use of mathematics in computer science

[gravityform id="1" title="false" description="false" ajax="true"]. It is generally agreed that students in undergraduate computer science programs should have a strong basis in mathematics and attempts to recommend which mathematics courses should be required, the number of mathematics courses and when the courses should be taken have been the source of much controversy (Berztiss, 1987; Dijkstra, 1989; Gries, 1990; Ralston and Shaw, 1980; Saiedian 1992). The transmis­sion speed indicates the frequency, or the number of times per second that the signal changes its value.

However, specialised facilities that use complicated coding schemes by using several voltage levels do exist and can transmit higher frequencies. And since the signal is shown as the transmitted voltage, this is the entity whose value changes with time. Technical Limitations of Communications:. This development was largely possible because of the developments in net­working. This text explains how to use mathematical models and methods to analyze prob-lems that arise in computer science. A b baud line, however, does not transmit 6 bits per second, since a signal might convey more than 1 bit at a time.
At any stage of the problem solving and modelling stage you will require numerical and computational tools. Therefore, the time to send 8 bits is 8/6 seconds and the frequency, which is the reciprocal of this rate is, therefore, 6/8 Hz. The rapid developments in Information Technology have primarily been possible because of the intro­duction of networking which made it possible for organisations to move away from the concept of a sterile “computer centre” (that gave the impression of being highly sophisticated and thereby beyond the reach of the average employee), to putting a computer on the desk of each employee. The above equation, therefore, breaks down each periodic function into all its possible harmonics (theoretically infinite, as the symbol ∞ above the summation sign ∑indicates) and expresses the wave shape in the form of the sum of its harmonics. It can be treated as a signal, whose characteristics are periodic over time and depending on the changes of the subject it represents.

Computer science as a formal discipline is about seven decades young. Usually all frequencies transmitted up to some cut-off frequency fc are transmitted undiminished (or diminished by trivial amounts). Communication, Computer Science, Use of Mathematics. to computer science, or that a good deal of it has played no role in computer science (e.g., think of the very significant part of set theory that deals with large c ardinals ). The amplitudes can be obtained by some simple mathematical jugglery.

Obviously, this will make accurate reception extremely difficult. Computational applied mathematics consists roughly of using mathematics for allowing and improving computer computation in applied mathematics. Most concepts of maths are taught through abstract language. This issue is treated below in an “engineering way”, that is in a way that is understandable in spite of the mathematics that is, occasionally, somewhat difficult to understand.
In 1948, Claude Shannon extended this work to include channels subject to random noise. However, it is virtually impossible to get an absolutely, noiseless channel. However, in transmission, some energy is invariably lost. Computational mathematics involves mathematical research in mathematics as well as in areas of science where computing plays a central and essential role, and emphasizes algorithms, numerical methods, and symbolic computations. In other words, a mathematical model must be formulated for the analysis of data communications.

However, a discussion on Fast Fourier Trans­forms becomes somewhat of an academic exercise, since they are likely to be used very rarely in design in data communications. “Welcome to Introduction to Numerical Mathematics. It should be remembered that this frequency is the theoretical limit that defines the ultimate achievable target. At any stage of the problem solving and modelling stage you will require numerical and computational tools. This helped in making the computer a more commonplace equipment by driving out the fear of computers from the minds of most employees. We shall look at some of the issues in such an analysis. Content Guidelines 2. By giving it a mathematical basis, we can model the transmission, the subject in question, and also analyse this model. Report a Violation 11. Such a method of describing a periodic function is usually called a Fourier Series of the periodic function. However, before we come to see how Fourier series is utilised, its mathematics may be of some interest. The root-mean-square amplitude is √ (an2 + bn2). The Working Group on Integrating Mathematical Reasoning into Computer Science Curricula defines mathematical reasoning as “Applying mathematical techniques, concepts and processes, either explicitly or implicitly, in the solution of problems—in other words, mathematical modes of thought that help us to solve problems in any domain. In order to do this, some character­istic of the transmitted signal, whether it is voltage or current, has to be given a mathematical value. Mathematics is a natural complementary discipline for learning, understanding and appreciating many fundamental computer science concepts. Before uploading and sharing your knowledge on this site, please read the following pages: 1. A point of interest about these values is the fact that their squares represent the energy transmitted at that frequency. Of course, the smaller terms have been omitted.

Suppose that only the first harmonic was being transmitted. These functions are largely used and are important in discrete computations particularly in probability computations.

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In particular, if the function f(t) with a time period T is expressed mathematically then its representation, in terms of a series of harmonics, would be.

