This document discusses the various applications of mathematics in real life. It describes how mathematics is used in fields like defense, cryptography, navigation, coding/communication, maps, supply chains, and medicine. Mathematics plays a key role in activities such as encrypting internet communications, GPS navigation, efficient cargo transportation, medical dosing calculations, weather prediction, and more. The document concludes that mathematics is essential across many domains and that applications are often discovered for pure mathematical concepts.

1. Application
of
mathematics
in
real life
By
Thasneem Razia
I-M.Sc. Mathematics
JBAS College for Women

2. INdex
 INTRODUCTION
 DEFENSE AND MILITARY
 PUBLIC KEY CRYPTOGRAPHY
 NAVIGATION
 CODES AND COMMUNICATION
 MAPS OF THE EARTH
 SUPPLY CHAINS
 MEDICAL FIELDS
 OTHER FIELDS
 CONCLUSION

3. INTRODUCTION
An essential discipline in today’s world.
Powerful tool for understanding the world around
us.
Math surrounds us.
See and use math skills and capabilities
everyday.
Everyone needs some level of specific math
knowledge.
To perform their job better and to get ahead in
the world.

4. DEFENSEANDMILITARY
Providing the framework.
Solutions to logistical problems.
Mathematical models can be used to develop
and simulate complex military stratergies.
Game theory , statics , and probability.
Cyber warfare has become increasingly
important.
Organizations develop and attempt to break
secret codes : Cryptography

5. PublicKeyCryptography
 Mathemathics used to encipher secret information exchanged between your computer and
a web server.
 Mathematical padlock : software that secures the internet.
 RSA public key cryptosystem : Ronald Rivest, Adi Shamir , and Leonard Adleman.
 The RSA padlock consists of two numbers : the encryption key e, and the modulus the
mathematics will be based on, N.
 Encrypting the message :
1. Turn the message into number by using standard method such as ASCII.
2. Change message m into ciphertext c using : c= me mod N
 Decrypting the message :
Decrypt cipher text c using : cd mod N=m mod N
 Example : e=3,N=55,d=27 and m=14
c= me mod N
= 143 mod 55
= 2744 mod 55
= 49 mod 55
since 49 is the remainder when 2744 is divided by 55. Therefore, the ciphertext c is 49.
This ciphertext can then be decrypted using a key, in this case, d = 27, in the following
way:
cd mod N= 4927 mod 55
which after some work ...
=14 mod 55
So for the RSA system to work you need to find numbers e, N and d such that raising any
message m to the power of ed modulo N is equivalent to raising a number to the power of 1
in our normal arithmetic.

6. Navigation
 The GPS satellites that power your sat-nav are the
modern equivalents of the Sun, Moon and stars.
 A GPS receiver replaces both the sextant and the clock,
but the maths and laws of motion are still needed as part
of the software programmed into the GPS systems.
 EUCLIDEAN METRIC : The most intuitive way to measure
distance is the straight line between two points.
 MANHATTAN METRIC : In some cities,
the distance between two points is only measured along
horizontal or vertical lines, not directly.
 BRITISH RAIL METRIC : In the UK, the distance, via rail,
between two distinct points always has to go via London.

7. Codesandcommunication
 During transmission, say via a phone, you might
encounter noise leading to all points moving slightly.
 Before transmitting, you don't know how the points will
move, leading to small 'spheres of uncertainty' around
every message point.
 To make a transmission as efficient as possible you want
to stack these 'spheres' as closely as possible.
 The Kepler conjecture states that no arrangement of
equally sized spheres filling space has a greater average
density than that of the cubic close packing (face-
centered cubic) and hexagonal close
packing arrangements.

8. Mapsof the earth
 Representing our spherical, 3-dimensional Earth on a flat
2-dimensional map is surprisingly difficult: we always
have to distort the world a little, by stretching or squishing
certain areas.
 The Mercator projection significantly distorts the relative
size of various countries, while the Gall-Peters and
Mollweide projections distort straight lines and bearings.
 There are many other projections to represent Earth on
maps, and you often use different projections to show
certain parts of Earth, or for particular applications such
as nautical navigation.

9. Supply chains
 Business leaders today are facing many challenges including cost, tax laws,
skills, material availability, and new market entry and others have driven
organizations to redesign and reconfigure their supply chains continually.
 The complexities to manage and control those globalized supply chains will
also increase and that usually results in inadequate existing experience and
intuition.
 To overcome that inadequacy the use of mathematical models becomes
necessary.
 The use of mathematical models to optimize supply chain has been
increasing, mainly because of their lower cost and greater capability.
 In supply chain management the use of mathematical modeling is not
specific to any particular level; those can be used at any level (strategic,
tactical, or operational).
 Linear programming, mixed-integer/integer linear programming, nonlinear
programming, multiobjective programming, fuzzy mathematical
programming, stochastic programming, heuristics algorithms, and
metaheuristics and hybrid models.

10. Medical field
 Both doctors and nurses use math every day while providing health care
for people around the world.
 They use math when they write prescriptions or administer medication.
 Numbers provide an abundance of information for medical professionals.
 Prescriptions indicate a specific medication and dosage amount.
 Doctors need to figure out how many milligrams of medication each patient
will need, depending on their weight.
 Doctors must also determine how long a prescription will last.
 Example :
If a patient needs to take their medication, say one pill, three times a
day. Then one month of pills is approximately 90 pills. However,
most patients prefer two or three month prescriptions for
convenience and insurance purposes. Doctors must be able to do
these calculations mentally with speed and accuracy.

11. Other fields
Other fields where mathematics is applied :
 Predicting the weather
 MRI and Tomography
 Finance and banking
 Internet and phones
 Cosmology
 Computers
 Construction
 Automotive Design
 Neurology
 Robotics
 Search Engines
 Breaking the Enigma
 Space Observations

12. conclusion
Mathematics is essential in many fields,
including natural science, engineering, medicine,
finance, and the social sciences. Applied
mathematics has led to entirely new mathematical
disciplines, such as statistics and game theory.
Mathematicians engage in pure mathematics
(mathematics for its own sake) without having any
application in mind, but practical applications for
what began as pure mathematics are often
discovered later.