The convergence of multiple disciplines into the coherent and well-structured whole that is a masters degree is a beautiful, intricate thing. During their college years, bachelor’s degree holders might have found studying fields apart from their majors a convenient, albeit nonessential practice. When they choose to pursue a master’s degree, however, they’ll find the nonchalant amusement absent.
Take students attending a graduate program in computer science, for example. The course spans a depth of computer engineering subjects but also takes its students into advanced math, physics, and problem solving.
Math: The Language of Computers
Computers communicate in 1s and 0s, and while the combinations of the binary or hexadecimal codes, for instance, don’t really follow the basic rules of math, the concepts derived from advanced math are the foundations of computer hardware and software.
From logic gates to recurring code, math is as inseparable to computer engineering as it is to science. From linear algebra that is applied to many steps of an engineering process to vector calculus which bridges the gap between the physical problem and the electronic solution that an engineer creates, the concepts of math are wed to computer engineering.
How about a more concrete example of advanced math in computer engineering? Take computer symbol processing. An engineer needs mathematical axioms to compute symbolically using natural numbers. If a computer engineer needed to simulate a modern-day bridge that would span a gigantic gap between land masses, does he not need to know the mathematical values that the natural forces would apply to this simulated bridge, and thereby design it to withstand said forces? Does he not need to know which calculation methods and rules to apply before they start dishing out bricks and mortar?
Where Do the Laws of Physics Apply in Computer Engineering?
Perhaps the more telling question is: Where doesn’t it? With the very tinkering of electronics, computer engineers are playing with physics. Vector analysis used to analyze circuit components, for instance, already requires the engineer to have a good grasp of the electrical demands of said components.
For a more concrete example: if an engineer were to create an algorithm using a specific language to compute for such physical values as speed, ephemeris, and almanac all while maintaining a zero margin of error, then he would need a very good grasp of the laws and dynamics of physics. Everything a computer engineer designs is grounded by the laws of physics — the more he knows about them, the more he can apply his expertise to the physical world.
In our previous example about the bridge, the mathematical values the computer engineer needs will come from the physical elements of the problem. The physical laws that bound the land masses, the gap, and the bridge need to be simulated with utmost care and error-free accuracy.
And Then, It’s Problem Solved
Problem solving, one could argue, is what computer engineering is all about most of the time. Given a situation and the chance to create something from computers that resolves said situation is what computer engineers do.
In our problem above — the bridge between land masses — the problem is before the bridge can be constructed, its design needs to be planned out to ensure that when it’s built, it doesn’t crumble right away. The problem in itself has several other problems: collecting data, simulating said data and its physical laws into a digital realm, minimizing errors, testing, the actual designing, implementation, and everything in between.
With a good working knowledge of advanced math concepts and the laws of physics, a master of computer engineering is indeed a master problem solver.
You can bet the garden variety extra courses of a bachelors degree would be easier on your gray matter, but the advanced courses of a masters degree is what actually makes you a master.