Engineering is a very broad subject. Thus, there has been attempts in categorizing such broad subject in terms of its application arena. For instance, electrical engineering is mainly dealing with engineering with electricity, electrical components and their interaction to create useful “signals”. Mechanical engineering, on the other hand, is mainly dealing with motion and forces of mechanical system, including solid and fluid systems, such that the mechanical power can be exchanged from one to another in a useful way. However, the field of engineering grows significantly over the past decade, making it no longer easy to draw the borders between these engineering disciplines. The simplest example that I, as a robotic engineer, can give is that of a DC motor, which is one of the most important early steps of making the robotics realization possible. A DC motor requires the circuit design in the electrical side to produce the useful signals such that the mechanical side of the system creates appropriate motion for the linkages, while satisfying the basic laws of motion. However, as I hinted a little in the last sentence, when performing engineering tasks, the system cannot violate the laws of physics. This is why math and science is the common language where engineers of different discipline can communicate effectively across the border to engage in the increasingly multi-discipline engineering challenges.
I recently listened to the lecture of the course “Fourier Series and Its Application” by Prof. Osgood from Standard University, where I like one of the comments he made very much. The general idea is that math is [also] such a broad area that you have to be able to organize in some form so that you can understand better, and apply it properly. I think this statement is strong, even though the course material itself is very advanced. I recently had a tutor session on Discrete Math, which itself is very different from traditional math. This particular subject deserves its classification since most of the other maths are dealing with continuous (and/or piecewise continuous) quantities, while Discrete Math deals with discrete quantities. Teaching the subject itself is a challenge, as it requires you to think very differently from the traditional numeric-based context. However, one thing that I think important is that, at some level, you are required to accept some of the math definitions and/or its operations before you can discover its usefulness and beauty. Some times, if you are fortunate enough, some analogy from the previously learned subjects can be drawn. For instance, in simplifying logic or Boolean expressions, a lot of the analogy of the algebraic laws, such as the distributivity and associativity, can be drawn, allowing easier “memorization”. However, once you have enough grasp of the context by the process of memorization, you can see that these seemingly strange objects eventually come together to form a complete meaningful picture. On one hand, you can then better appreciate the subject to better apply them in your work. On the other hand, if they do not come together in a good story, why would they be “organized” as a subject by the experts.
A Chinese proverb says, "getting started is always the hardest part", acceptance of something new during the initialization is always difficult. Hang in there, and you may discover something great. Even though you find no application of the subject, you would still learn something new. As for myself, I always am able to find that it may find its usefulness somehow in the future, so just keep learning something new!