This blog post explores why mathematical thinking and abstraction are essential in computer science. Discover the core elements that enable logical problem-solving and efficient system design.
The Fascinating Field of Computer Science
Computer science, grounded in mathematics and logic, encompasses dozens of diverse fields including computer architecture and design, software systems, networks, and graphics. Though its history is much shorter compared to mathematics or physics, computer science has rapidly evolved as an emerging science since its inception in the United States during the 1960s. Over the past half-century, as science advanced rapidly, computer science grew at an equally swift pace. It is now intertwined with nearly every scientific field and inextricably linked to our daily lives.
Particularly in modern society, the importance of computer science is emphasized more than ever before. Computers are not merely technical devices; they have become the core tools of the information society. Consequently, not only students majoring in computer science but also many others are studying computer science knowledge and programming skills with great interest. Here, rather than introducing all fields of computer science, I will explain two major characteristics of computer science based on my own experience.
The Relationship Between Mathematics and Computer Science
First, computer science is deeply intertwined with mathematics. Computer science is a science built upon mathematics. Decades of research into computation existed within mathematics long before computers were invented, and many mathematicians made significant contributions to the inception and development of computer science.
In the early 19th century, the great British mathematician Alan Turing created the Turing machine, considered the precursor to the modern computer. The Turing machine read binary numbers composed of 0s and 1s and proposed solutions to problems accordingly. Based on this principle, the CPUs in the PCs and smartphones we use today also process binary numbers. Thus, the foundation of computers is deeply rooted in mathematical principles, and mathematical thinking skills are essential for learning computer science.
Therefore, to learn computer science well, one must be proficient in mathematics. Computer engineering students must study discrete mathematics in addition to calculus and engineering mathematics. Discrete mathematics covers fundamental concepts used in computer engineering, such as logic, graph theory, algorithms, probability theory, and linear algebra. It is the key that unlocks the door to computer science. Only with a solid foundation in these mathematical basics can one achieve outstanding results in the diverse application fields of computer engineering.
Non-majors might think computer science is simply about learning to program, but the core of programming isn’t merely mastering language syntax. Programming is achieved through logical thinking and algorithms to solve problems. Algorithms are similar to the process of solving mathematical problems, defining the sequence of actions a computer takes to solve a problem. While the syntax of a programming language can be acquired relatively quickly, designing good algorithms requires a substantial mathematical foundation. This is precisely why computer engineering students take many mathematics courses.
Abstraction: The Power to Simplify Complexity
Another key characteristic of computer science is ‘abstraction’. Abstraction refers to extracting only the core concepts or functions from complex data or systems and presenting them simply to the user. Wikipedia defines abstraction as follows: “In computer science, abstraction is the process of distilling core concepts or functions from complex data, modules, systems, etc.”
This concept may feel somewhat abstract to those encountering it for the first time. However, even without computer science knowledge, we benefit from abstraction in daily life. For example, the process of saving a PowerPoint file created at home onto a USB drive and then opening it for a presentation at school appears very simple. Yet, hidden within this lies a complex series of computer engineering processes. The file opens through multiple steps: the PowerPoint program handles graphics, the file system stores the data, and the data is transmitted over a network. Yet, these intricate processes remain invisible to the user. Through abstraction, complexity is simplified, allowing users to focus solely on opening and working with the file.
Thanks to abstraction in computer science, we can easily use programs without needing specialized knowledge of graphics or networks. Operating systems like Windows or Linux also provide abstracted interfaces, enabling software developers to create diverse applications without directly handling the underlying hardware. Thus, abstraction is a crucial concept in computer science for solving complex problems and delivering user-friendly experiences.
I recall a statement from a professor during a lecture: “Computer science is abstraction.” The professor explained that the role of a computer scientist is to package complex concepts effectively and convey them simply to users. This is precisely the appeal of computer engineering and where its real-world impact becomes tangible.
Conclusion
Computer engineering has established itself as an indispensable discipline in modern society. It encompasses diverse theories and technologies, ranging from mathematical foundations to complex abstraction processes, enabling us to enjoy increasingly convenient lives. To understand computer engineering, one must first cultivate mathematical thinking skills and, building on this, develop logical problem-solving abilities. Based on this technical knowledge, we learn how to simplify the complex processes of computer systems and present them to users. All of this is part of computer science’s compelling nature.
Therefore, computer science is not merely a technical discipline; it is a vital tool driving modern society and will continue to evolve. Countless challenges and innovations await in this journey, and exploring them is undoubtedly fascinating.
