Download or read book On the Influence of Signs in Mathematical Reasoning written by Charles Babbage and published by . This book was released on 1826 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Influence of Signs in Mathematical Reasoning written by Charles Babbage and published by . This book was released on 1827 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Influence of Signs in Mathematical Reasoning written by Charles Babbage and published by . This book was released on 1826 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Visualization Explanation and Reasoning Styles in Mathematics written by P. Mancosu and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
Download or read book An Introduction to Mathematical Reasoning written by Peter J. Eccles and published by Cambridge University Press. This book was released on 2013-06-26 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
Download or read book The Mathematical Work of Charles Babbage written by J. M. Dubbey and published by Cambridge University Press. This book was released on 2004-02-12 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes Babbage's work on the design and implementation of the difference and analytical engines.
Download or read book A History of Mathematical Notations Notations in elementary mathematics written by Florian Cajori and published by . This book was released on 1928 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A History of Mathematical Notations Two Volume in One written by Florian Cajori and published by Cosimo, Inc.. This book was released on 2011-12-01 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: Described even today as "unsurpassed," this history of mathematical notation stretching back to the Babylonians and Egyptians is one of the most comprehensive written. In two impressive volumes, first published in 1928-9 and reproduced here under one cover, distinguished mathematician Florian Cajori shows the origin, evolution, and dissemination of each symbol and the competition it faced in its rise to popularity or fall into obscurity. Illustrated with more than a hundred diagrams and figures, this "mirror of past and present conditions in mathematics" will give students and historians a whole new appreciation for "1 + 1 = 2." Swiss-American author, educator, and mathematician FLORIAN CAJORI (1859-1930) was one of the world's most distinguished mathematical historians. Appointed to a specially created chair in the history of mathematics at the University of California, Berkeley, he also wrote An Introduction to the Theory of Equations, A History of Mathematical Notations, and The Chequered Career of Ferdinand Rudolph Hassler.
Download or read book The Search for Mathematical Roots 1870 1940 written by Ivor Grattan-Guinness and published by Princeton University Press. This book was released on 2011-02-11 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
Download or read book A History of Mathematical Notations written by Florian Cajori and published by . This book was released on 1928 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A History of Mathematical Notations written by Florian Cajori and published by Cosimo, Inc.. This book was released on 2007-06-01 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Described even today as "unsurpassed," this history of mathematical notation stretching back to the Babylonians and Egyptians is one of the most comprehensive written. In two impressive volumes-first published in 1928-9-distinguished mathematician Florian Cajori shows the origin, evolution, and dissemination of each symbol and the competition it faced in its rise to popularity or fall into obscurity. Illustrated with more than a hundred diagrams and figures, this "mirror of past and present conditions in mathematics" will give students and historians a whole new appreciation for "1 + 1 = 2." Swiss-American author, educator, and mathematician FLORIAN CAJORI (1859-1930) was one of the world's most distinguished mathematical historians. Appointed to a specially created chair in the history of mathematics at the University of California, Berkeley, he also wrote An Introduction to the Theory of Equations, A History of Elementary Mathematics, and The Chequered Career of Ferdinand Rudolph Hassler.
Download or read book Mathematical Perspectives written by Joseph W. Dauben and published by Academic Press. This book was released on 2014-05-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Perspectives: Essays on Mathematics and its Historical Development is a collection of 13 biographical essays on the historical advances of science. This collection is originally meant to comprise an issue of the journal Historia Mathematica in honor of Professor Kurt R. Biermann’s 60th birthday. This 12-chapter text includes essays on studies and commentaries on the problem of “figures of equal perimeter by various authors in antiquity, including Zenodorus, Theon, and Pappus. Other essays explore the comparison of the areas of polygons with equal perimeter; the concept of function; history of mathematics; the development of mathematical physics in France; and the history of Logicism and Formalism. The remaining chapters deal with essays on an early version of Gauss’ Disquisitiones Arithmeticae, ideal numbers, a mathematical-philosophilica theory of probability, and historical examples of problem of number sequence interpolation. This book will be of value to mathematicians, historians, and researchers.
Download or read book Charles Babbage on the Principles and Development of the Calculator written by Charles Babbage and published by Courier Corporation. This book was released on 1961-01-01 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant 19th-century mathematician, Charles Babbage articulated the principles on which all modern computing machines are based. This compilation of his writings, in addition to those of several of his contemporaries, illuminates the work that led to the development of the calculator. Essential reference for anyone interested in the history of computing technology.
Download or read book Transactions of the Cambridge Philosophical Society written by and published by . This book was released on 1883 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Longitudinal Study of Mathematical Reasoning written by C. Hoyles and published by . This book was released on 2003 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Language and the Rise of the Algorithm written by Jeffrey M. Binder and published by University of Chicago Press. This book was released on 2022-12-06 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wide-ranging history of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians well before the computer age: How do you draw the line between computational rules and the complexities of making systems comprehensible to people? By attending to this question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Here Jeffrey M. Binder offers a compelling tour of four visions of universal computation that addressed this issue in very different ways: G. W. Leibniz’s calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole’s nineteenth-century logic system; and the early programming language ALGOL, short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. Machine learning, in its increasing dependence on words, erodes the line between technical and everyday language, revealing the urgent stakes underlying this boundary. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction.
Download or read book When Physics Became King written by Iwan Rhys Morus and published by University of Chicago Press. This book was released on 2009-10-27 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: As recently as two hundred years ago, physics as we know it today did not exist. Born in the early nineteenth century during the second scientific revolution, physics struggled at first to achieve legitimacy in the scientific community and culture at large. In fact, the term "physicist" did not appear in English until the 1830s. When Physics Became King traces the emergence of this revolutionary science, demonstrating how a discipline that barely existed in 1800 came to be regarded a century later as the ultimate key to unlocking nature's secrets. A cultural history designed to provide a big-picture view, the book ably ties advances in the field to the efforts of physicists who worked to win social acceptance for their research. Beginning his tale with the rise of physics from natural philosophy, Iwan Morus chronicles the emergence of mathematical physics in France and its later export to England and Germany. He then elucidates the links between physics and industrialism, the technology of statistical mechanics, and the establishment of astronomical laboratories and precision measurement tools. His tale ends on the eve of the First World War, when physics had firmly established itself in both science and society. Scholars of both history and physics will enjoy this fascinating and studied look at the emergence of a major scientific discipline.
