presented using only a finite number of basic operations. In addition to these important findings, the authors describe the different relationships between the properties of lattices of equivalence relations and the systems of functions compatible with them. An introductory chapter surveys the appropriate background material, exercises in each chapter allow readers to test their understanding, and open problems offer new research possibilities. Thus Polynomial Completeness in Algebraic Systems constitutes an accessible, coherent presentation of this rich topic valuable to both researchers and graduate students in general algebraic systems.
Download or read book The Teaching of Mathematics in the United Kingdom written by Great Britain. Board of Education and published by . This book was released on 1912 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
