Inspiring Maths
Chris Budd €
e iπ = −1
1,1,2,3,5,8,13 …
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
• Why is it so hard to do this?
• What maths can we tell everyone about?
• What is being done?
• What works .. And what doesn’t?
But let’s face it, we have a problem
• 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
• Maths genuinely is hard, can be scary, and requires thought to do well
• And it suffers from an image problem with teenagers
Let−Df=f ( f ) . Aweak solution of this PDEsatisfies the identity
∫ÑfÑy dx=∫ f ( f ) y dx } } yÎH rSub { size 8{0} rSup { size 8{1} } } \( %OMEGA \) . } {} # Assume that f \( f \) grows ital - critically is clear ¿ Sobolev embedding that $fÎH rSub { size 8{0} rSup { size 8{1} } } {} } } {¿ ¿¿
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Things that have found to have worked with students
•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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e iπ = −1
• Maths and magic
• Mathematical surprises
• Maths in the Battle of Britain
• Maths will save your life
• Maths and art.
Some possibilities
10 1 9
11 2 9
12 3 9
13 4 9
14 5 9
15 6 9
16 7 9
17 8 9
18 9 9
19 10 9
Magical Maths: Where’s the Joker?
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.
Germans dismissed Radar thinking that a ground station could only control one aircraft at a time!!
H. Dowding
600 RAF vs. 2000 Luftwaffe
Maths was used to find and track the enemy aircraft!
Aircraft detected using a mixture of statistics and trigonometry
Last known position of German aircraft
Projected position using trigonometry
Estimates of position from Radar stations
Position combining the two
Maths can save the world!
VENTRICULUS
HAEMOLYMPH
0.05mm
X-Ray
Object
ρ : Distance from the object centre
θ : Angle of the X-Ray
Measure attenuation of X-Ray R(ρ, θ)
Source
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
Deer Beetle
Crease patterns are worked out using mathematics
• Maths is used to create origami patterns
• We can use origami to teach maths eg. Trisecting the angle