Obviously, every engineer knows the answer, the answer is NO, we cant solve any computing problem without mathematics. The foundation of the computer is mathematics. The brain of the computer that is the CPU is made up of the ALU, which run any program with the help of an Instruction Set which consists of different instructions based on different mathematical operations.
To solve any real word problem we have to model that problem based on some mathematical constructs. Lets, say we have to write a program to automatically park a car. For that we have to calculate the exact angle and distance to which a car can rotate or move back and fourth based on the size of the parking slot. There are two ways to solve the problem first one is the Hard Computing approach where we have to know the exact data of each and every thing. Since the program is hard coded, there is no flexibility in the program. So if we cant get the exact data then the program fails.
The second and the more efficient way to solve the problem is Soft Computing. So the program is soft coded and it is flexible. It will need very less data and the program can learn and improve itself based on the real time data. For that we need to get the data at real time to improve the program.
So many of the problems can be solved by Computer using mathematics more specifically by discrete mathematics. Discrete mathematics is mathematics that deals with discrete objects. Discrete objects are those which are separated from (not connected to/distinct from) each other. Automobiles, houses, people etc. are all discrete objects. 0, 1, 2 and 3 are all part of discrete mathematics. The same goes for -1, -2, -3 and so on. If you want to add the numbers from 0 to 3 the calculation would go like this. 0+1+2+3=6.
The model of computer is based on discrete structures. In computers, all the information is stored in bits, units of information that can take the value of either 0 or 1 that is binary. Since the bits are the building blocks of everything that happens in computer software, everything becomes discrete.The study of algorithms is also firmly in the discrete world. An algorithm is a step-by-step list of instructions to the computer and it’s what makes computer programs possible. When determining how much time an algorithm needs to run, you count (means again discrete) the number of operations it needs to perform.
We can use different discrete structures for formulating or model the real word problem. After model the problem we can write the algorithm to solve that problem using the discrete structure. For example the Facebook is a social network and if have to calculate the number of likes a friend gives to another friend then we have to thought the Facebook network as a Graph where the Nodes are the people and the edges are the communication between the people. So we can solve the above problem using the Graph algorithms. We can easily write the program because the graph is easily represented in computer.
Following are the different Discrete Structures.
logic and Boolean algebra
set theory
relations and functions
sequences and series (or "sums")
algorithms and theory of computation
number theory
matrix theory
induction and recursion
counting and discrete probability
graph theory
probability theory
Any kind of computing problem can be solved by the above discrete structures. So i suggest every computer science student and teacher to study these discrete structures thoroughly.
To solve any real word problem we have to model that problem based on some mathematical constructs. Lets, say we have to write a program to automatically park a car. For that we have to calculate the exact angle and distance to which a car can rotate or move back and fourth based on the size of the parking slot. There are two ways to solve the problem first one is the Hard Computing approach where we have to know the exact data of each and every thing. Since the program is hard coded, there is no flexibility in the program. So if we cant get the exact data then the program fails.
The second and the more efficient way to solve the problem is Soft Computing. So the program is soft coded and it is flexible. It will need very less data and the program can learn and improve itself based on the real time data. For that we need to get the data at real time to improve the program.
So many of the problems can be solved by Computer using mathematics more specifically by discrete mathematics. Discrete mathematics is mathematics that deals with discrete objects. Discrete objects are those which are separated from (not connected to/distinct from) each other. Automobiles, houses, people etc. are all discrete objects. 0, 1, 2 and 3 are all part of discrete mathematics. The same goes for -1, -2, -3 and so on. If you want to add the numbers from 0 to 3 the calculation would go like this. 0+1+2+3=6.
The model of computer is based on discrete structures. In computers, all the information is stored in bits, units of information that can take the value of either 0 or 1 that is binary. Since the bits are the building blocks of everything that happens in computer software, everything becomes discrete.The study of algorithms is also firmly in the discrete world. An algorithm is a step-by-step list of instructions to the computer and it’s what makes computer programs possible. When determining how much time an algorithm needs to run, you count (means again discrete) the number of operations it needs to perform.
We can use different discrete structures for formulating or model the real word problem. After model the problem we can write the algorithm to solve that problem using the discrete structure. For example the Facebook is a social network and if have to calculate the number of likes a friend gives to another friend then we have to thought the Facebook network as a Graph where the Nodes are the people and the edges are the communication between the people. So we can solve the above problem using the Graph algorithms. We can easily write the program because the graph is easily represented in computer.
Following are the different Discrete Structures.
Any kind of computing problem can be solved by the above discrete structures. So i suggest every computer science student and teacher to study these discrete structures thoroughly.
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