Download or read book Understanding Modern Mathematics Points lines and space written by and published by . This book was released on 1963 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Understanding Modern Mathematics Points lines and planes written by and published by . This book was released on 1963 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Primer of Infinitesimal Analysis written by John L. Bell and published by Cambridge University Press. This book was released on 2008-04-07 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Download or read book The Architecture of Modern Mathematics written by J. Ferreiros and published by OUP Oxford. This book was released on 2006-04-27 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.
Download or read book Geometry and Discrete Mathematics written by Benjamin Fine and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-08-22 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the two-volume set ‘A Selection of Highlights’ we present basics of mathematics in an exciting and pedagogically sound way. This volume examines many fundamental results in Geometry and Discrete Mathematics along with their proofs and their history. In the second edition we include a new chapter on Topological Data Analysis and enhanced the chapter on Graph Theory for solving further classical problems such as the Traveling Salesman Problem.
Download or read book Explanation and Proof in Mathematics written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2009-12-04 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Download or read book The Rise of Analytic Philosophy 1879 1930 written by Michael Potter and published by Routledge. This book was released on 2019-10-08 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book Michael Potter offers a fresh and compelling portrait of the birth of modern analytic philosophy, viewed through the lens of a detailed study of the work of the four philosophers who contributed most to shaping it: Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, and Frank Ramsey. It covers the remarkable period of discovery that began with the publication of Frege's Begriffsschrift in 1879 and ended with Ramsey's death in 1930. Potter—one of the most influential scholars of this period in philosophy—presents a deep but accessible account of the break with absolute idealism and neo-Kantianism, and the emergence of approaches that exploited the newly discovered methods in logic. Like his subjects, Potter focusses principally on philosophical logic, philosophy of mathematics, and metaphysics, but he also discusses epistemology, meta-ethics, and the philosophy of language. The book is an essential starting point for any student attempting to understand the work of Frege, Russell, Wittgenstein, and Ramsey, as well as their interactions and their larger intellectual milieux. It will also be of interest to anyone who wants to cast light on current philosophical problems through a better understanding of their origins.
Download or read book Intellectual Development and Mathematics Learning written by Chongde Lin and published by Springer Nature. This book was released on 2023-03-30 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the outcomes of author’s 40 years of research, especially the theory of “the Triangular Pyramid Structure of Thinking” that he independently proposed, and the application of his development theory in the field of mathematics education. The book firstly explains the substantial character of intelligence, the development law of intelligence, and the relationship between intelligence development and creativity cultivation. Secondly, it discusses the structure of mathematical thinking of children and adolescents from 0 to 18 years old, and the methods of developing students’ thinking ability and the quality of intelligence through arithmetic learning. In the end, this book also demonstrates the characteristics of the development of mathematical thinking ability of children at age 0-6, elementary school students, and secondary school students, and the related latest research in this field. Based on the theory of “the Triangular Pyramid Structure of Thinking”, a number of examples are given to illustrate how the theory of intelligence development can be used in mathematics teaching to promote the development of students’ thinking abilities and to improve the quality of teaching. This book covers various areas including psychology, mathematics, and education. It has a great reference value for scholars in the field of psychology to study the theory of intelligence and the structure of thinking, providing guidance for parents and mathematics teachers to promote children’s quality of intelligence and mathematical thinking abilities, and to enhance their mathematics learning effects. In addition, it provides examples for psychological research to serve specific subject teaching in elementary and secondary schools.
Download or read book A Mathematical and Philosophical Dictionary Containing an Explanation of the Terms and an Account of the Several Subjects Comprized Under the Heads Mathematics Astronomy and Philosophy Both Natural and Experimental written by Charles Hutton and published by . This book was released on 1795 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Mathematics in the Theory of Sets written by John P. Mayberry and published by Cambridge University Press. This book was released on 2000 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.
Download or read book Symmetries of Nature written by Klaus Mainzer and published by Walter de Gruyter. This book was released on 2013-12-02 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Perspectives on the Teaching of Geometry for the 21st Century written by C. Mammana and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.
Download or read book The Handy Math Answer Book written by Patricia Barnes-Svarney and published by Visible Ink Press. This book was released on 2012-05-01 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Sudoku to Quantum Mechanics, Unraveling the Mysteries of Mathematics! What's the formula for changing intimidation to exhilaration? When it comes to math, it's The Handy Math Answer Book! From a history dating back to prehistoric times and ancient Greece to how we use math in our everyday lives, this fascinating and informative guide addresses the basics of algebra, calculus, geometry, and trigonometry, and then proceeds to practical applications. You'll find easy-to-follow explanations of how math is used in daily financial and market reports, weather forecasts, real estate valuations, games, and measurements of all kinds. In an engaging question-and-answer format, more than 1,000 everyday math questions and concepts are tackled and explained, including ... What are a googol and a googolplex? What are some of the basic “building blocks” of geometry? What is a percent? How do you multiply fractions? What are some of the mathematics behind global warming? What does the philosophy of mathematics mean? What is a computer“app”? What's the difference between wet and dry measurements when you're cooking? How often are political polls wrong? How do you figure out a handicap in golf and bowling? How does the adult brain process fractions? And many, many more! For parents, teachers, students, and anyone seeking additional guidance and clarity on their mathematical quest, The Handy Math Answer Book is the perfect guide to understanding the world of numbers bridging the gap between left- and right-brained thinking. Appendices on Measurements and Conversion Factors plus Common Formulas for Calculating Areas and Volumes of shapes are also included. Its helpful bibliography and extensive index add to its usefulness.
Download or read book The Philosophy of Economics written by Subroto Roy and published by Routledge. This book was released on 2003-09-02 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first work to seriously and successfully bridge twentieth century economics and philosophy. Subroto Roy draws these two disciplines together and examines the intellectual roots of economics.
Download or read book Where Mathematics Come From How The Embodied Mind Brings Mathematics Into Being written by George Lakoff and published by . This book was released on 2000-11-02 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the cognitive science of mathematical ideas.
Download or read book Hilbert G ttingen and the Development of Modern Mathematics written by Joan Roselló and published by Cambridge Scholars Publishing. This book was released on 2019-02-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilbert’s contributions to mathematics, putting them in their historical, social and cultural context. In doing so, particular attention is paid to Hilbert’s axiomatic method and his proposal for the foundations of mathematics, the so-called Hilbert’s program. The book also discusses the development of algebraic number theory, the theory of integral equations, modern algebra and the structural image of mathematics. In addition, it considers the famous list of Mathematical Problems presented in Paris in 1900, the mathematical tradition of the University of Göttingen, the great debate on the foundations of mathematics in the twenties between formalists and intuitionists, and, finally, Hilbert’s work on the theory of relativity and the foundations of quantum mechanics. The book will primarily appeal to an academic audience, although it will also be of interest to general-interest science readers.
Download or read book A Companion to Analytic Philosophy written by A. P. Martinich and published by John Wiley & Sons. This book was released on 2008-04-15 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Companion to Analytic Philosophy is a comprehensive guide to many significant analytic philosophers and concepts of the last hundred years. Provides a comprehensive guide to many of the most significant analytic philosophers of the last one hundred years. Offers clear and extensive analysis of profound concepts such as truth, goodness, knowledge, and beauty. Written by some of the most distinguished philosophers alive, some of whom have entries in the book devoted to them.
