The gem that I have decided to share with you today, is Bertrand Russel‘s book from 1903: “The Principles of Mathematics”.
You can download the pdf, or you can read it below. You can also check out this site, for another online version of the book. Enjoy!
The last issue of TCRecord includes a review of a book that I wasn’t aware of before, but that certainly looks interesting: “Tools of American Mathematics Teaching, 1800-2000“, by Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts. The book was published last year. Here is a taster of Alexander P. Karp’s excellent review of the book:
In today’s classrooms graphing calculators have become routine, yet thousands of teachers can easily recall a time when they did not exist. Not so with the blackboard, which seems to us something that is almost as old as the idea of education itself. This, however, is by no means the case. Two hundred years ago, and for several decades afterwards, blackboards were a novelty in American classrooms and their use was regarded as a particular feature of teaching style. And indeed, the transition from small tablets made of slate to a large blackboard for the whole class went along with a transition to working simultaneously with a large group of students—a transition that can hardly be viewed as anything other than fundamental.
This gem from the history of mathematics is more recent. It was published in 1940 by British mathematician G.H. Hardy. The book/essay was written when Hardy (then 62) felt that he no longer had the ability to contribute to the field of mathematics. A main theme in the book is concerning mathematical beauty, and he believed that the most beautiful mathematics was that, which had no application! Luckily, this book is also in the public domain, and you can read it in below (or download the pdf):
Isaac Newton is arguably one of the greatest scientists (and mathematicians) of all times, and his Principia is one of the great works from the history of mathematics. Together with Leibniz, Newton is normally acknowledged as the founder of differential and integral calculus. If you want to download Principia to your computer, you can head over to the Internet Archive. The original was in Latin, but you can read an English translation below:
David Hilbert (1862-1943) was one of the most important mathematicians of last century. He worked most of his life in Göttingen, which had a very important mathematics center at the time. Here, Hilbert was surrounded by excellent mathematicians like Felix Klein, John von Neumann, Ernst Zermelo, Emmy Noether and more.
One of Hilbert’s achievements was to initiate a shift towards a more modern axiomatic method in mathematics, and in particular in geometry. In relation to this, he proposed a research project, called “Hilbert’s program”, which aimed at formulating a solid and complete logical foundation for mathematics. Hilbert’s “The Foundations of Geometry” is therefore one of the most important modern works in mathematics, although his program did not succeed. The book is therefore a natural follow-up for Gem #1: Euclid’s “The Elements” (which is regarded as one of the most important mathematics texts ever, and in particular related to geometry). If you want to download the book in pdf format, you can go to the Gutenberg Project. Otherwise, you can read it here:
David Hilbert – The Foundations of Geometry
When I was a student, I was lucky enough to study in a school which had a very good library of books related to mathematics and mathematics education. Nowadays, you can study many of the great classical texts online. In 2009, I am going to share with you several gems that I have found online. In my quest for these texts on mathematics/mathematics education, a natural first stop is with one of the greatest mathematical texts of all times: The Elements, by Euclid.
Here is the text:
Euclid Elements
You can also download (or read online) this great book in Google Books. See these two links for two versions of the text.
Happy new year, and happy reading!
Since then, my thesis – a 300 page long thesis in mathematics education – has been viewed 2779 times (as of writing), downloaded 4 times, liked by 4 people and 18 people have added the thesis to their favorites. It has also been awarded to the hot-list on Scribd. Although these numbers are not fantastic, I think it is pretty good for such a thesis. If you are interested in taking a look for yourself, you can either click on the link above, or you can read the embedded document below. If you rather want to read in fullscreen, click here. If you want to download it, click here (pdf).
Mathematics in everyday life – A study of beliefs and actions
Many great books have been written, and an increasing number are becoming part of the public domain. One of them, which I would like to point your attention to, is a classical book written by Benchara Branford in 1908! The title of the book is: “A Study of Mathematical Education, including The Teaching of Arithmetic”. Besides being an important book in the history of mathematics education, it also provides a nice insight into the teaching of mathematics as it was 100 years ago!
Personally, I think his very direct connection between the historical development of mathematics and the child’s development of mathematical thinking (often referred to as “the genetic approach” in mathematics education) is interesting.
A Study of Mathematical Education
If you want to read the book in fullscreen format, click here. For download (pdf), click here.
For those of you who haven’t already discover it, here is a tip for Christmas: Scribd! You can find lots of interesting books and papers here, and some are true gems. Here is one of them: A brief history of mathematics, by Karl Fink. This official translation was published in 1900, and therefore is in the public domain. You can read the book in its entirety here:
A brief history of mathematics
If you want to read the book in fullscreen, you can go here. To download the book as pdf, click on this link.
Reidar Mosvold 