Discrete mathematics is the study of mathematics limited to a set of integers. Discrete mathematics is becoming the basis for many real-world problems, especially in computer science. From our daily experience, we can say that natural languages ​​are not accurate because they can have different meanings. They are ambiguous and not suitable for coding purposes. We therefore develop a formal language called object language. In this language, we use a well-defined object followed by a definite statement about the same object. When we use mathematical expressions to refer to logical statements, we call this discrete mathematics, also commonly associated with graph theory. Discrete mathematics is gaining popularity these days due to its increasing use in computer science. Complex logic and calculations can be represented as simple statements. It is used in daily life in the following ways:Say no to plagiarism. Get a tailor-made essay on “Why violent video games should not be banned”? Get an original essay Algorithms We all write codes on the computer on a platform with built-in languages ​​like C, Python, Java, etc. , but before writing the codes itself, we prefer to write the algorithms, which involves basic logic for the code using discrete mathematics. A computer programmer uses discrete mathematics to design efficient algorithms. This design includes discrete mathematics applied to determine the number of steps an algorithm should take, which implies the speed of the algorithm. Algorithms are the rules by which a computer operates. These rules are created by the laws of discrete mathematics. Because of discrete mathematical applications in algorithms, computers today operate faster than ever. Example of algorithm: procedure multiply(a, b: positive integers) {the binary expansions of a and b are ( ) and ( ) respectively for j=0 to j=n-1 if then shifted by j places elsewhere 0 { } p =0 for j=0 to j=n-1 p = p + return p {p is the value of ab} We can clearly see the application of logic and discrete mathematics in the above algorithm. Cryptography The field of cryptography is entirely based on discrete mathematics. Cryptography is the study of how to create security structures and passwords for computers and other electronic systems. One of the most important parts of discrete mathematics is number theory, which allows cryptographers to create and decipher numeric passwords. Because of the amount of money and amount of confidential information involved, cryptographers must first have a strong background in number theory to demonstrate that they can provide secure passwords and encryption methods. Below is an example of discrete mathematics in encryption. Computer Programs Tasks performed on a computer use some form of discrete mathematics. The computer operates in a specific way based on decisions made by the user. For example: Discrete mathematics is very closely related to computer science. Theoretical computer science, the foundation of our field, is often considered a subfield of discrete mathematics. Computer science relies on logic and many, if not most, areas of discrete mathematics used in this field. For example: p(x) denotes “the number x+4 is an even integer”~p(x) denotes “the number x+4 is not an even integer” q(x,y) to represent an open instruction which contains 2 variables. With p(x) and q(x,y) as above, the universe still cares about integers only, replace x,y we get: p(5) = (5+2) is an even integer ~p (7) = (7+2) is not an even integer q(4,2) = the numbers 4,2,8 are even integers “For some x” and “For some x,y” are supposed to quantify the open statement p( x) and q(x,y) respectivelyFor some x, p(x)For some x,yq(x,y)Computer classifications Discrete mathematics describes processes that consist of a sequence of individual steps . Many ways of producing rankings use both discrete mathematics and graph theory. Specific examples include ranking the relevance of search results using Google, ranking teams for tournaments or pecking orders of chickens, and ranking sports team performance or restaurant preferences that include paradoxes apparent. Train delay Discrete mathematics is being used in a truly new way in the UK. Discrete mathematics is used to choose the most punctual route for a given train journey. The software is under development and uses discrete mathematics to calculate the most efficient route for a passenger. Each train change of a traveler at a station is like an obstacle due to possible delays, stretching out the traveler's arrival time at the next station on the route. For each part of the journey, the kernel of each station is applied successively, giving the distribution of arrival time at the final destination. How the system works: - Each station has a 60 x 60 matrix for a particular time of the day. It is 60 on one side because the maximum delay considered is one hour. On the other hand, it is 60 because the hour is divided into discrete one-minute intervals, the closest value provided by train timetables. The matrix is ​​adjusted with the probability that if you arrive at the station at minute I, you leave. at the minute j. This is based on schedule information and delay profile information obtained from website data entry. The matrices of each station are in turn applied to a column vector. The column vector contains the probability distribution of your arrival time at the next station, with each value indicating the probability of being late by 0, 1.2, 3 minutes, etc. The total column vector adds up to one. Before we go, the first value of the column vector is 1 and the rest are zeros – a delta function. This is because you haven't had the chance to be subject to delays yet. By applying the matrix of your departure station to this column vector, a new one is generated containing the probability distribution of your arrival time at the next station. The matrix for that station is then applied to the new column vector, and so on until you reach your destination. The resulting final column vector provides the distribution of your likely arrival times. This can then be compared to the final column vector for other routes and the selected optimal route. A railway control office using mathematics and graphics to analyze patterns. Plane deviation graphs are nothing but connected nodes (vertex). So all real applications related to networking, routing, finding relationship, path, etc., use graphs. Plane planning: assuming that there are ak planes and that n flights must be assigned to them. The ith flight must take place during the time interval (ai,bi). If two flights overlap, the same aircraft cannot be assigned to both flights. This problem is modeled graphically as follows. The peaks of the graph correspond to flights. Two vertices will be connected if the corresponding time intervals overlap. Therefore, the graph is an interval graph which can be colored optimally in polynomial time. Below is an example of mathematical and graphical data used to check the overlap of different flights in a unanimous flight pattern to neglect flight causalities and deviations: If you've ever used Google, you're looking at the most of flights in the world (financially) a valuable application of graph theory. At the heart of their search engine technology is an algorithm called PageRank, which uses many concepts from graph theory, including cliques and lots of connectivity information, to determine the importance of a given web page. It does this by essentially starting with a rough notion of the importance of each page, then refining its estimates repeatedly by "circulating" the importance values ​​from page to page. Relational Database Keep in mind: this is just a sample. Get a custom paper now from our expert writers.Get a Custom EssayThey play an important role in almost every organization that keeps track of their employees, customers or resources. A relational database helps to connect other information. All this is achieved with the concept of sets in discrete mathematics. Sets allow you to group and bring together information. For example: A databThe character of Charlotte and the theme of isolation in Wuthering Heights