Discrete mathematics is the study of mathematics limited to a set of integers. Discrete mathematics is becoming the basis of many real-world problems, particularly in computer science. From our daily experience, we can say that natural languages ​​are not accurate as they can have different meanings. They are ambiguous and not suitable for coding purposes. Therefore we 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 denote logical statements, we call it Discrete Mathematics, also commonly combined with Graph Theory. Discrete mathematics is gaining popularity these days due to its increasing use in computing. Complex logic and calculations can be represented in the form of 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 Shouldn't Be Banned"? Get Original EssayAlgorithms We all write codes on computer on some platforms with built-in languages ​​like C, Python, Java etc. but before writing the same, we prefer to write the algorithms, which involve the basic logic of the code using discrete mathematics. A computer programmer uses discrete mathematics to design efficient algorithms. This project includes discrete mathematics applied to determine the number of steps an algorithm must complete, which implies the speed of the algorithm. Algorithms are the rules by which a computer works. These rules are created through the laws of discrete mathematics. Due to discrete mathematical applications in algorithms, computers today run 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 a j=n-1 if then moved j places otherwise 0 { } p =0 for j =0 until 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 based entirely 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 crack numeric passwords. Due to the amount of money and sensitive information involved, cryptographers must first have a solid understanding of number theory to demonstrate that they can provide secure passwords and encryption methods. Below is an example of discrete mathematics in cryptography. Computer Programs Tasks performed on the computer use one or another form of discrete mathematics. The computer works in a specific way depending on the decisions made by the user. For example: discrete mathematics is closely connected with computer science. Theoretical computer science, the foundation of our field, is often considered a subfield of discrete mathematics. Computer science is based on logic and many, if not most, areas of discrete mathematics used in the 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 that contains 2 variables. With p(x) and q(x,y) as above, the universe continues to deal only with integers, substituting 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 It is saidthat “For some x” and “For some x,y” quantify the open instruction p( x) and q(x,y) respectivelyFor some x, p(x)For some x,yq(x,y)Computer classifications The Discrete mathematics describes processes that consist of a sequence of individual steps. Many ways to produce rankings use both discrete mathematics and graph theory. Specific examples include ranking the relevance of search results using Google, ranking teams for tournaments or chicken hierarchies, and ranking sports team performances or restaurant preferences that include apparent paradoxes. The discrete mathematics of rail delays 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 trip. The software is under development and uses discrete mathematics to calculate the most time-efficient route for a passenger. Each change of train of a passenger at the station is like an obstacle due to possible delays, it postpones the passenger's arrival time at the next station on the route. For each part of the journey, the kernel for each station is applied in succession, providing the distribution of the arrival time at the final destination. System Operation:- Each station has a 60 x 60 matrix for a particular time of the day. There are 60 on the one hand 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. Entered into the matrix is ​​the probability that if you arrive at the station at minute I, you leave at minute j. This is based on timetable information and delay profile information obtained from website data. The matrices for each station are in turn applied to a column vector. The column vector contains the probability distribution of the arrival time at the next station with each value showing the probability of being late by 0, 1,2, 3 minutes, etc. The sum of the column vector is one. Before we go, the first value in the column vector is 1 and the rest are zeros: a delta function. This is because you haven't had the chance to experience 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 the destination is reached. The resulting final column vector provides the distribution of probable arrival times. This can then be compared to the final column vector for other routes and to the selected optimal route. A railway control office that uses mathematics and graphs to analyze patterns. Plane deviation graphs are nothing more than connected nodes (vertex). Therefore, any real-life application related to networking, routing, relationship finding, routing etc. use graphs. Aircraft Scheduling: Assuming there are k aircraft and n flights need to be assigned. The ith flight should occur during the time interval (ai, bi). If two flights overlap, it is not possible to assign the same aircraft to both flights. This problem is modeled as a graph as follows. The vertices of the graph correspond to the flights. Two vertices will be connected if the corresponding time intervals overlap. Therefore, the graph is an interval graph that can be optimally colored in polynomial time. Below is an example of the mathematical and graphical data used to verify the overlap of various flights in a unanimous flight pattern so as toNeglecting Causality and Flight Deviation: If you've ever used Google, you're looking at the world's most (financially) valuable application of graph theory. At the heart of their search engine technology is an algorithm called PageRank, which uses numerous concepts from graph theory – including cliques and lots of connectivity information – to determine how important a particular web page is. It does this by, essentially, starting with a rough notion of each page's importance and then repeatedly refining its estimates by "sliding" importance values ​​from one page to the next. Relational Database Keep in mind: This is just an example. Get a custom paper now from our expert writers. Get a Custom Essay They play an important role in almost every organization that keeps track of their employees, customers, or resources. A relational database helps to merge different information. This is all done with the concept of sets in discrete mathematics. Sets allow you to group and put information together. For example: A databCharlotte's character and the theme of isolation in Wuthering Heights