• 01
  Feb 2023

• The role of mathematics in computer science

  
  

  Aaryan Baadkar | International School

I. INTRODUCTION

Since its inception students all over the world did not enjoy math, however, after watching the news about a teenager who made millions of dollars by selling his website students suddenly want to pursue computer science. However, we have all asked ourselves this question if it’s that simple? Unfortunately, it’s not and if you aren’t a fan of mathematics, life just got a little bit worse for you. To tell you the truth mathematics and computer science and quite closely connected. The debate about whether mathematics plays a vital role in computer science still rages on. According to the University of Sheffield, “Computer Science is built on Math” [1]. I guess we need to dive deeper to figure out why.

II. WHY MATHEMATICS?

Mathematics is a discipline that “develops the ability to reason precisely and analytically about formally defined abstract structures” [2]. An example can be the Eiffel Tower and how much it relies on its foundation, if it did not have a strong solid foundation it would collapse. Similarly, math teaches us how to work with algorithms, accurately modeling real-world solutions, and can help develop the logic required to understand computer science, enhance critical thinking and reasoning, analytical skills for problem-solving, and much more, which is crucial and the basis of computer science. Therefore, multiple universities integrate mathematics into their computer science program for example at Stanford University the undergraduate curriculum requires two CS math classes: Mathematical Foundations of Computing (CS103) and Introduction to Probability for Computer Scientists (CS109) [3]. Math also teaches students to reevaluate their method and if they are wrong to go through their steps and figure out where have they made the mistake.

III. WHAT BRANCHES OF MATHEMATICS ARE IMPORTANT FOR COMPUTER SCIENCE?

Discrete mathematics, Algebra, Statistics, Calculus, etc. Are vital to study computer science and make understanding how the computer/application works much easier. Let’s go more in-depth and state how a few of these branches are important and their roles in computer science.

a) Discrete mathematics: Involves several concepts, including Logic, Graph Theory, Number Theory, Recurrences, etc. It provides an important foundation for all areas of computer science. The methods help develop problem-solving skills that will be useful while making a software. “Problem-solving skills: Programmers check the code for errors and fix any they find” [4]. Number Theory plays a crucial role in coding, hash functions, random number generations, etc. It is useful in computer security, computer architecture, machine learning, algorithms, etc.

b) Algebra: This includes your standard matrices, polynomials, quadratic equations, linear equations, rational expressions, radicals, ratios, proportions, etc. Linear transformations have multiple applications in graphics. Boolean algebra is used to evaluate code paths, processor optimization, etc. Matrices are very important in computer science for example matrix multiplication is very useful in graphics as it can convert geometric data into different coordinating systems. Graph matrices are especially useful in software engineering as it helps in the understanding of software testing concepts and its theory. In many time-sensitive engineering applications, multiplying matrices can give quick approximations of more complicated calculations [5].

c) Statistics: It is widely used in artificial intelligence, speech recognition, image analysis, data mining, etc. It can also be used to develop models that can analyze data and make predictions on it. Wherever there are uncertain parameters or behavior statistical, methods are used to solve the problem. The use of statistics can drastically increase the efficiency of an algorithm. Time and methods engineering uses statistics to study repetitive operations in manufacturing in order to set standards and find optimum manufacturing procedures [6]. Permutation is used for analyzing and sorting algorithms. Probability helps us predict performance and helps design and analyze randomized algorithms. One field that relies heavily on Statistics is Data Science.

d) Calculus: It is widely used in simulations, problem-solving applications, graphics, etc. It is very prominent in topics such as machine learning, Image processing, data mining, signal processing, computation statistics, etc. In graphics, calculus is used to determine how a 3d model will change when it is subjected to a change in the environment. Everything you see in a video game is likely driven by different models from calculus it covers everything from all the physics to the light bouncing from various surfaces. In machine learning, calculus plays a very important role in understanding algorithms. It is practically impossible to do machine learning without calculus.

IV. CONCLUSION

This paper has analyzed the importance of mathematics in computer science and has shown where the different branches of mathematics are used in computer science. So, what did we learn from this? Well, math is very prominent in computer science and helps strengthen the foundation which is always beneficial. It is better to start loving math (if you don’t already) because if you want to study computer science it isn’t going away any time soon.

BIBLIOGRAPHY

[1]https://www.sheffield.ac.uk/dcs/blog/maths-computer-science#:~:text=Computer%20Science%20is%20built%20on%20maths

[2] Devlin, K. (2003). Why Universities Require Computer Science Students to take Math.Communications of the ACM,46(9), 37-39.

[3]https://cs.stanford.edu/degrees/ug/Requirements.shtml#:~:text=The%20undergradute%20curriculum%20requires%20two%20CS%20math%20classes%3A%20Mathematical%20Foundations%20of%20Computing%20(CS103)%20and%20Introduction%20to%20Probability%20for%20Computer%20Scientists%20(CS109)

[4]https://www.bls.gov/ooh/computer-and-information-technology/computer-programmers.htm#tab-4:~:text=Problem%2Dsolving%20skills.%20Programmers%20check%20the%20code%20for%20errors%20and%20fix%20any%20they%20find.

[5]https://news.mit.edu/2013/explained-matrices-1206#:~:text=In%20many%20time%2Dsensitive%20engineering%20applications%2C%20multiplying%20matrices%20can%20give%20quick%20but%20good%20approximations%20of%20much%20more%20complicated%20calculations

[6] International Journal of Computer Applications Technology and Research Volume 4–Issue 12, 952 - 955, 2015, ISSN:2319–8656

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