The notion of a proof plays a central role in this work. Fast Fourier Transform algorithms generally fall into 2 classes: Decimation in time or decimation in fre­quency. Disclaimer 8. The developments in networking, in turn, were possible because of the improvements in the methods of communication. The following are the principal areas of interest of the journal: Modeling using PDEs. If an arbitrary signal has been run through a low-pass filter of bandwidth H then the signal can be reconstructed exactly by taking 2H samples per second. The time required to transmit the signal—in the above case a character—depends upon both, the encoding method and the signal transmission speed. In a voice grade telephone, there is a frequency cut off introduced at about 3000 Hz. The power associated with the transmission is related to the frequency of transmission and therefore, the power loss is also naturally associated with the frequency of transmission.

On the other hand, one of the things that are covered in computer science is the study of programming languages. Terms of Service 7. for every real number w, when the independent variable t represents time in seconds and the transform variable w represents angular frequency in radians per second. Fourier analysis of this wave shape will give us some information.

After reading this article you will learn about the use of mathematics for the improvement in the methods of communication. Discrete mathematics is the background behind many computer operations (A. Purkiss 2014, slide 2) and is therefore essential in computer science. This ratio, expressed in decibels, is defined by, Shannon’s modification to Nyquist’s theorem gives the maximum data rate of any channel whose signal to noise ratio is S/N, is given by. Privacy Policy 9. … The coefficients an, bn and c can be computed to be. Plagiarism Prevention 5. In normal cases, the amount of noise present is measured by the signal to noise ratio. This will obviously change the wave shape. Top 4 Linear Methods of Setting out Curves | Surveying, Unconventional Machining Processes: AJM, EBM, LBM & PAM | Manufacturing, Material Properties: Alloying, Heat Treatment, Mechanical Working and Recrystallization, Design of Gating System | Casting | Manufacturing Science, Forming Process: Forming Operations of Materials | Manufacturing Science, Generative Manufacturing Process and its Types | Manufacturing Science. Fast Fourier Transform—sometimes referred to by its initials FFT—is a discrete Fourier Transform algorithm where, for N points required for a reasonable transform the number of computations required to obtain these N points reduces from 2N2 to 2N log2 N, where log2 N is logarithm to base 2. Fortunately, there exists a mathematical method of analysis, known as the Fourier analysis. If the function is single-valued, then the analysis becomes much easier. If the signal consists of N discrete levels, then according to Nyquist’s theorem. Similarly, we can obtain the value of bn by multiplying both sides of the above equation by cos(27pkft) and by integrating both sides of the equation, the value of c can be obtained. Doing this we get the following values for an, bn and c: If X is a complex-valued Lebesgue integrable function, then the fourier transform to the frequency domain w, is given by the function. Account Disable 12. Copyright 10. This ratio is expressed in the form of the logarithm to base 10 of the ratio S/N, where S is the power generating the signal and N that of the noise. “Welcome to Introduction to Numerical Mathematics. The behaviour of this mathematical value, when represented as a single-valued function of time, can then be analysed. Now given a bit rate of say 6, b bits are being sent per second. The 19th century French mathematician Jean-Baptiste Fourier analysed periodic functions and proved that any periodic function can be expressed as a combination of a series of sine- and cosine-based functions. For a mathematical analysis of transmission, the first necessity is to find out some means whereby, the transmitted signal can be coded and expressed in mathematical terms. If all the components in the Fourier analysis above are diminished in the same proportion, there would be no problem. I'll use examples from computer games you've probably already played. Mathematics has been an important intellectual preoccupation of man for a long time.

Huge Collection of Essays, Research Papers and Articles on Business Management shared by visitors and users like you. Sampling at higher rates is useless because the higher frequencies will have been filtered out. Beyond 38.4 kbps, by the same token, sending digital signals using single voltage levels becomes impossible, even if the transmission facility is completely noiseless. The Relationship between Mathematics and Computer Science. Therefore, the number of the highest harmonic passed through is 24000/6 (or 3000/b/8). Offered by University of London. For the sake of argument, if each signal level was used to convey three bits—possible if various voltage levels are used to convey signals—then the baud rate would be one-third of the bit rate. Mathematics is actually very important in learning the basic usage of algorithms that are utilized in an advanced form in Computer Science. For example, a 3-kHz bandwidth with a signal to noise ratio of 30 dB cannot transmit beyond about 30,000 bps irrespective of the number of harmonics transmitted or the sampling interval.

Statistics is a form of math used in computer science that uses quantified models, representations, and synopses for a provided collection of experimental data or actual studies.

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