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Author : Auguste Comte
Publisher : Unknown
Page : 292 pages
File Size : 46,7 Mb
Release : 1851
Category : Electronic
ISBN : BL:A0018199741
Author : Christopher Hollings
Publisher : American Mathematical Society
Page : 457 pages
File Size : 45,7 Mb
Release : 2014-07-16
Category : Mathematics
ISBN : 9781470414931
The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.
Author : Florian Cajori
Publisher : Unknown
Page : 330 pages
File Size : 46,9 Mb
Release : 1897
Category : Mathematics
ISBN : HARVARD:HW2D3N
Author : R.L. Tieszen
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789400922938
"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.
Author : Gaea Leinhardt,Ralph Putnam,Rosemary A. Hattrup
Publisher : Routledge
Page : 472 pages
File Size : 44,7 Mb
Release : 2020-11-25
Category : Education
ISBN : 9781135440657
This volume emerges from a partnership between the American Federation of Teachers and the Learning Research and Development Center at the University of Pittsburgh. The partnership brought together researchers and expert teachers for intensive dialogue sessions focusing on what each community knows about effective mathematical learning and instruction. The chapters deal with the research on, and conceptual analysis of, specific arithmetic topics (addition, subtraction, multiplication, division, decimals, and fractions) or with overarching themes that pervade the early curriculum and constitute the links with the more advanced topics of mathematics (intuition, number sense, and estimation). Serving as a link between the communities of cognitive researchers and mathematics educators, the book capitalizes on the recent research successes of cognitive science and reviews the literature of the math education community as well.
Author : A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev
Publisher : Courier Corporation
Page : 1120 pages
File Size : 41,8 Mb
Release : 2012-05-07
Category : Mathematics
ISBN : 9780486157870
Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.
Author : Paolo Mancosu
Publisher : Oxford University Press, USA
Page : 286 pages
File Size : 42,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780195084634
Includes bibliographical references and index.
Author : Stewart Shapiro
Publisher : Oxford University Press
Page : 856 pages
File Size : 45,9 Mb
Release : 2005-02-10
Category : Mathematics
ISBN : 9780190287535
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.
Author : Francis Su
Publisher : Yale University Press
Page : 287 pages
File Size : 41,7 Mb
Release : 2020-01-07
Category : Mathematics
ISBN : 9780300237139
"The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.
Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 462 pages
File Size : 51,5 Mb
Release : 2016-12-31
Category : Mathematics
ISBN : 9781614441229
This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.
Author : M. I. Moro
Publisher : Unknown
Page : 224 pages
File Size : 52,6 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:39015029578898
Author : Felix Klein
Publisher : Springer
Page : 315 pages
File Size : 41,8 Mb
Release : 2016-06-29
Category : Education
ISBN : 9783662494455
These three volumes constitute the first complete English translation of Felix Klein’s seminal series “Elementarmathematik vom höheren Standpunkte aus”. “Complete” has a twofold meaning here: First, there now exists a translation of volume III into English, while until today the only translation had been into Chinese. Second, the English versions of volume I and II had omitted several, even extended parts of the original, while we now present a complete revised translation into modern English. The volumes, first published between 1902 and 1908, are lecture notes of courses that Klein offered to future mathematics teachers, realizing a new form of teacher training that remained valid and effective until today: Klein leads the students to gain a more comprehensive and methodological point of view on school mathematics. The volumes enable us to understand Klein’s far-reaching conception of elementarisation, of the “elementary from a higher standpoint”, in its implementation for school mathematics./div This volume II presents a paradigmatic realisation of Klein’s approach of elementarisation for teacher education. It is shown how the various geometries, elaborated particularly since the beginning of the 19th century, are revealed as becoming unified in a new restructured geometry. As Klein liked to stress: “Projective geometry is all geometry”. Non-Euclidean geometry proves to constitute a part of this unifying process. The teaching of geometry is discussed in a separate chapter, which provides moreover important information on the history of geometry teaching and an international comparison.
Author : Stewart Shapiro
Publisher : Oxford University Press
Page : 290 pages
File Size : 45,9 Mb
Release : 1997-08-07
Category : Mathematics
ISBN : 9780195094527
Shapiro argues that both realist and anti-realist accounts of mathematics are problematic. To resolve this dilemma, he articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
Author : Rolf Biehler,Michael Liebendörfer,Ghislaine Gueudet,Chris Rasmussen,Carl Winsløw
Publisher : Springer Nature
Page : 723 pages
File Size : 51,9 Mb
Release : 2023-01-01
Category : Education
ISBN : 9783031141751
This edited volume presents a broad range of original practice-oriented research studies about tertiary mathematics education. These are based on current theoretical frameworks and on established and innovative empirical research methods. It provides a relevant overview of current research, along with being a valuable resource for researchers in tertiary mathematics education, including novices in the field. Its practice orientation research makes it attractive to university mathematics teachers interested in getting access to current ideas and results, including theory-based and empirically evaluated teaching and learning innovations. The content of the book is spread over 5 sections: The secondary-tertiary transition; University students' mathematical practices and mathematical inquiry; Research on teaching and curriculum design; University students’ mathematical inquiry and Mathematics for non-specialists.
Author : Lim Chap Sam,Chew Cheng Meng,Sriraman Bharath
Publisher : Penerbit USM
Page : 299 pages
File Size : 51,5 Mb
Release : 2020
Category : Mathematics
ISBN : 9789674614119
This book presents an exceptional collection of 11 articles on contemporary research studies that address current and critical issues of researches, theories and practices in the fields of mathematics education at various levels from primary to tertiary education. In addition, the book covers various innovative research studies from both local and abroad such as cognitive diagnostic assessment (CDA) and assessment for learning (AfL), teaching and learning of mathematics using the dynamic geometry software (DGS), action-process-object-schema (APOS) theory and relationship mapping and inverse (RMI) principle, as well as mathematics lesson structure (MLS) and collaborative lesson research (CLR). The contents of this book should be of interest to both national and international researchers and scholars, particularly mathematics educators, mathematics education researchers, teacher trainers, university students, teachers, curriculum planners, as well as policymakers.
