Applications of Discrete Mathematics

Information is made from Data that is numerical which is changed and used to make it seem sense. For an example train timetable, the number of trains and how much it weights.

Deductive reasoning entails the argument in which the hypothesis is true and, therefore, the conclusion remains to be true. This argument follows a correct logical form whereby if the hypothesis is true then its conclusion is valid and if the premises are untrue then the conclusion is invalid. Louis Pojman explicates that deductive reasoning preserves the truth, and the arguments are of soundness while;

Information security is the protection of information against accidental or malicious disclosure, modification or destruction. Information is an important, valuable asset of IDI which must be managed with care. All information has a value to IDI. However, not all of this information has an equal value or requires the same level

- Information: is a knowledge which can be transferred or received concerning a particular fact or situation. And is a sequence of symbols that can be explained as a message. Information can be recorded as signs, or transmitted as signals.

Mathematics is a logical and precise subject. Without precision in math everything is imprecise. A modest inaccuracy can produce a catastrophe. For example, if a doctor fails to calculate the correct amount of medicine to give a patient, it could result in a serious complication, such as death. A further example is the logic and precision it takes to construct a building. If there is one minor miscalculation the whole building could collapse, causing mass destruction.

Looking up the definition of mathematics you will get the simple definition, “the abstract science of number, quantity, and space”. I believe the definition of mathematics to be more than this. I believe mathematics is study of science using basic rules or truths, such as truth 1 + 1 = 2, applying these rules in different ways, since 1 + 1 = 2, we can expand on that and say 1 x 2 = 2, and then extrapolating upon those rules. We then can use these rules to apply and make models to represent the world we live in. Some of these models are used in engineering and physics where using these rules of mathematics to then design structures such as bridges, sky-scrapers, and roads.

“Logical-Mathematical Intelligence is quantifying things and making hypotheses and proving them.” It connects to “from Blue Nines and Red Words” By: Daniel Tammet. Daniel Tammet eats exactly 45 grams of porridge for breakfast. He weighs it to see

Information is data that has been processed so that it has meaning and value to a recipient,

Information is data which is accurate and timely specific and organized for a purpose presented within a context that gives it meaning and relevance. Information can lead to an increase in understanding and decrease in uncertainty.

Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions. This latter view encompasses mathematical or symbolic logic, the science of using symbols to provide an exact theory of logical deduction and inference based on

Biology is the study of living organisms, chemistry is the study of chemicals, physics is the study of the universe and its forces, so what is maths the study off? Well the online Oxford Dictionary states that maths is “the abstract science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering ( applied mathematics)”. A more scientifical website states that maths is “the science that deals with the logic of shape, quantity and arrangement”.

However, according to Shannon himself, what really launched him into the theorization of information was Ralph Hartley’s paper Transmission of Information. This paper developed “a measure of information that could in principle be used for discrete or continuous signals.” Hartley’s publication also proved that a channel’s bandwidth defines how much information can be sent through it. Since a channel’s bandwidth was limited and since continuous signals could be broken down in small steps before being sent through the channel, Hartley concluded that if the steps were small enough, the approximated signal would be not only close but identical to the original signal. Finally, Hartley realized that information could be the “resolving of uncertainty.” He developed a mathematical formula according to this concept to quantify the amount of information in a message but unfortunately, this formula was not complex enough and could not be applied to cases in which the constituents of a message did not have all the same chances of being selected. Indeed, “in written English for instance, some letters are used more frequently than others.” Hartley’s formula would not work when trying to encode sentences for example because he couldn’t model the fact that the letter E had more chances to be selected than any other.

Likewise, in the set of ail Real numbers RU, 1.1, 1.11, 1.111,...} there are an infinite amount of members as weli. This sets cardinality is represented by t’ or, as Cantor proved in 1874, N1. it there are an infinite amount of Real values between each of the infinite amount of

Mathematics is a type of reasoning. Thinking mathematically includes thinking in a rational way, developing and checking conjectures, understanding things, and forming and validating judgments, reasoning, and conclusions. We show mathematical habits when we acknowledge and explain patterns, build physical and theoretical models of sensations, develop sign systems to assist us stand for, control, and review concepts, and create treatments to address issues (Battista, 1999).

The purpose of this report is to give information on the subject known as Logical reasoning and its use in Computer Science and computers in general. A historical background behind logic and Logical reasoning is firstly given, followed by an overview of the modern subject and the types it’s divided into. The types are then explained. The overlap between the field of logic and that of computer science is also given an explanation. The report ends with a brief overview on the subject and its tie to computer science and computing.