Inspiring Maths Chris Budd 1,1,2,3,5,8,13 …. What are we really trying to achieve in a maths...

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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• 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

Twitter: @RobEastaway

www.robeastaway.com

Chris Budd mascjb@bath.ac.uk