The Legacy Of Felix Klein

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The Legacy of Felix Klein

Gert Schubring,Michael Neubrand,Marta Menghini
The Legacy of Felix Klein Book PDF

Author : Gert Schubring,Michael Neubrand,Marta Menghini
Publisher : Unknown
Page : 224 pages
File Size : 49,9 Mb
Release : 2020-10-08
Category : Education
ISBN : 1013271882

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The Legacy of Felix Klein by Gert Schubring,Michael Neubrand,Marta Menghini Pdf

This open access book provides an overview of Felix Klein's ideas, highlighting developments in university teaching and school mathematics related to Klein's thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein's ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein's ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

The Legacy of Felix Klein

Hans-Georg Weigand,William McCallum,Marta Menghini,Michael Neubrand,Gert Schubring
The Legacy of Felix Klein Book PDF

Author : Hans-Georg Weigand,William McCallum,Marta Menghini,Michael Neubrand,Gert Schubring
Publisher : Springer
Page : 226 pages
File Size : 53,8 Mb
Release : 2018-12-11
Category : Education
ISBN : 9783319993867

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The Legacy of Felix Klein by Hans-Georg Weigand,William McCallum,Marta Menghini,Michael Neubrand,Gert Schubring Pdf

This open access book provides an overview of Felix Klein’s ideas, highlighting developments in university teaching and school mathematics related to Klein’s thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein’s ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein’s ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint.

Felix Klein

Renate Tobies
Felix Klein Book PDF

Author : Renate Tobies
Publisher : Springer Nature
Page : 677 pages
File Size : 50,5 Mb
Release : 2021-06-23
Category : Mathematics
ISBN : 9783030757854

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Felix Klein by Renate Tobies Pdf

About Felix Klein, the famous Greek mathematician Constantin Carathéodory once said: “It is only by illuminating him from all angles that one can come to understand his significance.” The author of this biography has done just this. A detailed study of original sources has made it possible to uncover new connections; to create a more precise representation of this important mathematician, scientific organizer, and educational reformer; and to identify misconceptions. Because of his edition of Julius Plücker’s work on line geometry and due to his own contributions to non-Euclidean geometry, Klein was already well known abroad before he received his first full professorship at the age of 23. By exchanging ideas with his most important cooperation partner, the Norwegian Sophus Lie, Klein formulated his Erlangen Program. Various other visionary programs followed, in which Klein involved mathematicians from Germany and abroad. Klein was the most active promoter of Riemann’s geometric-physical approach to function theory, but he also integrated the analytical approaches of the Weierstrass school into his arsenal of methods. Klein was a citizen of the world who repeatedly travelled to France, Great Britain, Italy, the United States, and elsewhere. Despite what has often been claimed, it must be emphasized that Klein expressly opposed national chauvinism. He promoted mathematically gifted individuals regardless of their nationality, religion, or gender. Many of his works have been translated into English, French, Italian, Russian, and other languages; more than 300 supporters from around the world made it possible for his portrait to be painted by the prominent impressionist Max Liebermann. Inspired by international developments, Klein paved the way for women to work in the field of mathematics. He was instrumental in reforming mathematical education, and he endorsed an understanding of mathematics that affirmed its cultural importance as well as its fundamental significance to scientific and technological progress.

Proceedings of the 13th International Congress on Mathematical Education

Gabriele Kaiser
Proceedings of the 13th International Congress on Mathematical Education Book PDF

Author : Gabriele Kaiser
Publisher : Springer
Page : 766 pages
File Size : 43,8 Mb
Release : 2017-10-31
Category : Education
ISBN : 9783319625973

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Proceedings of the 13th International Congress on Mathematical Education by Gabriele Kaiser Pdf

This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. Directly before the congress activities were offered for 450 Early Career Researchers. The proceedings give a comprehensive overview on the current state-of-the-art of the discussions on mathematics education and display the breadth and deepness of current research on mathematical teaching-and-learning processes. The book introduces the major activities of ICME-13, namely articles from the four plenary lecturers and two plenary panels, articles from the five ICMI awardees, reports from six national presentations, three reports from the thematic afternoon devoted to specific features of ICME-13. Furthermore, the proceedings contain descriptions of the 54 Topic Study Groups, which formed the heart of the congress and reports from 29 Discussion Groups and 31 Workshops. The additional important activities of ICME-13, namely papers from the invited lecturers, will be presented in the second volume of the proceedings.

