M. Gavrilovich, Point-set topology as diagram chasing computations, The De Morgan Gazette 5 no. 4 (2014), 23-32.
We observe that some natural mathematical definitions are lifting properties relative to simplest counterexamples, namely the definitions of surjectivity and injectivity of maps, as well as of being connected, separation axioms \(T_0\) and \(T_1\) in topology, having dense image, induced (pullback) topology, and every real-valued function being bounded (on a connected domain).
We also offer a couple of brief speculations on cognitive and AI aspects of this observation, particularly that in point-set topology some arguments read as diagram chasing computations with finite preorders.
An experimental MOOC (Massive Open Online Course) Citizen Maths is launched and the first phase of the course is open for registration. It is free and open for everyone; its motto is Powerful Ideas in Action.
The readers of this blog may like to register for the course, because, as the organisers say,
The success of this first phase of Citizen Maths will depend crucially on the feedback that we obtain. We are particularly keen to get feedback from:
- learners who do the course;
- those with an interest in the learning and teaching of maths, and in the design of online courses.
There is a link to a feedback form on every page of the Citizen Maths web site, and there will be a similar link on every page of the course when it goes live on or around 12 September.
The first pilot stage will run for four weeks and cover the first “powerful idea”: proportion. An admirable choice (a detailed discussion of the role of proportions in elementary mathematics can be found in this paper by Tony Gardiner).
[Republished from Terry Tao's Blog -- because of the importance of the issue.-- AB]
[This guest post is authored by Matilde Lalin, an Associate Professor in the Département de mathématiques et de statistique at the Université de Montréal. I have lightly edited the text, mostly by adding some HTML formatting. -T.]
Mathematicians (and likely other academics!) with small children face some unique challenges when traveling to conferences and workshops. The goal of this post is to reflect on these, and to start a constructive discussion what institutions and event organizers could do to improve the experiences of such participants.
The first necessary step is to recognize that different families have different needs. While it is hard to completely address everybody’s needs, there are some general measures that have a good chance to help most of the people traveling with young children. In this post, I will mostly focus on nursing mothers with infants ( months old) because that is my personal experience. Many of the suggestions will apply to other cases such as non-nursing babies, children of single parents, children of couples of mathematicians who are interested in attending the same conference, etc..
The mother of a nursing infant that wishes to attend a conference has three options:
Top 5: Harvard, MIT, Oxford, Berkeley, Cambridge
British Universities in top 50: 3 Oxford. 4-5 Cambridge, 11 Imperial, 25 Warwick, 31 Edinburgh, 34 Bristol, 36 UCL, 50 Manchester
From Maryam Mirzakhani’s interview to the Clay Institute:
My older brother was the person who got me interested in science in general. He used to tell me what he learned in school. My first memory of mathematics is probably the time that he told me about the problem of adding numbers from 1 to 100. I think he had read in a popular science journal how Gauss solved this problem. The solution was quite fascinating for me. That was the first time I enjoyed a beautiful solution, though I couldn’t find it myself. [...]
I was very lucky in many ways. The war ended when I finished elementary school; I couldn’t have had the great opportunities that I had if I had been born 10 years earlier. I went to a great high school in Tehran – Farzanegan – and had very good teachers.[...]
Our school was close to a street full of bookstores in Tehran. I remember how walking along this crowded street, and going to the bookstores, was so exciting for us. We couldn’t skim through the books like people usually do here in a bookstore, so we would end up buying a lot of random books. Also, our school principal was a strong-willed woman who was willing to go a long way to provide us with the same opportunities as the boys’ school.
Later, I got involved in Math Olympiads that made me think about harder problems. As a teenager, I enjoyed the challenge. But most importantly, I met many inspiring mathematicians and friends at Sharif University. The more I spent time on mathematics, the more excited I became.
Read the full text of the interview at The Guardian website.
Team results, individual result. British teams, out of 73:
39. University of Warwick
0n 16 July 2014 Department for Education launched a consultation on new subject content for AS and A Level Mathematics and Further Mathematics. The consultation closes at 19 September 2014 5:00pm. Respond by e-mailing to email@example.com or by filling in response form.
A. E. Kyprianou: The UK financial mathematics M.Sc. arXiv:1405.6739v2 [math.HO]
Postgraduate taught degrees in financial mathematics have been booming in popularity in the UK for the last 20 years. The fees for these courses are considerably higher than other comparable masters-level courses. Why? Vendors stipulate that they offer high-demand, high-level vocational training for future employees of the financial services industry, delivered by academics with an internationally recognised research reputation at world-class universities.
We argue here that, as the UK higher education system moves towards a more commercial environment, the widespread availability of the M.Sc. in financial mathematics exemplifies a practice of following market demand for the sake of income, without due consideration for the broader consequences. Indeed, we claim that, as excellent as such courses can be in intellectual content and delivery, they are mismatching needs and expectations for such education and confusing the true value of what is taught.
The story of the Mathematical Finance MSc serves as a serious case study, highlighting some of the incongruities and future dangers of free-market education.
An article by in the NYT; it is about America, but is very timely in the context of the National Curriculum reform in England. A quote:
It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious “new math,” only to find, a few years later, that nothing actually changed. In fact, efforts to introduce a better way of teaching math stretch back to the 1800s. The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices.
The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them. [Emphasis is mine -- AB.]
Read the whole article.
A. D. Gardiner, Teaching mathematics at secondary level. The De Morgan Gazette 6 no. 1 (2014), 1-215.
From the Introduction:
This extended essay started out as a modest attempt to offer some supporting structure for teachers struggling to implement a rather unhelpful National Curriculum. It then grew into a Mathematical manifesto that offers a broad view of secondary mathematics, which should interest both seasoned practitioners and those at the start of their teaching careers. This is not a DIY manual on How to teach. Instead we use the official requirements of the new National Curriculum in England as an opportunity:
- to clarify certain crucial features of elementary mathematics and how it is learned — features which all teachers need to consider before deciding `How to teach’.