(PDF) Discrete Mathematics for Computer Science

Added on - 18 Feb 2021

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Discrete Mathematicsfor IT
Table of ContentsINTRODUCTION...........................................................................................................................3PROBLEM DEFINITION..............................................................................................................3REAL WORLD APPLICATION...................................................................................................3SOLUTION TO THE PROBLEM................................................................................................5POSSIBLE ALGORITHM.............................................................................................................5CONCLUSION...............................................................................................................................7REFLECTION................................................................................................................................7REFRENCES.................................................................................................................................8
INTRODUCTIONDiscrete mathematics refers to the important topic that deals mainly with discrete objects. Itincludes Integers (positive and negative whole numbers), rational numbers (numbers that canbe represented in the form of quotient of two integers), sets and more. But others real numbersthat include irrational numbers are not considered as discrete. Therefore, discrete mathematicsincludes a limited set of integers only. This subject becomes a most important one in real worldproblems, especially within computer science. Using discrete mathematics, a formal languagethat also known as object language can be formed, in the form of mathematical expression todenote logical statements. The present assignment is going to evaluate the concept of discretemathematics and its importance in solving real life problems. As this topic includes a number oftopics like Polynomial Evaluation Algorithm; Algorithm for constructing a Euler circuit; Kruskal’salgorithm; Insertion sort and more. Therefore, problem chosen here is Polynomial EvaluationAlgorithm, which will be solved by using both mathematical formula and computerlanguage –PROBLEM DEFINITIONPolynomial evaluation algorithm also known as Horner’s method, i.e. expressed inthe form of –p(x) = a0+ a1x + a2x2+ a3x3+ a4x4+ ... + anxnor, p(x) = ∑ aixifor all values of i=0 to n.Let, a problem is defined in the form of anxn+ an-1xn-1+ an-2xn-2+ ... + a1x+ a0,where an,a1,a1and so on are integers and x is a variable, asProblem: Evaluate the value of 2x3– 6x2+ 2x – 1REAL WORLD APPLICATIONAs normal language is not suitable for coding languages. Therefore, in ICT (Information andCommunication Technology), algorithm is preferred to write codes to build language, C, JAVA,Python and more. Complex logical problems and difficult questions can easily be solved byusing discrete maths. A computer programmer can use this subject for designing efficientalgorithms, which defines as a set of rules to operate a program. Such rules are created by thelaws of discrete mathematics, that helps in running a computer more faster. For example –For multiplication, algorithm can be written in following way –a,b are positive integers, then binary expression for a & b are (), () respectively;
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