Elementary Mathematics from an Advanced Standpoint - Arithmetic - Algebra - Analysis

Felix Klein
Elementary Mathematics from an Advanced Standpoint Arithmetic Algebra Analysis Book PDF

Author : Felix Klein
Publisher : Aslan Press
Page : 288 pages
File Size : 51,5 Mb
Release : 2007-03
Category : Mathematics
ISBN : 9781406700145

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Elementary Mathematics from an Advanced Standpoint - Arithmetic - Algebra - Analysis by Felix Klein Pdf

This book provides a fascinating and inspirational read for anyone with an interest in advanced mathematics, written by the great German mathematician Felix Klein. It is highly recommended for inclusion on the bookshelf of anyone with an interest in the subject.

A Beautiful Math

Tom Siegfried
A Beautiful Math Book PDF

Author : Tom Siegfried
Publisher : National Academies Press
Page : 272 pages
File Size : 49,8 Mb
Release : 2006-09-21
Category : Science
ISBN : 9780309133807

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A Beautiful Math by Tom Siegfried Pdf

Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

Vita Mathematica

Ronald Calinger
Vita Mathematica Book PDF

Author : Ronald Calinger
Publisher : Cambridge University Press
Page : 380 pages
File Size : 44,5 Mb
Release : 1996
Category : Mathematics
ISBN : 0883850974

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Vita Mathematica by Ronald Calinger Pdf

Enables teachers to learn the history of mathematics and then incorporate it in undergraduate teaching.

Introduction to Symmetry Analysis Paperback with CD-ROM

Brian Cantwell
Introduction to Symmetry Analysis Paperback with CD ROM Book PDF

Author : Brian Cantwell
Publisher : Cambridge University Press
Page : 660 pages
File Size : 48,5 Mb
Release : 2002-09-23
Category : Mathematics
ISBN : 0521777402

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Introduction to Symmetry Analysis Paperback with CD-ROM by Brian Cantwell Pdf

An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.

The Legacy of Tatjana Afanassjewa

Jos Uffink,Giovanni Valente,Charlotte Werndl,Lena Zuchowski
The Legacy of Tatjana Afanassjewa Book PDF

Author : Jos Uffink,Giovanni Valente,Charlotte Werndl,Lena Zuchowski
Publisher : Springer Nature
Page : 198 pages
File Size : 54,6 Mb
Release : 2020-11-28
Category : Science
ISBN : 9783030479718

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The Legacy of Tatjana Afanassjewa by Jos Uffink,Giovanni Valente,Charlotte Werndl,Lena Zuchowski Pdf

This book presents a collection of essays that explore the life and works of Tatjana Afanassjewa (1876–1964), a Russian–Dutch physicist–mathematician. Readers will discover a scientist whose work on the foundations of thermodynamics significantly influenced the field itself as well as the philosophy of physics. This book highlights the philosophical consequences of her work in physics and mathematics and discusses historical aspects of her writings on the foundations of physics. In addition, it features English translations and critical reviews of key selections from her texts. First and foremost, the book highlights the numerous contributions that Afanassjewa made to the field. In particular, the authors examine her work on the foundations of thermodynamics and statistical physics, starting in the 1920s and extending to 1956, well after the untimely death of her husband in 1933. They also explore her almost entirely forgotten work on the didactics of mathematics. In addition, they discuss her influential collaboration with her husband, the Austrian physicist Paul Ehrenfest (1880–1933). The portrait that emerges is that of a highly original physicist and mathematician, whose legacy continues to influence scientists and philosophers today and whose lesser-known works deserve more attention than they have received. Readers will find a rich body of work that continues to this day to yield insights into the foundations of physics and mathematics.

