This document discusses the importance of mathematics in everyday life through several examples. It begins by addressing common misconceptions that mathematics is hard, boring, and irrelevant to real life. It then provides examples of how mathematics is used in crime detection, medicine, finding landmines, art, music, and predicting the future. The document goes on to discuss how the modern world would not exist without mathematics and provides scenarios of what life would be like without numbers. It then focuses on specific examples of how mathematics is used in crime detection using image processing techniques, medicine through medical imaging technologies like CAT scans and MRI, and finding hidden trip wires for landmines. It emphasizes that mathematics allows us to see inside the body and world without cutting them open

1. ‘’THE MATHEMATICS IN OUR
LIFE ‘’
Université Sultan Moulay Slimane FST-BM
Prepared by :
 BAHTAT AYOUB
 AZIZI ABDELLATIF

2. SOME COMMON VIEWS OF 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 modern world 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
HAPPENDED IF MATHS HAD
NOT CREATED ?

5. Imagine living your days 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, and why
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, graph theory, 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 CAN SAVE YOUR
LIFE
AND SEE THE WORLD IN A DIFFERENT WAY

10. MATHS AND CRIME
A short mathematical story
• Burglar robs a bank
• Escapes in getaway car
• Pursued by police
• GOOD NEWS Police take a photo
• BAD NEWS Photo is blurred

11. Original
Blurred

12. SOLUTION
Take the photo to 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
PICTURES AND 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 THE PICTURES IN THE FIRST PLACE
TRANSMITTING THE PICTURES WITHOUT MISTAKES
Error Correcting Codes
Galois

16. 0 0 0 0
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 Binary Number: 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 you can 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 got to do with it?
From visual images to numbers (or digital images)

20. SOME MORE APPLICATIONS
DEBLURRING ORIGINALS
FINDING THINGS HIDDEN IN AN IMAGE

21. From Numbers to Images
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…
Now we’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 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
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 Image to 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)
The middle 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
Modern medicine 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 A CAT 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 MATHS WE 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-ray at detector depends on width of object
We can find the thickness … can we find the shape?
Intensity
X

31. MOVE SOURCE AND DETECTOR AROUND
GET SHADOWS OF THE OBJECT FROM MANY
ANGLES AND MEASURE X-RAY INTENSITY

32. 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

33. Object
Attenuation
R(ρ, θ)
θ
ρ

34. REMARKABLE FACT
If we can 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’s formula
Many other applications
X-raying Mummies
Monitoring Furnaces
Remote Sensing

36. USING THE RADON TRANSFORM 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 trip wires

38. Digital picture of foliage 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 of mathematics 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 the car keypad number?
PI KP 6006A
PI PK 6006B PI PK 606D
1
PI KP 606C

41. Quiz
the car keypad number is :
PI KP 6006A
PI PK 6006B
PI KP 606C
PI PK 606D