3Blue1Brown presents animated videos about mathematics. It was created by Grant Sanderson, a graduate student from Stanford University who worked for Khan Academy. He created a YouTube-channel with videos on calculus, linear algebra, geometry, topology, and many special topics such as Fourier transformations or the Riemann hypothesis. He answers questions like “But why is a sphere’s surface area four times its shadow?” or “Ever wondered why slicing a cone gives an ellipse?”. The videos use 3D-animations and they explain mathematical problems from a visual perspective.
The channel name and logo reference the colour of Grant’s right eye, which has blue-brown sectoral heterochromia.
See also: https://en.wikipedia.org/wiki/3Blue1Brown
August’s book of the month is Developing Research in Mathematics Education: Twenty Years of Communication, Cooperation and Collaboration in Europe, edited by Tommy Dreyfus, Michèle Artigue, Despina Potari, Susanne Prediger, and Kenneth Ruthven.
It is the first book in the series New Perspectives on Research in Mathematics Education, to be produced in association with the prestigious European Society for Research in Mathematics Education. This inaugural volume sets out broad advances in research in mathematics education which have accumulated over the last 20 years through the sustained exchange of ideas and collaboration between researchers in the field.
An impressive range of contributors provide specifically European and complementary global perspectives on major areas of research in the field on topics that include:
- the content domains of arithmetic, geometry, algebra, statistics, and probability;
- the mathematical processes of proving and modeling;
- teaching and learning at specific age levels from early years to university;
- teacher education, teaching and classroom practices;
- special aspects of teaching and learning mathematics such as creativity, affect, diversity, technology and history;
- theoretical perspectives and comparative approaches in mathematics education research.
This book is a fascinating compendium of state-of-the-art knowledge for all mathematics education researchers, graduate students, teacher educators and curriculum developers worldwide.
December’s Book of the Month is The Legacy of Felix Klein by Hans-Georg Weigand, William McCallum, Marta Menghini, Michael Neubrand and Gert Schubring (Eds.) (2018).
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, and he strongly promoted the modernisation of mathematics in the classroom. Felix Klein developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books Elementary Mathematics from a higher standpoint. At the 13th International Congress on Mathematical Education (ICME-13) 2016 in Hamburg, the “Thematic Afternoon” with the The Legacy of Felix Klein as one major theme, provided an overview of Felix Klein’s ideas. It highlighted some developments in university teaching and school mathematics related to Felix Klein’s thoughts stemming from the last century. Moreover, it discussed the meaning, the importance and the legacy of Klein’s ideas nowadays and in the future in an international, global context.
The whole book intends to show that many ideas of Felix Klein can be reinterpreted in the context of the current situation, and give some hints and advice for dealing today with current problems in teacher education and teaching mathematics in secondary schools. In this spirit, old ideas stay young, but it needs competent, committed and assertive people to bring these ideas to life.
(–> Link to Springer)
The November Book of the Month is Elementary Mathematics from a Higher Standpoint by Felix Klein.
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.
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. These translations were done bei Marta Menghini (University of Rome) und Gert Schubring (University of Bielefeld and University of Rio de Janeiro).
(–> Link to Springer)
The May Book of the Month is Journey Through Genius: The great theorems of mathematics by William Dunham, first published by John Wiley in 1990, and republished in Penguin Paperback in 1991.
Dunham places each theorem within its historical context and explores the life of the creator — from Archimedes to Gerolamo Cardano to Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. His approach is to present this material as a work of art like music or literature.
May’s Site of the Month is: ScienceDaily – Mathematics News
This site is part of the ScienceDaily website. Here are updated articles that give short overviews of recent applications of mathematics. The entries are backed up with references for further reading.
March Book of the Month is Unsolved Problems in Number Theory by Richard Guy, first published by Springer Verlag in 1981. Third edition (nearly three times the size!!) published in 2004.
These problems are mostly very easy to understand, but are as yet unsolved. Guy gives an account of the problems, and the progress made on them. He does this in such a way that they provide food for thought and avenues for exploration for mathematicians at varying levels of maturity in number theory.
March Site of the Month: The Wolfram MathWorld List of Unsolved Problems
This updated list explains the most famous unsolved problems in mathematics and progress made on each, with references for further reading.
January’s Book of the Month is Famous Problems in Mathematics by Heinrich Tietze, first published in German in 1959, and republished in 1990 by DTV. An English translation published by Graylock Press in 1964. The preface contains a beautiful metaphor and explanation of the nature of mathematical learning.
The original work is entitled Gelöste und ungelöste mathematische Probleme aus alter und neuer Zeit.
The full English translation has the title Famous Problems of Mathematics: Solved and Unsolved Mathematical Problems from Antiquity to Modern Times.
January’s Site of the Month is Famous Problems in the History of Mathematics.
This site is part of NCTM’s MathForum and continues the problems theme of recent Sites and Books of the Month.