In this newsletter:
* Do you know what's good for you? The maths of infectious diseases
* Latest news
* Your Universe questions
* Maths in a minute
* Browse with Plus
* Live maths
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* Do you know what's good for you? The maths of infectious diseases
How do scientists predict how an infectious disease will spread? How
do they make sure that a vaccine is safe? And why is the flu virus so
dangerous?
We give you some answers in the first of a series of packages about
the role of maths and stats in the biomedical sciences. The package
consists of five articles, a podcast, a classroom activity on how to
build your own disease, and an online opinion poll. So get reading and
listening, and tell us what you think!
http://plus.maths.org/latestnews/sep-dec09/disease_package/?nl=1
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Latest news
* Pandora's 3D box
A new 3D version of the Mandelbrot set
http://plus.maths.org/latestnews/sep-dec09/mandelbrot/index.html?nl=1
Plus... read more on the Plus blog
http://plus.maths.org/blog?nl=11
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Your Universe questions
In our last poll to find out what you'd most like to know about the
Universe you nominated the question "Is time travel allowed?". We put
it to the esteemed theoretical physicist Kip Thorne and you can now
read his answer in Plus:
http://plus.maths.org/latestnews/sep-dec09/timetravel/index.html?nl=1
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Maths in a minute - The knapsack problem
You're about to smuggle a bag full of stolen jewellery into Switzerland to
deposit it anonymously at a bank. Unfortunately you can't put all your
items of jewellery into the bag because BudgetAir only let you have 7
kilograms of luggage. The various items are worth different amounts of
money and they have different weights. So which of them should you put in
the bag to maximise the total value, without exceeding the maximal weight?
You might try out all different combinations of items to find the best one.
This is fine as long as you've got only a few items of jewellery to choose
from, but rapidly becomes totally impractical as the number of items
increases. If you have too many items to choose from, Swiss banking laws
will have changed or you will have died long before you've finished
deciding! So to purists, such a brute force solution is unacceptable. These
purists, let's call them mathematicians, ask whether there is an algorithm
- a recipe for finding a solution - which works for any number of items,
and so that the time it takes to complete the algorithm grows with the
number of items in a reasonable, non- explosive fashion.
Mathematicians have a clear definition of "reasonable and non-
explosive" in this context: the time it takes to complete the
algorithm should grow with the number N of items no faster than the
polynomial N to the power of K, for some integer K, grows with N.
That's still pretty rapid growth, especially if K is large, but at
least it's not exponential.
So does such a "polynomial time algorithm" exist for our problem? The
answer is that nobody knows - not yet - though most mathematicians
believe that there isn't. In fact, if you can prove or disprove that a
polynomial time algorithm exists, you will be given 1 million dollars
by the Clay Mathematics Institute. Not just because this particular
problem is so important, but because it is actually equivalent to a
whole range of other open maths problems: if you can solve this one in
polynomial time, then you can solve all the others in polynomial time
too. These problems are known as "NP complete problems": if you do
come up with a solution, then you can easily check that it really is a
solution, but so far it's been impossible to find one that works in
polynomial time. It's one of the biggest open questions in maths.
Optimisation problems such as this one, which is known as the
"knapsack problem", crop up in real life all the time, but practical
people are usually less fussy than mathematicians. They use
algorithms that don't take very long, and which might not give the
very best combination of bundles of cash, but get sufficiently close.
To find out more about NP complete problems, see the following Plus
articles: http://plus.maths.org/issue32/features/dartnell/index.html?nl=1
http://plus.maths.org/issue24/features/budd/index.html?nl=1
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Browse with Plus - The Maths Careers Site
What do zombies and hairdressers have in common? Well, it's maths of
course! The newly revamped maths careers site has just been launched,
exploring the huge range of real-life uses of maths, from styling your
hair to zombification. Organised by age group as well as topics like
entertainment and sport, the site targets students from age 11
onwards, as well as maths undergraduates, graduates and adult
learners. Apart from exploring what you can do with the maths you're
learning about, it gives you hands-on advice on university courses and
CV writing. There's also a list of career profiles and information for
teachers and career advisors.
http://www.mathscareers.org.uk/
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Live Maths
Codebreaking in everyday life
Everything we buy, from books to baked beans, has a product code
printed on it. More sophisticated check-digit codes exist on official
documents, bank notes and air tickets. What are they for and what do
they mean? John D Barrow takes a look at the mathematical structure of
these codes, and asks if in this age of boundless surveillance, there
are enough numbers for each of us to have a serial number of our own.
When: 12th January 2010, 1pm
Where: Museum of London, London Wall, London EC2Y 5HN
Tickets: Free
More info: http://www.gresham.ac.uk/event.asp?PageId=45&EventId=972
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Happy reading from the Plus team!
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