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- 1. ‘’THE MATHEMATICS INOUR LIFE ‘’ Université Sultan Moulay Slimane FST-BM Prepared by : BAHTAT AYOUB AZIZI ABDELLATIF
- 2. SOME COMMON VIEWSOF MATHEMATICS • MATHS IS HARD • MATHS IS BORING • MATHS HAS NOTHING TO DO WITH REAL LIFE • ALL MATHEMATICIANS ARE MAD! BUT I CAN SHOW YOU THAT MATHS IS IMPORTANT IN CRIME DETECTION MEDICINE FINDING LANDMINES
- 3. The modernworld would not exist without maths Maths lies at the heart of art and music With maths you can tell the future and save lives
- 4. WHAT WOULD HAVE HAPPENDEDIF MATHS HAD NOT CREATED ?
- 5. Imagine living yourdays without a use numbers, the most basic and important of mathematic characters. How would you know the time of the day? Wouldn’t you miss your birthday without a calendar? How we can built the bridge ? How we can do everthing? Consider this, you go to a shop to buy something but since this is a world without math's, you don’t know what money is, you don’t know measurements. So what do you do?
- 6. Spot the mathematician, andwhy are they important?
- 7. E B t M, H D t J, .D , .B 0. Spot the mathematician, and why are they important? Maxwell and the discovery of electromagnetic waves Electromagnetism, radio, WiFi,TV, radar, mobile phones, microwaves all come from the work of Maxwell!
- 8. Linear algebra, graphtheory, SVDGoogle: Error correcting codes: Galois theory Internet: Network theory Security: Fermat, RSA Mathematicians really have made the modern world possible Medical imaging: Radon Transform Communications: FFT, Shannon Medical Statistics: Nightingale A few examples ….
- 9. HOW MATHS CANSAVE YOUR LIFE AND SEE THE WORLD IN A DIFFERENT WAY
- 10. MATHS AND CRIME Ashort mathematical story • Burglar robs a bank • Escapes in getaway car • Pursued by police • GOOD NEWS Police take a photo • BAD NEWS Photo is blurred
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- 12. SOLUTION Take the phototo a mathematician Original f(x) Blurring h(x) = f(x)*g(x) • Maths gives a formula for blurring convolution • By inverting the formula we can get rid of the blur g(x)
- 13. Processed image :Image Processing
- 14. MATHS AND PICTURES PICTURESAND IMAGES ARE ALL AROUND US • TV • DVD • COMPUTER GRAPHICS • SPECIAL EFFECTS IMAGES ARE STORED AS NUMBERS USING THESE NUMBERS WE CAN PROCESS THE PICTURES BY USING MATHEMATICS
- 15. SOME APPLICATIONS PRODUCTING THEPICTURES IN THE FIRST PLACE TRANSMITTING THE PICTURES WITHOUT MISTAKES Error Correcting Codes Galois
- 16. 0 0 00 1 0 0 1 2 0 1 0 3 0 1 1 4 1 0 0 5 1 0 1 6 1 1 0 7 1 1 1 Binary numbers
- 17. 3 Bit BinaryNumber: x x represented by three digits a b c eg. 101 a,b,c are 0 or 1 x = 4*a + 2*b + c eg. 101 = 4+0+1 = 5 011 = 0+2+1 = 3
- 18. Using binary youcan count from 0 to 31 on one hand with 5 bit binary numbers How does a monster count to 25? On his fingers! eg. 10110 = 16 + 4 + 2 = 22 11001 = 16 + 8 + 1 = 25
- 19. What’s math gotto do with it? From visual images to numbers (or digital images)
- 20. SOME MORE APPLICATIONS DEBLURRINGORIGINALS FINDING THINGS HIDDEN IN AN IMAGE
- 21. From Numbers toImages Let us type the following numbers 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 We then color them so 1=black, 8=white rest of colors are in between
