Mathematics and Computers, Research Paper Example

Relationship Between Mathematics And Computer Programming

Mathematics comprises different mathematical methods like arithmetic’s and proof of mathematical concepts. Different mathematical topics contain different arithmetic implementations. The mathematical concepts in a particular problem and the proverb joining them define the method of verification or the computation criteria applied in seeking a solution to the problem. Therefore, there is no solution to a problem without knowledge of the fundamental models engaged in it and method for solving the issue.

Mathematics is also a scientific language, which is part of our day-to-day communications. Computing has become an elementary tool in mathematical applications. Computer science involves the study of algorithms, data structures, and their realization in hardware and software systems. The relationship between mathematics and computers compares to the story of Shakespeare. Visualizing his works without language is difficult. At the same time, language supplements his poems and plays as they progress.

Technicians must relate their understanding of mathematics to plan, implement, and troubleshoot networks resourcefully. Their capability to resolve real-world concerns is rooted in their approval that for every confront they come across, there is a logical, mathematical answer. It also is significant that IT technicians can be in touch efficiently with co-workers and consumers who are not as technologically perceptive as they are.

At their hub, networks connect together and allow individual computers to interrelate and work together. Making sure that each computer recognizes the “name” and locality of every other computer is the first stride in structuring a network. Network technicians embark on the task of linking them together by assigning different and unique IP addresses to every machine and network device — while considering in the option of growth in any particular division of the company (McDougall & Murnane, 2010). They then must change those provisions into a specific numeric code — an IP address — related to each machine in the network. By connecting the uniqueness of each machine to its subnet and network functions, network technician start the procedure of connecting the hardware into an efficiently integrated system (Day, 2008).

Network technicians employ their mathematical understanding to use at every stage when creating and sustaining a computer network. Technicians frequently relate algebra and statistical analysis to compute the electrical demands of network equipment and depict on their understanding of number functions to allocate unique ID codes to each computer. Their facts of mathematical averaging and statistical studies come into play in the assignment of bandwidth as they plan programming subroutines invoking multiple variables to classify where to send information from one network to another. They employ Boolean algebra for scheming and applying security features, principles, and linear algebra for budgeting, and algorithms when troubleshooting. Even though successful network technicians depend on their familiarity of mathematics, they also depend on one another. Owing to the difficulty of today’s computer systems, firms increasingly are directing their network technicians not only to be the last line of security when it comes to sustaining the network, but also to perform on the directly with customer service and employee support. Opposition from the worldwide marketplace puts ever-rising demands on firms to hire technicians who have not only the educational knowledge and know-how to do well in business but also the communication and cooperation skills to put that knowledge to use (Day, 2008).

Computers were born in a mathematical language. Representation of words, music, and images is in binary numbers. This facilitates communication between one machine to another across the internet. The binary representation is either 1’s or 0’s. Mathematics is the core element representing security of messages and financial dealings. Maths is the fundamental tool for data compression, coding and error correction during the transfer of huge files. It is also the basis for databases for directing email addresses and for exploring the World Wide Web. It also manages networks. With we can comfortably note that, mathematics is used in different areas.

In computer programming, the programmer’s duty is to develop applications that meet their requirements. Mathematical proofs on the other hand establish the accuracy of the verdicts the programmer comes up with. The process of construction is essential and mathematical design apparatus has to symbolize this.

Mathematical logic just as in computer programming involves decision-making. Venn diagrams assist in comprehending logic concepts. They are also useful in programming. For example, in programming, we use De Morgan’s laws in writing statements and Venn diagrams make these laws easy to comprehend.

Calculations are also essential in computer programming. In programming, we represent different texts in different formats. Calculations play an important role in this context. We develop graphics from geometry. In graphics, the screen resembles the coordinate plane, which contains pixels. It is important to note that the numbers of pixels in a graphic screen are numerous. On the contrary, we use several transformations in programming during the process of software development.

In programming, while using C programming language, there is a lot of mathematics involved. The graphic commands incorporated contain mathematical logic concepts. The background commands on the other hand, use hexadecimal numbers.

Computer programs are also mathematical formulas. However, unlike customary mathematical formulas, computer programs always often broaden up to thousands and sometimes to millions of code lines. The great simplicity of computers programs is compounded by the notion of undependable software making defensive programming.

A greater application of mathematics implementation is in C programming. C contains building-blocks representing the unit of the system. We jumble up the building-blocks to develop several programs within the main system. C programming comprises several commands. We can come up with different sets of programs using these commands. C programming contains C graphics. C graphics contains a diverse collection of commands. These instructions are according to the rules of logic. These are OR_PUT, AND_PUT, XOR_PUT, and NOT_PUT commands.

One other desirable relationship between c programming and mathematics is on the background formation. The background formation of C comprises tiles of 8 by 8 representing strings of 8-bit length. The hexadecimal numbers represent the binary string. The string controls the formation of the tile thus constituting the formation of the entire background.

Mathematical logic assists in making decisions. Taking an example of comparison statements, if neither n is greater than 5 nor m is less than 4, then p=p+1. To translate this statement into a programming language we could write the statement as, if n is not greater than five and m is not less than 4, then p=p+1 which we can fully interpret as if n<=5 and m>=4, then p=p+1. Here we use De Morgan’s Law, which interprets neither A nor B is same as not A and not B.

Mathematical calculations too play a part in the programming. Imagine the presence of a  data file having data, which its representation  is in a different  format. For this, we need mathematical calculations. We can also use graphic to get the actual representation and have user-friendly software. In graphic there are ordered pairs. This way representation of figures on the screen is simplified. The graphics screen corresponds to the co-ordinate plane.

There are two transformations used to control movements of graphic. These are pop and push transformations. Pop transformation represents movement of pixels towards the left while push represents the movement of pixels to the right.

In conclusion, we can say that computer programming is an application of mathematics as programming cannot do without the use of binary numbers. Our lives and livelihoods are also highly reliable on programming. The basic design concepts applied in programming and their implementation makes them an extremely demanding rational activity. Gathering these needs has raised a resolution in the way we conduct mathematics

References

Backhouse R. (2001). Mathematics and Programming: A Revolution in the Art of Effective Reasoning Inaugural Lecture

Davis P. Mathematics and the Internet MAW 97 (full version 2.1) Mathematical Sciences Department Worcester Polytechnic Institute http://www. [email protected]

Day, J. (2008). Patterns in Network Architecture: A Return to Fundamentals. Boston: Pearson Education.

McDougall, A. & Murnane, J. (2010). Researching It in Education: Theory, Practice and Future Directions. Taylor & Francis.