Mathematics in Computer Science

As much as Computer Science may sound an interesting course, there is one thing that most people don’t like it: the close relationship between computer science and mathematics.


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Many people associates mathematics with topics such as arithmetic, geometry, trigonometry, algebra and calculus when in fact it is more far reaching than that. It encompasses the whole philosophy of dealing not just with numbers but with logic and the validity of logical propositions. We have all heard, computer described as number crunchers or glorified calculators, but the mathematical basis for computers is far more fundamental than defining, say what the product of two numbers or the area under a curve might be. Indeed mathematics is about as fundamental to computing as you can get. It was Turling’s 1938 paper “on computable number” that laid the foundation of modern-day computers. However, besides the formal description of logic and calculations involved in the engineering design of computer-which are of course significant, it is not sure that mathematics now plays a significant role in either their design or their use. Although mathematical principles are at the core of computer design, computer designers do not need to know them any more than they need to know how calculus is being used to determine the trajectory of a spacecraft in a computer game or that circuit designer need to understand the quantum theory behind semiconductors. However to reverse the proposition, there can be no doubt that computing is a fundamental intellectual tools of mathematics and is a key component in problem solving. Whether the task is simulating weather or flying an aircraft, the model that are constructed by a computer are above all mathematical. They can come in the form of formulae describing physical behavior, statistical methods evaluating probabilities to truth tables governing logical process. What they all have in common is that they can be represented digitally. And if you can represent them digitally, you can compute them.

Computer science is quite an interesting course. Many people study it with the hope of being the next big computer programmer; become a hacker, system administrator among other lucrative careers. As much as it may sound an interesting course, there is one thing that most people don’t like it: the close relationship between computer science and mathematics.

For years, the importance of mathematics in computer science has been quite controversial topic. Some people believe that mathematics is important for computer science students. Other sees it as a subject that adds only little value in computer science. So, which side is saying the truth? Most concepts of maths are taught through abstract language. On the other hand one of the things that are covered in computer science is the study of programming languages. Most of these languages are also abstract in nature. They are characterized by syntax, well-defined process, symbols, single words and even visuals. Given the abstract nature of maths, you will have a smooth sailing where learning programming languages. Mathematics will impart a student with the art of reading, understanding and analyzing a problem before coming up with a solution. All these skills are vital when it comes to programming and computer science in general.

An algorithm is a commonly used term in the field of computer science and technology in general. It provides a basis under which any program or application should be created and implemented. Although most people encounter this term for the first time in a computer science class, the truth of the matter is they introduced to it in a math class. Do you know that a simple equation such as 6+4=10 is an algorithm? From such simple equations, students are then introduced to complex algorithm in computer science. Coding is not a one-way process. You have to keep coming back to inspect what you have written and verified whether it is correct. This is because you are bound to make one or several mistakes when coding. In the field of mathematics, students are usually forced to analyze their work. The answers that you might have given are not always accurate. You need to come back and inspect the formula and the figures that you have used. You will fix the mistake or errors before reaching out to your final answer. In other words, math prepares students for the task of identifying and fixing bugs. Even if there are tools that can do this job automatically, students will still have the zeal of doing this job effortlessly. Apart from these skills, you will also encounter lots of math in computer science. Here you will be required to use mathematics knowledge to solve real-life problems through a computer. Woe unto you if you never took your math class seriously. For instance, there are lots of mathematical equations and formulas that are used to design a program for controlling a self-driven car. It will be very difficult if not impossible to write such programs if you are completely green in the field of mathematics. It is not secrete that discrete mathematics forms a strong foundation for the study of programming   and computer science. It will equip you with deep knowledge about algorithms, computability and complexity which you will use in programming. Boolean algebra – a subject in discrete mathematics is applied in creating control functions when programming. Once you master these mathematical theories, you will have an easy time putting them into practice in computer science.

Often, most schools and colleges embed mathematics into computer science. However they rarely inform students why they are doing so. They just do this as a basic routine. This makes most students feel short-changed. It is crystal clear that the theories of mathematics are practical. They can be applied to implement various core aspects of computer science. Students are starting to realize that advances in computer science are central to achieving many of our national priorities- in energy, education, health care, national and homeland security, scientific discovery and open government. As more fields become information fields, facility with what we call “Computational thinking” is necessary for success in just about any endeavor. So, if you are planning to study computer science, maybe it is high time you build some passion for mathematics.

 

First Published:Feb. 22, 2021, 10:32 a.m.

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