# 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.