The Importance of Mathematics in Engineering
NASA Scientists with their board of calculations, 1957
Algebra. Trigonometry. Calculus. Statistics. In the pursuit of becoming an engineer, aspirants must take a course load rich in mathematics. This is because math forms the base for engineering, shaping how engineers approach problems, design solutions, and innovate across various disciplines. From high school to college, numerous math courses train engineers in critical problem solving and analytical skills, along with uses in practical situations.
Starting in high school, prospective engineers lay the ground by taking courses like algebra II, AP Pre-calculus, AP Calculus AB and/or BC, and AP Statistics, or other equivalents to these courses. These courses provide essential problem-solving skills and a solid understanding of mathematical principles. According to the National Society of Professional Engineers, high school-level mathematics helps students develop critical thinking and analytical reasoning, which are fundamental for engineering disciplines (NSPE, 2023). To be clear, it is not required that a student take all these courses during high school, though it is highly recommended that students take as many of these courses as possible, especially Calculus courses. During university, students build upon these concepts and learn more topics by taking Calculus III, Linear Algebra, Differential Equations, and further courses in Statistics, notably Calculus-based Statistics. Of course, students may also take Calculus I, Calculus II, or an introductory statistics course if these courses weren’t taken in high school, and also may take additional math courses in college if their degree requires it. These advanced courses prepare students to model and analyze the complex systems engineers may encounter in the workplace.
To dive deeper into why math is particularly crucial for engineering, one of the main reasons is that math is essential to modeling and analyzing physical phenomena, outcome, and optimizing designs. For example, in civil engineering, calculus is used for hydraulic analysis programs, which are needed for designing storm drains (Lissner). In general, understanding calculus, the study of change, can help solve and model problems relating to motion and change, and calculus III specifically works to model these situations in a three dimensional setting. Differential equations builds on calculus, as the equations themselves are used to further model change over time. Linear algebra is important for understanding and modeling systems by using matrix operations. Finally, a strong understanding of statistics allows engineers to make informed decisions based on numerical data. Fortunately, participation in FInE helps with attaining all this mathematical knowledge. Through various mathematics events in the academic testing category, FInE offers students the opportunity to learn advanced concepts in math, allowing them to excel in their future as an engineer.
Math also has many applications in technology. In the era of artificial intelligence and machine learning, math serves as the language underpinning these innovations. Engineers strong in math and computer science can use AI for tasks such as finding the optimal shape for a mechanical part or analyzing trends in data to optimize product quality (Neural Concept). The reason a strong base in mathematics is needed here is because math is what’s used to build machine learning models. Probability is used to understand frequencies, and machine learning models often use probability models to dictate optimal decisions and predict future trends. Differential equations are used for in-silico modeling, an artificial intelligence application, to evaluate therapeutic targets and test hypotheses (Jamal). Ultimately, because mathematics is the backbone to advanced technologies used for various engineering applications, it’s essential that prospective engineers have a strong background in order to have a successful career.
Mathematics forms an integral part of engineering, guiding engineers through design, analysis, and innovation. From high school algebra to university-level calculus and beyond, mathematics equips engineers with the tools needed to face real-world challenges across a variety of subfields. Through math, engineers can model physical phenomena, leverage advanced technologies, and drive transformative innovations. As technologies advance and engineering continues to evolve, math will remain at the heart of the field, allowing engineers to solve problems and improve the world of tomorrow.
Bibliography
Eyerman, J. R. “NASA Scientists with Their Board of Calculations, 1957.” Rare Historical Photos, LIFE Magazine, 24 Nov. 2021, rarehistoricalphotos.com/nasa-scientists-board-calculations-1957/. Accessed 08 July 2024.
Lissner, Eric. “The Use of Calculus in Engineering.” Sciencing, 02 Mar. 2019, sciencing.com/info-8785081-use-calculus-engineering.html. Accessed 08 July 2024.
“What Is Artificial Intelligence Engineering?” Neural Concept, www.neuralconcept.com/post/what-is-artificial-intelligence-engineering#:~:text=As%20an%20AI%20engineer%20or,the%20slightest%20possible%20mechanical%20stress. Accessed 08 July 2024.
Jamal, Madhia. “Math for AI: A Guide.” Built In, 19 Jan. 2024, builtin.com/articles/math-for-ai#:~:text=Math%20helps%20AI%20scientists%20solve,known%20for%20hundreds%20of%20years. Accessed 08 July 2024.
