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What have mathematicians done for us? Chris Budd

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A common scenario You meet someone at a party and (foolishly) Tell them you are a mathematician Their immediate reaction is to … Panic Leave quickly Tell you that.. Mathematics is completely useless Mathematicians are souless geeks All mathematicians are mad!

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In response you can … Deny that you are a mathematician Not go to any more parties Agree that mathematicians are evil or …. Say that The modern world would not exist without maths With maths you can tell the future and save lives Maths lies at the heart of art and music Mathematicians organise great parties

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Some ways that maths has changed the modern world Maxwell: Electromagnetism … radio, TV, radar, mobile phones Google Error correcting codes Galois Matrices, eigenvalues

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What mathematicians did to tell the future? Where it all started ….

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Kepler Conic sectionAppollonius Nature has order and pattern and follows rules

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1686 In the Principia Newton showed that this order and pattern could be expressed by using mathematics (calculus)

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Key idea …. Write down the equations describing a physical system Solve the equations Predict the future An astonishing discovery!!!!!!!

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Neptune: discovered by maths Newtons law of gravity

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Weather forecasting Navier-Stokes equations

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US Tidal predictorKelvin Tidal predictor Mathematicians also invented the computer!

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What mathematicians have done to save lives? Florence Nightingale

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Mathematics can look inside you Modern CAT scanner CAT scanners work by casting many shadows with X-rays and using maths to assemble these into a picture

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Also used to X-ray mummies Detect land mines Radon 1917

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What have mathematicians done for music? Was Bach a mathematician?

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Music is based on the idea of the scale … Some musical notes sound better when played together than others The notes C and G (a perfect 5 th ) The notes C and E (a perfect 3 rd ) The octave C to C

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Reason was discovered by Pythagaros Length of strings giving C and G, and C and E, were in simple fractional proportions C:G … 3/2 C:E … 4/3

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Pythagoras invented the Just Scale.. Sequence of notes with frequencies in simple fractional proportions

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Problem: Keyboard instruments could only be tuned for one key Mathematicians invented a new Well Tempered scale with all notes in the same proportion which works well in all keys

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Bach so liked the new scale that he wrote the Well Tempered Clavier to popularise it! It is still used today!

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You have five friends, Annabel, Brian, Colin, Daphne, Edward Want to invite three to a party Annabel hates Brian and Daphne Brian hates Colin and Edward Daphne hates Edward Who do you invite? A C EA C E What have mathematicians done for parties?

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Now have 200 friends and want 100 to come to a party Have a book saying who hates who Who do you invite? Parties to check Takes a high speed computer Years to check them

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Works for a party and many other problems Using maths we can solve it in seconds SATNAV devices! Simulated annealing

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Conclusion …. your Future Life Music Party Are safe in the hands of a mathematician

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