AIMS-Senegal – picture story of a maths communication adventure

Dear all,

this is a picture story, so be prepared to see many pictures! And it is an adventure too, since we (I will explain later who is “we”) tried something quite new: an interactive highly technical mathematical exhibition in Senegal, including a road show with high school students and Master maths students, talks, conferences, workshops and discussions, and games! And: all in three days!

Let’s start:

Day 0:

The day before the opening of the exhibition and the start of the roadshow. And my first day in Senegal. I arrive around 1:30 am in the morning and spend the night in Dakar. At 11:00 I am picked up by a car from AIMS-Senegal, who is organising the event together with the Next Einstein Initiative and IMAGINARY. In the car, I meet two other international participants: Niane Kode from Senegal, who works at AIMS-Cameroon, and Marcos Cherinda from Mocambique, an ethno-matematician, who also attended the AIMS-IMAGINARY workshop in 2014.…

By | November 16th, 2015|English, Event, Level: Simple, Uncategorized|6 Comments
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A little medical statistics

Originally written by John Webb

tw: fictionalised statistics of disease rates.

———

Today there are many tests that are widely used to detect life-threatening diseases early. How effective are they? Should they be believed?

At a routine checkup, your doctor tells you that there is a simple and inexpensive blood test that can detect a rare but particularly
nasty form of cancer. You agree to have the test done, and the doctor takes a blood sample and sends it off to the pathology laboratory.

Two days later the doctor calls to tell you that the test has come up positive. The good news is that the cancer can be cured since it
has been caught at an early stage. The bad news is that the treatment, though effective, is very expensive and has a number of unpleasant side-effects.

Before agreeing to treatment you need to do a little bit of basic arithmetic.…

By | November 2nd, 2015|English, Level: Simple|0 Comments
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Mathematically speaking, what is a contradiction?

The world of predicate logic interests me, especially how it provides a foundation for understanding the logic behind many mathematical proofs. It is interesting to know how the negation, contrapositive and inverse are defined with respect to some implication A \Rightarrow B   ( A \wedge \neg B, \neg B \Rightarrow \neg A  and   B \Rightarrow A respectively). What got me thinking about predicate logic again was when I asked myself, “What is a contradiction?”

My big Collins Dictionary and Thesaurus defines ‘contradict’ as “to declare the opposite of (a statement) to be true” (verbatim). But, this leaves some room for debate as the meaning of the word “opposite” is not logically clear. Is the negation true? Is the inverse true? My reasoning says that a contradiction of the above implication is defined as A \Rightarrow \neg B . In a less formal way (and also less strongly), A \not \Rightarrow B .

Let me briefly pause here for the sake of those unfamiliar with the symbols I have already used. \neg denotes ‘not’, \Rightarrow denotes ‘implies’, \wedge denotes ‘and’, and A and B are symbols which represent a statement, such as “dogs are black” or “black animals are dogs”.…

By | November 1st, 2015|Level: Simple, Uncategorized|1 Comment
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UCT MAM1000 lecture notes part 38 – 3D geometry and vectors part i

A lot of the following is going to be rather intuitively clear, but we need to build up a framework where we are all speaking the same language to develop the powerful tools that we are going to find over the coming sections. We will be dealing here specifically with three dimensional space but we will discuss along the way the extension of these concepts to higher dimensional spaces. The higher dimensional stuff is not examinable but I think that sometimes it helps to understand the things which are special about three dimensions, and the things which are not.

In particular, I can recommend having a look at the web page of John Baez who discusses the regular polytopes in different numbers of dimensions here.

It’s clear that to define where you are in three dimensional space you need to set up a few key ingredients first. What you need is first of all an origin – a place to call home from which you will relatively describe your position.…

By | September 4th, 2015|Courses, English, First year, Level: Simple, MAM1000, Uncategorized, Undergraduate|1 Comment
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The Varsity Maths Problem

The following post is written by John Webb from The Department of Mathematics and Applied Mathematics at The University of Cape Town. With his permission I include it here as an advert for a book which is discussed at the bottom of the post. Mathemafrica receives no payment for including this text. I hope that in addition to being an advert for the book, this may be a chance for students to discuss some of the problems they see with the transition between school and University here in South Africa for maths students.

