A Mathematician in Systems Engineering

By: Bryan Petrak, PhD, Systems Engineer at Boeing

My first experience with systems engineering came when I was in graduate school. I was working on some code for my research and I was struggling. There was another graduate student who stopped by periodically to ask questions about a course he was taking. While making small talk, he found out that I was struggling with my code and told me he was going to help. I had been skeptical because what I was coding was outside his knowledge base. After about an hour of working with me, he had helped lay out my code and get it working. The most amazing part to me was that I spent almost no time explaining my research to him. I thought it was magic. He explained to me that he worked as a systems engineer, and his job was to solve problems that way. When I finished my PhD, I got a job as a systems engineer and I have been doing that for the past nine years. 

Systems engineering is a discipline that was born out of designing complicated systems. As things get larger and more complicated (think cars, planes, or space shuttles), it becomes impossible for one person to know how every part of the system works. So, the system gets broken down into subsystems that are more manageable. Systems engineers are the ones responsible for ensuring that all the pieces come together. Additionally, the subsystems may need to be subdivided further. This creates the need for multiple levels of system engineers. It also makes the definition of who is a systems engineer rather fluid. In my career, I have been labeled an Electrical Engineer, a Software Engineer, and a Systems Engineer; however, my work in all these roles has been very similar.

The amount of mathematics that a systems engineer does depends on the job. Given my background in mathematics, I have gravitated towards subsystems with a mathematical bias. However, how much mathematics is done depends on how one approaches the tasks. The idea of breaking up a problem into smaller parts is very familiar to anyone who has written a proof with a phrase like “consider the following cases”. The parallels only begin there. A well-defined problem in mathematics is based on a set of assumptions with a clear goal statement. In systems engineering, there are requirements stating what must happen and under what conditions.  Systems engineers set those requirements and aid in their implementation. The main difference is that in a proof, the assumptions and completion criteria are defined with standard definitions. In systems engineering, the boundaries that define the beginning and the end of a task tend to be gray areas. The systems engineer collaborates with other stakeholders to make those boundaries as clear as possible. Once the boundaries are defined, the process is very similar to proving a theorem. Analysis is done to determine if current algorithms can be used to handle the new requirements. New algorithms are developed where the existing algorithms are insufficient. The end product may not be mathematical, but the logic involved makes the process very familiar to those with experience in solving mathematical problems.

It may not be easy to pinpoint how much mathematics a systems engineer does, but it is simple to explain why a mathematician should consider systems engineering as a career.  Anyone who studies mathematics has heard that they can do anything with mathematics.  It is easy to find mathematicians who have thrived in every career field. The first step to a successful career in a field is to step into that field. That step can be bigger than it sounds. Breaking into an area usually requires education or experience.  Systems engineers are intended to be transferable. This provides an opportunity to learn about different areas while gaining experience as a systems engineer. It should be given serious consideration by anybody interested in a career in industry.

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