Mathematics in every day life (2)

MATHEMATICS IS MORE IMPORTANT THAN YOU MIGHT THINK ….

BY

SHIVA KRISHNA REDDY CH.....

IIMC HYD.

SOME COMMON VIEWS OF MATHEMATICS

MATHS IS HARD

MATHS IS BORING

MATHS HAS NOTHING TO DO WITH REAL LIFE

BUT I CAN SHOW YOU THAT MATHS IS IMPORTANT IN

EVERYDAY LIFE AND CRIME DETECTION MEDICINE

sports FINDING LANDMINES

AND MANY OTHER CAREERS!!!!!!!!!

A.COOKING, B.GROCERY SHOPPING.

C.DIET.

D.BUDJET.

THESE ARE SOME OF THE USES OF MATHEMATICS IN OUR DAILY LIFE.BY SEEING ITSELF,WE CAN UNDERSTAND MATHEMATICS PLAYS AN IMPORTANT ROLE IN OUR DAILY LIFE.

HOW MATHS WILL GET YOU ON TV

PICTURES AND IMAGES ARE ALL AROUND US

• TV

• DVD

• COMPUTER GRAPHICS

• SPECIAL EFFECTS

IMAGES ARE STORED AS NUMBERS – bitmap

USING THESE NUMBERS WE CAN PROCESSTHE PICTURES BY USING MATHEMATICS

They look for skid marks and measure them. Then use a certain formula S= 15.9 √df To figure out if the accident was preventable. Helps find the quickest route to a citizen in

trouble. (Geometry)Find out how many crooks you need to bust

to make your town twice as safe.(Algebra) In order to become a cop you need to pass a

test and math is required.(fact)

Maths and crime: Deblurring a number plate

A short crime story

• Burglar robs a bank

• Escapes in a getaway car

• Pursued by police

GOOD NEWS

Police take a photo

BAD NEWS

Photo is blurred

SOLUTION

Find a model of the blurring process

Original image

f

Blurred image

h

• Blurring formula

• Inverting the formula we can get rid the blur

• BUT need to know the blurring function g

Blurring function g

ydygyxfxh 2)()()(

An example of Image Processing

2// 222 dxgdexhdeef xixiyi

Inversion formula

h(x) f(x)

Maths is widely used in the forensic service!!

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!!

two-dimensional images12

X-ray film

Just as we have replaced film in our cameras with a light detector that creates a digital image, in some situations X-ray film has been replaced by X-ray detectors that create a digital image.....

13

detectors

Modern CAT scanner & MRI

Lots of mathematicians work in medicine

This has been physics and engineering so far, but we are now ready to This has been physics and engineering so far, but we are now ready to add the MATH! add the MATH!

In CAT Scans (Computer Aided Tomography) and MRI’s (Magnetic Resonance In CAT Scans (Computer Aided Tomography) and MRI’s (Magnetic Resonance Imaging), and similar diagnostic technologies, images are made from thousands, Imaging), and similar diagnostic technologies, images are made from thousands, even millions of different perspectives –– even millions of different perspectives ––

and mathematics is used to integrate the information from all these perspectives into and mathematics is used to integrate the information from all these perspectives into a single THREE-dimensional digital image!.a single THREE-dimensional digital image!.

This new use of mathematics has revolutionized diagnostic medicine, yet few in our This new use of mathematics has revolutionized diagnostic medicine, yet few in our society recognize it as new mathematics helping all of us! society recognize it as new mathematics helping all of us!

Mathematics is a subject that is included in each and every field that we do whether it is subject, cooking or any sports.

Topics that we will discuss

What is a cricketWhere it is played (along with its measurements)Measurement of a bat and ballHow to declare a top batsman

Measurements of ground

68.5 yards

70 yards

90 yardsShorte

st boundary

longest boundary

b/w pitch & boundary

22 yards

pitch

International Cricket Council (I.C.C) hasn't the fixed dimension of cricket field how big a cricket ground should be but, it has indicated the minimum range of a ground. A cricket ground should be minimum of diameter 137.16 meters(nearly minimum 68.5 from pitch to boundary) on the square of the pitch where as the shortest boundary should be 65 yards (nearly 59.50 meters) and longest boundary should be 90 yards(82.29 meters) from center of cricket pitch to the boundary which obviously made a cricket ground a elliptical in shape in most cases.

A cricket ball is between 8 13/16 and 9 inches (22.4cm and 22.9cm) in circumference, and weighs between 5.5 and 5.75 ounces (155.9g and 163g) 

The bat. The bat is no more than 38 inches (96.5cm) in length, and no more than 4.25 inches (10.8 cm) wide. The hand or glove holding the bat is considered part of the bat.

Like all sports rankings, cricket ratings involve some math's. In this case, they use a mathematical technique known as exponential weighting for comparing the bats man.

Suppose now you consider the case of Virat and Raina

both of these players have scored 150 runs in five matches, so their  average score per match is 150/5 = 30.

However these score are not accurate when you look at the score from starting and when you find its average you will find that Kohli score is more than that of Raina and this is what we call it as exponential average

FINALE: USING MATHS TO FIND

ANTI-PERSONEL LAND MINES

Land mines are hidden in foliage and triggered by trip wires

Land mines are well hidden .. we can use maths to find them

Find the trip wires in this picture

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

Mathematics finds the land mines!

Who says that maths isn’t relevant to real life?!?

Some interesting mathematical facts

Over 70% of all jobs require maths

On average maths graduates earn more than any other profession

Many degrees require maths including statistics, physics, engineering, economics, chemistry, medicine, IT, computer games, computer science, social-science, psychology, fashion design, business studies, accountancy, actuarial studies, electronics, aeronautics, cryptography,...

Without maths we would have no TV, mobile phones, Internet, credit cards, computer games, CDs, Radar, aeroplanes, DNA profiling, …

Maths is vital working out your mortgage payments, APR calculations, family budget

You can make a lot of difference in this world. If you study math because it’s gives you the basis to do all kinds of new things to make all kind of discoveries and make an impact in your life in the life of your family and friends and to those many other people you always wanted to help.

If you know mathematics you can do that you want..

With out mathematics you can’t live in this world…