Essay: Discrete Maths

Mathematical reasoning that to nowadays represent more essential to say that verbal reasoning, plays a fundamental role in the development of our life and the progress of humanity. Such area as, social science, physics, management and computer science. But in computing, we need more of a particular branch of the mathematics so called: discrete mathematics. Discrete mathematics has become popular thanks to their applications in computer science. Notations and concepts of discrete mathematics are used to study problems in algorithmic and programming. Such method helps to think logically and mathematically. Information system along with Information Technology learning require to have a high understanding of Discrete math to build and putting project to a completion. So the process or ability of mastering such unique subject require a particular set of mathematical facts, this will let you know when and how to apply them to a project. Learning proof techniques and mathematical reasoning are the building block of understanding the real purpose of discrete maths.

From the historical point of view, computing has roots dating back to the mathematics of antiquity, through two main currents: algorithms, which systematizes the notion of computation and logic that formalizes the notion of demonstration. These two aspects are already strongly present in Greek science: Archimedes and Diophantus ‘calculate’ the area under a parabolic and solution of systems of equations in integers method, while Euclid has the notion of an axiomatic system for elementary geometry, and Aristotle of speech abstract propositional logic. It is piquant to note that these two fundamental currents still constitute the basis of modern computing.

Until the 19th century great mathematicians such as Newton, Leibniz, Euler or Gauss, invented original methods of numerical and symbolic computation. These methods were intended for a human calculator, but their systematic nature already foreshadows what will serve to lay the first foundations of computer science. In parallel, at the turn of the 20th century, the axiomatic current conquers many branches of mathematics, with for corollary of the methodological questions giving rise to a new discipline – mathematical logic. This current method of discrete math will be issues in particular a general theory of computability (Post, Turing, Kleene, and Church) and several theories of the demonstration (Gentzen, Herbrand, and Heyting). These listed theories are the second basis of computing: as soon as it will be necessary to formalize the notion of defining languages of programming specific to the unambiguous expression of algorithms, algorithm to verify the consistency of languages and programs, they will prove particularly valuable.

The discrete mathematics provides a rich and varied source of problems for exploration and communication. Discrete mathematics also helped to analyse and have several types of reasoning such as logical thinking (logic used in mathematics statements and arguments), relational thinking (solving a mathematical problem and describe the relationships), thinking quantitatively (element counting), analytical thinking (algorithms) and recursive thinking.

Although discrete maths is difficult to understand, it is a major skill to have when pursuing a career in computer science or mathematics, sciences, if the concept of such maths is not learned then the ability achieving a qualification in one of those examples given will not happen. Discrete maths provide the skills one need to go into a lot of different computer course qualification for example database. Schools are teaching the basic skills of discrete maths such as algorithm, but even so the student always said it is very complicated and they can’t get their head around it and why they have to do it because it’s one of those math that they will rarely use in their daily life. So why not just stuck to the common mathematics that they will come across in the future, but they have the wrong about the concept, because most things that we do on the internet involve such type of maths, for example shopping online, browsing the web, not because we can’t see it with our naked eyes doesn’t mean it is not working in the background, with the fast growing of computer problems and data entry which most of us come across even once in our lifetime uses discrete maths. It also helps students to think mathematically and logically when they are doing a project to completion, it is important for students if they wanted to master the concept of computer science, then knowing how discrete maths works used necessary to achieve a high level of understanding of computer science.

