Discrete mathematics and its applications
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Everyday applications of discrete mathematics
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.
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.
Doing web searches in multiple languages at once, and returning a summary, uses linear algebra.
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.
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.
An analog clock has gears inside, and the sizes/teeth needed for correct timekeeping are determined using discrete math.
Wiring a computer network using the least amount of cable is a minimum-weight spanning tree problem.
Encryption and decryption are part of cryptography, which is part of discrete mathematics. For example, secure internet shopping uses public-key cryptography.
Area codes: How do we know when we need more area codes to cover the phone numbers in a region? This is a basic combinatorics problem.
Designing password criteria is a counting problem: Is the space of passwords chosen large enough that a hacker can't break into accounts just by trying all the possibilities? How long do passwords need to be in order to resist such attacks? (find out here!)
Machine Job Scheduling: Scheduling tasks to be completed by a single machine uses graph theory. Scheduling tasks to be completed by a set of machines is a bin-packing problem, which is part of discrete optimization. Google describes the issue for multiple types of jobs on multiple machines.
Railway planning uses discrete math:deciding how to expand train rail lines, train timetable scheduling, and scheduling crews and equipment for train trips use both graph theory and linear algebra.
Hope this helps :)
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.
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.
Doing web searches in multiple languages at once, and returning a summary, uses linear algebra.
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.
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.
An analog clock has gears inside, and the sizes/teeth needed for correct timekeeping are determined using discrete math.
Wiring a computer network using the least amount of cable is a minimum-weight spanning tree problem.
Encryption and decryption are part of cryptography, which is part of discrete mathematics. For example, secure internet shopping uses public-key cryptography.
Area codes: How do we know when we need more area codes to cover the phone numbers in a region? This is a basic combinatorics problem.
Designing password criteria is a counting problem: Is the space of passwords chosen large enough that a hacker can't break into accounts just by trying all the possibilities? How long do passwords need to be in order to resist such attacks? (find out here!)
Machine Job Scheduling: Scheduling tasks to be completed by a single machine uses graph theory. Scheduling tasks to be completed by a set of machines is a bin-packing problem, which is part of discrete optimization. Google describes the issue for multiple types of jobs on multiple machines.
Railway planning uses discrete math:deciding how to expand train rail lines, train timetable scheduling, and scheduling crews and equipment for train trips use both graph theory and linear algebra.
Hope this helps :)
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Discrete Mathematics and Its Applications is the best book to start with
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