Inspiring Maths
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Chris Budd
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What are we really trying to achieve in a maths lesson
• To communicate some real mathematics and developing
an argument
• To get the message across that maths is important,
fun, beautiful, powerful, challenging, all around us and
central to civilisation
• To entertain and inspire our students
• To leave them wanting to learn more about maths and
not less
But let’s face it, we have a problem
Let    f ( ). A weaksolutionof this PDE satisfies the identity
   dx  
f ( )  dx
   H 0 ().
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Assum ethat f ( ) grows sub  critically it is clear from Sobolevem beddingthat    H 01
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• Maths genuinely is hard, can be scary, and requires thought to do well
• And it suffers from an image problem with teenagers
• The challenge is to convey the excitement and importance of maths in
a way which does not trivialise the subject or switch off the audience
Things that
students
have found to have worked with
•Hooking them with an application relevant to their
lives and then showing the maths involved eg. Mazes,
ipods, Google, Facebook
• Being proud of our subject!
• Surprising them …. Maths is magic!
• Linking maths to real people … all maths was invented
by someone!
• Not being afraid to present them with a real formula
or real mathematics!!!
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Some possibilities
• Maths and magic
• Mathematical surprises
• Maths in the Battle of Britain
• Maths will save your life
• Maths and art.
Magical Maths: Where’s the Joker?
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Surprising Mathematics
What is the chance of winning the lottery?
6/49*5/48*4/47*3/46*2/45*1/44=1/13 983 816
How likely are you to live to see the result?
Chance of dying in one week in a car crash
(3000/52)/60 000 000 = 1/1 040 000
How predictable is maths?
Chaos, climate change
Useful Maths: The Battle of Britain
July-Sept 1940.
H. Dowding
600 RAF vs. 2000 Luftwaffe
Germans dismissed Radar thinking that a ground station could only
control one aircraft at a time!!
Maths was used to find and track the enemy aircraft!
Aircraft detected using a mixture of
statistics and trigonometry
Position
combining the
two
Projected
position using
trigonometry
Last known
position of
German aircraft
Estimates
of position
from Radar
stations
HAEMOLYMPH
VENTRICULUS
0.05mm
Maths can save the world!
Source
X-Ray
Object
ρ : Distance from the object centre
θ : Angle of the X-Ray
Measure attenuation of X-Ray
R(ρ, θ)
Detector
REMARKABLE FACT
If we can measure R(ρ, θ ) accurately we can calculate
the X-ray attenuation factor f(x,y) of the object at any
point
Knowing f tells us the structure of the object
• Mathematical formula discovered by Radon (1917)
• Took 60 years before computers and machines were
developed by Cormack to use his formula
Artistic Maths
Robert Lang
Crease patterns are worked out using mathematics
Deer
Beetle
• Maths is used to create origami patterns
• We can use origami to teach maths eg. Trisecting the
angle
Twitter: @RobEastaway
www.robeastaway.com
Chris Budd mascjb@bath.ac.uk