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Discrete Mathematics in the Real
World
1
GROUP MEMBERS :
MUNTASIR MUHIT
ID : 191-35-399
JAKIAH FAIROOZ
ID : 191-35-396
ASHIQUR RAHMAN
ID : 191-35-410
2
GOOGLE MAPS
Google Maps uses discrete mathematics to determine fastest driving routes and
times. There is a simpler version that works with small maps and technicalities
involved in adapting to large maps
3
COMPUTER GRAPHICS
use linear algebra in order to transform (move, scale, change perspective)
objects. That's true for both applications like game development, and for
operating systems.
4
WEB SEARCHING
Doing web searches in multiple languages at once, and returning a summary,
uses linear algebra.
5
DIGITAL IMAGE PROCESSING
Digital image processing uses discrete mathematics to merge images or apply
filters.
Hidden Markov models, which are part of linear algebra, are used for large
vocabulary continuous speech recognition.
6
FILE MANAGEMENT
Computers run software and store files. The software and files are both stored
as huge strings of 1s and 0s . Binary math is discrete mathematics.
7
SCHEDULING PROBLEMS
like deciding which nurses should work which shifts, or which airline pilots should
be flying which routes, or scheduling rooms for an event, or deciding timeslots
for committee meetings, or which chemicals can be stored in which parts of a
warehouse---are solved either using graph coloring or using combinatorial
optimization, both parts of discrete mathematics. One example is scheduling
games for a professional sports league.
8
APPOINMENT SCHEDULING
In the U.S., the legislative branch of the government has a House of Representatives
with 435 members. The process of deciding how many of these members should be
allocated to each state is called apportionment, and there is a lot of discrete
mathematics involved---both in creating and implementing various apportionment
methods.
9
ENCODING DATA
Methods of encoding data and reducing the error in data transmission---such as
are used in bar codes, UPCs, data matrices, and QR codes---are discrete
mathematics.
10
CELL PHONE COMMUNICATION
Making efficient use of the broadcast spectrum for mobile phones uses linear
algebra and information theory. Assigning frequencies so that there is no
interference with nearby phones can use graph theory or can use discrete
optimization.
11
NETWORKING
Networks are, at base, discrete structures. The routers that run the internet are
connected by long cables. People are connected to each other by social media
("following" on Twitter, "friending" on Facebook etc.). The US highway system
connects cities with roads.
12
CRYPTOGRAPHY
Encryption and decryption are part of cryptography, which is part of discrete
mathematics. For example, secure internet shopping uses public-key
cryptography
13
14

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Discrete mathematics for real world applications

  • 1. Discrete Mathematics in the Real World 1
  • 2. GROUP MEMBERS : MUNTASIR MUHIT ID : 191-35-399 JAKIAH FAIROOZ ID : 191-35-396 ASHIQUR RAHMAN ID : 191-35-410 2
  • 3. GOOGLE MAPS Google Maps uses discrete mathematics to determine fastest driving routes and times. There is a simpler version that works with small maps and technicalities involved in adapting to large maps 3
  • 4. COMPUTER GRAPHICS use linear algebra in order to transform (move, scale, change perspective) objects. That's true for both applications like game development, and for operating systems. 4
  • 5. WEB SEARCHING Doing web searches in multiple languages at once, and returning a summary, uses linear algebra. 5
  • 6. DIGITAL IMAGE PROCESSING Digital image processing uses discrete mathematics to merge images or apply filters. Hidden Markov models, which are part of linear algebra, are used for large vocabulary continuous speech recognition. 6
  • 7. FILE MANAGEMENT Computers run software and store files. The software and files are both stored as huge strings of 1s and 0s . Binary math is discrete mathematics. 7
  • 8. SCHEDULING PROBLEMS like deciding which nurses should work which shifts, or which airline pilots should be flying which routes, or scheduling rooms for an event, or deciding timeslots for committee meetings, or which chemicals can be stored in which parts of a warehouse---are solved either using graph coloring or using combinatorial optimization, both parts of discrete mathematics. One example is scheduling games for a professional sports league. 8
  • 9. APPOINMENT SCHEDULING In the U.S., the legislative branch of the government has a House of Representatives with 435 members. The process of deciding how many of these members should be allocated to each state is called apportionment, and there is a lot of discrete mathematics involved---both in creating and implementing various apportionment methods. 9
  • 10. ENCODING DATA Methods of encoding data and reducing the error in data transmission---such as are used in bar codes, UPCs, data matrices, and QR codes---are discrete mathematics. 10
  • 11. CELL PHONE COMMUNICATION Making efficient use of the broadcast spectrum for mobile phones uses linear algebra and information theory. Assigning frequencies so that there is no interference with nearby phones can use graph theory or can use discrete optimization. 11
  • 12. NETWORKING Networks are, at base, discrete structures. The routers that run the internet are connected by long cables. People are connected to each other by social media ("following" on Twitter, "friending" on Facebook etc.). The US highway system connects cities with roads. 12
  • 13. CRYPTOGRAPHY Encryption and decryption are part of cryptography, which is part of discrete mathematics. For example, secure internet shopping uses public-key cryptography 13
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