Some of the different topics of discrete mathematics are:
-Theoretical computer science; commonly used to describe areas or areas of research focus on universal truths (axioms) in relation to the computer.
-Information theory; is the common name for the theory of Shannon information, which is a probabilistic theory to quantify the average information of a set message, which the computer coding satisfied a precise statistical
-Distributed Logic; which is given as an object the study of mathematics as a language.
-Set theory; as primitive notions together and belonging, from which it rebuilds the everyday objects of Mathematics such objects include: functions, nature, relations, real, whole, rational, complex and numbers… Because of such objects theory is considered to be a fundamental theory which Hilbert was able to say that she was a ‘paradise’ created by Cantor for mathematicians.
-Combinatorics, also known as combinatorial analysis, that studied configurations collections finite objects or combinations of finite sets, and counts. One of its major tasks is counting and the way things can be arranged in different orders, figuring out how can things be put in order to another so that its value can be determined.
-Graph theory; the algorithms developed to solve problems concerning objects of this theory has many applications in all areas related to the concept of networking (social network, computer network, telecommunications, etc.) And in many other areas (e.g. Genetics) the concept of graphs, roughly equivalent to that concept of binary relations, graph theory also can be found in Sat Nav that is the love of the world today, this method is used to calculate time distance etc., This is a massive part of discrete maths
-Probability, a law of probability describes the random behavior of a dependent phenomenon of chance. The study of random phenomena began with the games study of chance. Dice Games, balls are drawn in urns and game of heads or tails were motivated to understand and predict random experiments.
-Number theory, is a branch of mathematics that deals with the properties of integers, these are natural numbers or integers, and also contain a very wide range of open issues that it is easy to understand, even by the exercises. More generally, the fundamental study of this theory concerns a large class of problems that come naturally from the study of integers, these are numbers that we used daily for several different reasons.
-Algebra, is the branch of mathematics that focuses on the study of algebraic structures and their relationships. The algebra term opposed to elementary algebra; the latter teaches algebraic calculation, i.e. The rules for manipulating formulae and algebraic expressions. A lot of students in school today will do such calculation and it’s a good way to help them master the basic method of algebra, so that when they get into higher education they are equipped with the principle, so if they wanted to do anything in the field of computer science they know the root of the subject.
-Geometry, is a branch of mathematics that focus on the different shapes that surrounded us, which is a lot, the world is surrounded by these different shapes, learning this type of math’s not only give insights of medicine taken, but the heart of everything that is existed in the world at large. This type of math is most widely used in everyday life.
-Topology, this math deals with properties that through stretching, twisting of objects that is maintained through deformation. It also deals with the study of objects in dimension, such as three-place, plane, surface and curves. Topology can be divided into two specific different types, algebraic-topology that is the highest level and point-set topology which is the low level topology language. Networking uses this type of topology method in a LAN which is used in four different topologies principle, such as, bus-topology, ring-topology, star topology and final tree-topology, these examples are used in computer science, hence is a part of discrete math, because it deals with different calculation to maintain connections are correct and accurate
-Game Theory, otherwise known as a cartoon like method that is used in economics, it is used to differentiate and give an idea of the basic outcome of how a business competitor behaves, with this method a computer programmer can create and predicts the annual forecast. Although it the method is created by a programmer, the Information Technology Professional will be the one to introduce it within a company.
– Giant’s Chart, this module is used in project management, the main purpose is to highlight activities and displayed them, such as task or events. Gantts Chart was first used in the mid-1890s by a man called Karol Adamieka, a Polish engineer, Data in those days was entered hand manually in books, but as time progress and computer are available it is easier to use a computer to enter and amend the Data. The function of this type of discrete math is used in tracking a project schedule.
Discrete maths are a forever challenging topic, but can be very excited to work with and because of it is used in so many different fields of this that we used and enjoyed in our everyday life, it is a very useful method to get a full understanding of how it works and where it has been used. The computer as a whole represents an artificial construction which has hardly any equivalent in history. Its simple adaptation to the evolving needs of the company requires a technical activity of great magnitude. The temptation may then exist for some leaders don’t perceive the needs of technological development of the current computer. This would be sufficient hordes of technicians and engineers trained in the operation of what exists or is in gestation for the near future.
Through its relationships with technology, we illustrated the fact that the discrete mathematics is a science widely included in the tradition of other sciences. As in other areas, progress is based on a number of clever and innovative ideas, an abstraction of mathematical nature, and relative distancing with respect to the technology of the moment. It’s the method that could hatch most of the major innovations that have shaped the computer landscape. It should be noted that the fact that several branches ‘unnecessary’ long considered pure mathematics, but at least recognized as having some “depth”, found unexpected applications in computer science. An historical source which consists of very theoretical needs of understanding of formal calculations underlying mathematical analysis. It is thanks to these achievements that the public can now have the Internet, the Web, DVD, mobile phone, computers, Sat Nav etc.

Source: Essay UK -

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