Why do so many first-year students fail varsity maths?
Thousands of students across South Africa have started their university careers, and many of them have enrolled for a course in Mathematics. Some will be aiming at a maths major, in particular those who hope to teach mathematics at school level. But far more will be doing maths as a requirement for their degrees in a whole range of areas.…

By | June 3rd, 2015|Background, English, Level: Simple|4 Comments
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Mathematics or dreams, which is more real?

Mathematics can sometimes seem dream-like, at least on first encounter. Later on, one gets
used to a new mathematical object, and it seems everyday. I remember how strange the idea of
a group was to me, how mysteriously it grew from three almost trivial axioms to a forest
of subgroups and quotient groups and equivalence classes and so on. Of the few dreams I
now recall, there was one with a huge hall full of people, perhaps a giant cave, and I was descending a long,
rickety staircase — or was I sliding down a cable? — feeling myself among a heretofore
completely unsuspected part of humanity, who perhaps nobody from above ground had ever seen.
Groups were a bit like that, and saying that a square had a symmetery group did not
make them appear any less unexpected.

Furthermore, dreams and mathematics have a lot in common—I mean here the dreams that
people, when awake, remember having had when asleep.…

By | April 13th, 2015|Background, English, Level: Simple|2 Comments
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Presentation of the Mathemafrica framework to an Italian audience

Today I am presenting some of the ideas behind the Mathemafrica project to an Italian meeting, discussing the outcomes of the AIMS-imaginary meeting last month. The presentation can be found here:

Mathemafrica – Italian discussion

How clear is this post?
…
By | December 17th, 2014|Background, English, Level: Simple, News|1 Comment
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A personal introduction

I write this before Mathemafrica publicly launches. I want to give a little background about myself, what I am doing now, and what I see as the potential for Mathemafrica.

I am originally from England, Oxford to be precise. From a very early age I was fascinated with the way the world worked, being that pestering, questioning child who won’t take ‘just because’ for an answer. I was very lucky to discover early on that not only were there fascinating questions to be asked, but answers when you knew the right places to look. I was lucky to have resources at my fingertips and museums just down the road where there were mysteries to be solved on every trip. My curiosity was not sated by reading books and so I went on to study physics at University. After four years and still hungry for more I thought that a PhD might finally put a stop to my questioning, but of course that only added to the arsenal of tools at my disposal for answering them.…

By | December 13th, 2014|Background, English, Level: Simple|0 Comments
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Mathematics in Africa – news from the EMS Newsletter

News from the EMS Newsletter, November 29, 2014:

1. CANP4, the fourth event in the Capacity and Network Project organized by the International Commission of Mathematical Instruction (ICMI) and supported by the International Council of Science (ICSU) held its first meeting in East Africa in Dar es Salaam, Tanzania, on September 1-12 204, with more than 80 participants from Tanzania, Kenya, Uganda and Rwanda, This event led to the creation of a new ‘East Africa Mathematics Education and Research Network’. The founding President is Dr Alphonse Uworwabayeho (Rwanda) and the founding Secretary is Dr. Angelina Bijura (Tanzania).

2. Call for Candidates for Ibni Prize 2014.
The Prize “Ibni Oumar Mahamat Saleh” has been created in memory of our colleague and to continue its commitment to Mathematics in Africa. The prize is awarded annually to a young mathematician from Central Africa or West Africa. Applications are evaluated by a scientific committee set up by CIMPA.…

By | November 30th, 2014|English, Level: Simple, News|0 Comments
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A foray into a new number system – an introduction to imaginary numbers

This is the introduction which I give to my first year mathematics class when they see imaginary numbers for the first time. I thought I’d type it up here as it’s received good reactions the two times that I’ve introduced it in this format. Note that this probably isn’t the canonical way to introduce complex numbers, but then most of my lectures don’t necessarily take the normal route…

Complex Numbers, a philosophical detour

Before we get on to talking about imaginary numbers and complex numbers, let’s try and break down our preconceptions about numbers in general.

We look at the world around us and see many things which we categorise. We see a computer, a piece of paper, we see other people, we see our hands. These are labels that we use to categorise the world, but these objects seem very physical and very real. We rarely question their existence, though if one wants to take the Cartesian view, we should also question the reality we are in.…

By | November 11th, 2014|Background, English, Level: Simple|0 Comments
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A project initiated at the AIMS-IMAGINARY workshop, November 2014, Cape Town | All Rights Reserved
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