The Legacy of Felix Klein
The Legacy of Felix Klein

Author: Gert Schubring

Publisher:

Published: 2020-10-08

Total Pages: 224

ISBN-13: 9781013271892

DOWNLOAD EBOOK

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
The Legacy of Felix Klein

Author: Hans-Georg Weigand

Publisher: Springer

Published: 2018-12-11

Total Pages: 225

ISBN-13: 3319993860

DOWNLOAD EBOOK

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
Felix Klein

Author: Renate Tobies

Publisher: Springer Nature

Published: 2021-06-23

Total Pages: 677

ISBN-13: 3030757854

DOWNLOAD EBOOK

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
Proceedings of the 13th International Congress on Mathematical Education

Author: Gabriele Kaiser

Publisher: Springer

Published: 2017-10-31

Total Pages: 735

ISBN-13: 3319625977

DOWNLOAD EBOOK

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.

Vita Mathematica
Vita Mathematica

Author: Ronald Calinger

Publisher: Cambridge University Press

Published: 1996

Total Pages: 380

ISBN-13: 9780883850978

DOWNLOAD EBOOK

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

A Beautiful Math
A Beautiful Math

Author: Tom Siegfried

Publisher: National Academies Press

Published: 2006-09-21

Total Pages: 272

ISBN-13: 0309133807

DOWNLOAD EBOOK

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.

Office Hours with a Geometric Group Theorist
Office Hours with a Geometric Group Theorist

Author: Matt Clay

Publisher: Princeton University Press

Published: 2017-07-11

Total Pages: 456

ISBN-13: 1400885396

DOWNLOAD EBOOK

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.

Descriptive Geometry, The Spread of a Polytechnic Art
Descriptive Geometry, The Spread of a Polytechnic Art

Author: Évelyne Barbin

Publisher: Springer

Published: 2019-07-01

Total Pages: 446

ISBN-13: 3030148084

DOWNLOAD EBOOK

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.

Hilbert-Courant
Hilbert-Courant

Author: Constance Reid

Publisher: Springer Science & Business Media

Published: 1986-05-22

Total Pages: 620

ISBN-13: 9780387962566

DOWNLOAD EBOOK

I am very pleased that my books about David Hilbert, published in 1970, and Richard Courant, published in 1976, are now being issued by Springer Verlag in a single volume. I have always felt that they belonged together, Courant being, as I have written, the natural and necessary sequel to Hilbert the rest of the story. To make the two volumes more compatible when published as one, we have combined and brought up to date the indexes of names and dates. U nfortu nately we have had to omit Hermann Weyl's article on "David Hilbert and his mathematical work," but the interested reader can always find it in the hard back edition of Hilbert and in Weyl's collected papers. At the request of a number of readers we have included a listing of all of Hilbert's famous Paris problems. It was, of course, inevitable that we would give the resulting joint volume the title Hilbert-Courant.