Descriptive Geometry, The Spread of a Polytechnic Art

Évelyne Barbin,Marta Menghini,Klaus Volkert
Descriptive Geometry The Spread of a Polytechnic Art Book PDF

Author : Évelyne Barbin,Marta Menghini,Klaus Volkert
Publisher : Springer
Page : 437 pages
File Size : 47,8 Mb
Release : 2019-07-01
Category : Mathematics
ISBN : 9783030148089

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Descriptive Geometry, The Spread of a Polytechnic Art by Évelyne Barbin,Marta Menghini,Klaus Volkert Pdf

This book seeks to explore the history of descriptive geometry in relation to its circulation in the 19th century, which had been favoured by the transfers of the model of the École Polytechnique to other countries. The book also covers the diffusion of its teaching from higher instruction to technical and secondary teaching. In relation to that, there is analysis of the role of the institution – similar but definitely not identical in the different countries – in the field under consideration. The book contains chapters focused on different countries, areas, and institutions, written by specialists of the history of the field. Insights on descriptive geometry are provided in the context of the mathematical aspect, the aspect of teaching in particular to non-mathematicians, and the institutions themselves.

Galileo Unbound

David D. Nolte
Galileo Unbound Book PDF

Author : David D. Nolte
Publisher : Oxford University Press
Page : 384 pages
File Size : 47,5 Mb
Release : 2018-07-12
Category : Science
ISBN : 9780192528506

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Galileo Unbound by David D. Nolte Pdf

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Abraham Robinson

Joseph Warren Dauben
Abraham Robinson Book PDF

Author : Joseph Warren Dauben
Publisher : Unknown
Page : 0 pages
File Size : 40,8 Mb
Release : 2016-04-19
Category : Electronic
ISBN : 0691632367

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Abraham Robinson by Joseph Warren Dauben Pdf

One of the most prominent mathematicians of the twentieth century, Abraham Robinson discovered and developed nonstandard analysis, a rigorous theory of infinitesimals that he used to unite mathematical logic with the larger body of historic and modern mathematics. In this first biography of Robinson, Joseph Dauben reveals the mathematician's personal life to have been a dramatic one: developing his talents in spite of war and ethnic repression, Robinson personally confronted some of the worst political troubles of our times. With the skill and expertise familiar to readers of Dauben's earlier works, the book combines an explanation of Robinson's revolutionary achievements in pure and applied mathematics with a description of his odyssey from Hitler's Germany to the United States via conflict-ridden Palestine and wartime Europe. Robinson was born in Prussia in 1918. As a boy, he fled with his mother and brother Saul to Palestine. A decade later he narrowly escaped from Paris as the Germans invaded France. Having spent the rest of World War II in England, at the Royal Aircraft Establishment in Farnborough, he began his teaching career at the Royal College of Aeronautics. Subsequently he moved to universities in Canada, Israel, and finally the United States. A joint appointment in mathematics and philosophy at UCLA led to a position at Yale University, where Robinson served as Sterling Professor of Mathematics until his untimely death at the age of fifty-five. Originally published in 1995. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The Legacy of Niels Henrik Abel

Olav Arnfinn Laudal,Ragni Piene
The Legacy of Niels Henrik Abel Book PDF

Author : Olav Arnfinn Laudal,Ragni Piene
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 53,6 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9783642189081

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The Legacy of Niels Henrik Abel by Olav Arnfinn Laudal,Ragni Piene Pdf

A unique series of fascinating research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century.

Formulations

Andrew Witt
Formulations Book PDF

Author : Andrew Witt
Publisher : MIT Press
Page : 433 pages
File Size : 52,7 Mb
Release : 2022-01-11
Category : Architecture
ISBN : 9780262366854

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Formulations by Andrew Witt Pdf

An investigation of mathematics as it was drawn, encoded, imagined, and interpreted by architects on the eve of digitization in the mid-twentieth century. In Formulations, Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects. Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design. Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.

The Legacy of Mario Pieri in Geometry and Arithmetic

Elena Anne Marchisotto,James T. Smith
The Legacy of Mario Pieri in Geometry and Arithmetic Book PDF

Author : Elena Anne Marchisotto,James T. Smith
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 53,7 Mb
Release : 2007-12-05
Category : Mathematics
ISBN : 9780817646035

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The Legacy of Mario Pieri in Geometry and Arithmetic by Elena Anne Marchisotto,James T. Smith Pdf

This book is the first in a series of three volumes that comprehensively examine Mario Pieri’s life, mathematical work and influence. The book introduces readers to Pieri’s career and his studies in foundations, from both historical and modern viewpoints. Included in this volume are the first English translations, along with analyses, of two of his most important axiomatizations — one in arithmetic and one in geometry. The book combines an engaging exposition, little-known historical notes, exhaustive references and an excellent index. And yet the book requires no specialized experience in mathematical logic or the foundations of geometry.