The Applications of Mathematics

1. APPLICATIONS OF
MATHEMATICS
In Real Life
Presented By
Ms.S.R.Vidhya
Department of Mathematics

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

3. Maths and crime: Deblurring a number plate
A short crime story
• Burglar robs a bank
• Escapes in a getaway car
• Pursued by police
Nasa

4. GOOD NEWS
Police take a photo
BAD NEWS
Photo is blurred

5. 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
)()()(

6. An example of Image Processing
  
2// 222
dxgdexhdeef xixiyi



Inversion formula
h(x) f(x)
Maths is widely used in the forensic service!!

7. 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
USING THESE NUMBERS WE CAN PROCESS
THE PICTURES BY USING MATHEMATICS

8. SOME APPLICATIONS
PRODUCING THE PICTURES IN THE FIRST PLACE
TRANSMITTING THE PICTURES WITHOUT MISTAKES
Lots of mathematicians work in IT and mobile phone
companies
Galois
Lots of mathematicians
work in computer
graphics, computer
games and Hollywood

9. 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!!

10. 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, …

11. 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

12. Find the trip wires in this picture

13. 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

14. Mathematics finds the land mines!
Who says that maths isn’t relevant to real life?!?

15. An astronomer, biologist, an engineer and a mathematician
were crossing the border into Scotland from England on a train
when they saw a field with a black sheep in it.
The astronomer said, "Look--all sheep on Earth are black."
The biologist said, "Look, in Scotland the sheep are black."
The engineer replied, "No, in Scotland some of the sheep
are black."
Mathematically Precise

16. The mathematician rolled his
eyes to heaven and said, very
patiently, "In Scotland,
there exists at least one field,
in which there is at least one sheep
which is black on at least one side."

17. • Graph theory is the study of points and lines. In particular, it
involves the ways in which sets of points, called vertices, can be
connected by lines or arcs, called edges. In 1735 Leonhard Euler
published an analysis of an old puzzle concerning the possibility of
crossing every one of seven bridges (no bridge twice) that span a
forked river flowing past an island. Euler's proof that no such path
exists and his generalization of the problem to all possible networks
are now recognized as the origin of both graph theory and
topology. Since the mid-20th century, graph theory has become a
standard tool for analyzing and designing communications
networks, power transmission systems, transportation networks,
and computer architectures.

18. • Graph theory has proven useful in the design of integrated circuits (
IC s) for computers and other electronic devices. These
components, more often called chips, contain complex, layered
microcircuits that can be represented as sets of points
interconnected by lines or arcs. Using graph theory, engineers
develop chips with minimum total interconnecting conductor length
(dilation-sum problem, also known as wirelength problem). This is
important for optimizing processing speed and electrical efficiency.
Very-large-scale integration (VLSI) is the process of creating
integrated circuits by combining thousands of circuits into a single
chip. VLSI began in the 1970s when complex communication
technologies were being developed. The microprocessor is a VLSI
device.

19. ORIGIN OF O.R.
Operations Research started from the results achieved by a
group of British Scientists headed by Prof. Blackett to study
various war operations during the second war. Since "research"
was carried out in the war "operations", the subject is titled as
Operations Research. O.R. groups were first formed in England
with interdisciplinary teams with experts in Mathematics,
Statistics, Engineering, Accountancy, Psychology and given the
task of recommending courses of action associated with
tactical problems. The organisers of World War II - Franklin D.
Roosevelt, Churchill, Eisenhower soon found out that war had
really ceased to be a mere soldier's business: It means an
intimately co-ordinated working of many specialists from
several disciplines: Atomic, physics, chemistry, Biology,
Aeronautics, Industrial Management to mention only a few.
Scientists were organised into O.R. teams, which were
addressed initially to optimising the use of resources.

20. SCOPE OF O.R.
 Product Mix, Blending of Raw Materials.
 Equipment downtime.
 Optimum number of service facilities (Mechanics,
Chemists, Doctors and Engineers).
 Inventory of raw materials, spares, consumables, finished
products and packing materials.
 Increase in scrap, rework and material losses.
 Customers satisfaction, delight and intoxication.
 Reduction in cost / expenses.
 Control on absenteeism.
 Effective utilisation of cash flow
 Marketing strategies.
 Choosing the best alternative for investment.
 Optimal utilisation of resources.

21. QUEUE
We find queues of human beings, automobiles, aircrafts, ships,
machines, equipments, samples and so on. From the time we
get up till we go to bed, we wait for something or other. For
example, we wait for food, transport, encashment of cheque,
sending speed post, taking treatment and for teachers to come.
On an average one-third of our time is spent in waiting. Queuing
models help us in finding optimum number of service facilities in
order to minimize cost/ time.

22. REPLACEMENT
The amount of cash loss and time loss due to
failure of machines/ equipments is very
significant. For example, we come across with
replacement problems with regard to vehicles,
machines, equipments, ships, aircrafts,
buildings, bridges, roads and so on.
Replacement models help us in finding out the
optimum period for replacement.

23. NETWORK ANALYSIS
Many projects like flyovers, buildings, water
canals, industries, hospitals, schools and colleges,
launching a new product, getting married,
releasing an advertisement and announcing
results get delayed. The loss due to such delays is
enormous. For example, the delay in starting
Bhilai Steel plant caused an excess loss of 180
crores as against the project cost of 200 crores.
PERT/CPM are the handy tools for PLANNING,
SCHEDULING AND CONTROLLING.

24. SEQUENCING
In cases like work shops or job orders we come across with
the problem of finding out the sequence in which the
various jobs will have to be taken so that the total elapsed
time is minimized. The O.R technique called Sequencing
helps, in fnding out the order in which various jobs to be
undertaken in order to minimize the total elapsed time.

25. TRANSPORTATION PROBLEM
Many organisations deal with problems of transporting
products from origins to destinations leading to find out
from which origin to which destination, how much to be
transported meeting the constraints of availability and
requirement so the transportation cost is minimum or the
profit is maximum.

26. ASSIGNMENT PROBLEM
In USA, during 1940s, the marriage matching organisations
used the technique to find out which girl to be matched to
which boy so that the married couples derive the maximum
pleasure with a condition that only one girl to one boy, and only
one boy to one girl. This technique was then popularly known
as Matching problems. The same technique was being used to
match tasks with task performance in order to minimize cost/
time or maximize profit/ sales/ outcome. For example,
Contractors and projects, marketing areas and sales managers,
batting positions with batsmen in cricket, Buses and Drivers and
so on. The product mix blending, transportation and
assignment problems are branches of Linear Programming
Problems.

27. Pascal Triangle
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28. MATLAB
• Numerical computing environment and programming
language
• Has a toolbox to interface with Maple engine which
turns it into a CAS
• Invented in late 1970s by Cleve Moler, chairman of
computer science at the University of New Mexico
• Used mainly for linear algebra and numerical analysis
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29. Golden Ratio
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1.61803398874989484820...
The digits just keep on going,
with no pattern.
In fact the Golden Ratio is
known to be an Irrational Number..

30. Golden Ratio of Human Body
He was the first to show that the human body was
literally made of building blocks whose proportional
ratios always equal to PHI.
Measure the distance from the tip of your head to the
floor.
Then divide that by the distance from your belly
button to the floor.

31. Concluding Remarks
If:
A B C D E F G H I J K L M N O P K R S T U V W X Y Z
Is represented as :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26.

32. Concluding Remarks
If:
H-A-R-D-W-O-R-K
8+1+18+4+23+15+18+11=98%
And
K-N-O-W-L-E-D-G-E
11+14+15+23+12+5+4+7+5=
96%

33. THANK
YOU
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