- 22. One more time… Nowwe’ll try the following numbers 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8 16 16 16 16 16 16 16 16 32 32 32 32 32 32 32 32 64 64 64 64 64 64 64 64 128 128 128 128 128 128 128 128 We then color them so 1=black, 128=white rest of colors are in between
- 23. Let’s compare 1 11 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8 16 16 16 16 16 16 16 16 32 32 32 32 32 32 32 32 64 64 64 64 64 64 64 64 128 128 128 128 128 128 128 128
- 24. From an Imageto Its Numbers We start with clown image It has 200*320 numbers I can’t show you all… Let’s zoom on eye (~40*50)
- 25. Image to Numbers(Continued) We’ll zoom on middle of eye image (10*10)
- 26. The Numbers (Continued) Themiddle of eye image (10*10) 80 81 80 80 80 80 77 77 37 11 81 80 81 80 80 80 77 37 9 6 80 80 80 80 80 80 37 11 2 11 80 80 80 80 80 77 66 66 66 54 80 80 80 80 77 77 77 80 77 80 80 80 79 77 66 54 66 77 66 54 77 80 77 70 22 57 51 70 51 70 77 73 70 22 2 2 22 37 37 22 77 77 54 37 1 6 2 8 2 6 77 70 70 22 2 2 6 8 8 6 Note the rule: Bright colors – high numbers Dark colors - low numbers
- 27. MATHS AND MEDICINE Modernmedicine has been transformed by methods of seeing Inside you without cutting you open! • Ultra sound: sound waves • MRI: magnetism • CAT scans: X rays ALL USE MATHS TO WORK!!
- 28. WHAT IS ACAT SCAN?? CAT = Computerised axial tomography Based on X-Rays discovered by Roengten X-Rays cast a shadow GOOD for looking at bones BAD for looking at soft tissue
- 29. USING MODERN MATHSWE CAN DO A LOT BETTER Modern CAT scanner CAT scanners work by casting many shadows with X-rays and using maths to assemble these into a picture
- 30. X-Ray source Object Detector X Intensity of X-rayat detector depends on width of object We can find the thickness … can we find the shape? Intensity X
- 31. MOVE SOURCE ANDDETECTOR AROUND GET SHADOWS OF THE OBJECT FROM MANY ANGLES AND MEASURE X-RAY INTENSITY
- 32. X-Ray Object ρ : Distancefrom the object centre θ : Angle of the X-Ray Measure attenuation of X-Ray R(ρ, θ) Source Detector
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- 34. REMARKABLE FACT If wecan measure R(ρ, θ) accurately we can calculate The density f(x,y) of the object at any point • Mathematical formula discovered by Radon (1917) • Took 60 years before computers and machines were developed to use his formula • Machine inventor Cormack got a Nobel prize • Radon got nothing! • Process is called Back Projection
- 35. Radon transform Back Projection Radon’sformula Many other applications X-raying Mummies Monitoring Furnaces Remote Sensing
- 36. USING THE RADONTRANSFORM TO FIND ANTI-PERSONEL LAND MINES Land mines are hidden in foliage and triggered by trip wires Trip wires are well hidden – can they be quickly and safely detected
- 37. Find the tripwires
- 38. Digital picture offoliage is taken by camera on a long pole Image intensity f(x,y) • • • • Trip wires are like X-Rays Radon transform x y f(x,y) R(ρ,θ) Points of high intensity in R correspond to trip wires θ ρ Isolate points and transform back to find the wires
- 39. The uses ofmathematics in one’s life is infinite, the use of mathematics is unquestionable for every individual ,being the queen of all sciences and the king of all arts it offers a wonderful approach to us successful in life .
- 40. Quiz What is thecar keypad number? PI KP 6006A PI PK 6006B PI PK 606D 1 PI KP 606C
- 41. Quiz the car keypadnumber is : PI KP 6006A PI PK 6006B PI KP 606C PI PK 606D