How do you use math?

In my field of work, marine and environmental engineering, I use math everyday. I could write a book on the many ways math is involved in the environment. However, the two ways I am using it today are to design a living shoreline and to calculate the volume of dredge material.

The design of the living shoreline includes calculations to determine the anticipated wave force on the shoreline structures, the design of those structures based upon the forces and the existing soil conditions, the volume of clean fill and aggregates necessary to fill the template, the area of erosion control matting for the slopes, as well as the number of plants required to fill the area based upon their spacing requirements.

The dredging component of the project involves volumetric calculations as well as knowing how to account for "fluff", saturation, various soil types, and organic matter. These are all things that affect the end volume of dried out material that has to be loaded into the trucks and disposed of properly.

Sure, many of the calculations can be completed using various computer programs, but many are done by hand quicker and with more accuracy. Bathymetric sonars are not as reliable for soft, loose bottoms as they are for hard bottoms. Additionally, you have to constantly be running calculations and estimates to make sure that the results from the computer programs are reasonable. There is always the possibility of bad data and outliers that will drastically affect the output. You have to stay alert and understand the math to be a successful engineer.

I wish you all the best on your engineering journey!

I do use maths fairly often at work but to honest it's mostly pretty basic maths (adding, dividing, percentages and ratios) and I use a spreadsheet most of the time but it still helps to be able to sense check the answers I get from computers. I think what I use more often is the broader problem solving aspect of maths. I'm definitely not doing complex algebra as part of my job but think it probably teaches very useful transferable skills.

Math (and especially mental math) is very important when understanding/checking engineering results. When we have completed a calculation it’s essential that the numbers are correct. How do I tell if the numbers are correct or incorrect? I look at the results that are plotted on a graph or presented in a table and do some mental math to see if the numbers all agree with each other. Sometimes, the wrong units are quoted, and the number is wrong by a factor of 1000. Being able to look at results and apply some mental math to see if everything is in alignment is a special skill that is essential to catching mistakes. Of course, I don’t catch all of the mistakes that way, but being able to do math in my head catches many mistakes.

Maths teaches us a topic called “Calculus” which is Derivatives and Integration. Both, Derivatives and Integration are applied in speed, velocity, acceleration, deceleration calculations etc. So be it for research in cars, airplanes, rockets, bombs/ missile warfare, satellite launches, space missions etc. these are used to understand path, speed, velocity, acceleration, orientation, fuel efficiency, car braking and safety, optimum comfort etc. etc.

Maths gives us a perspective to appreciate that such things exist and tunes our brain to acknowledge these things; though every maths topic is not applicable to every profession that one takes up in life.

Why do we study history? We study history to understand the past so that mistakes of the past can be avoided and the success of the past can be replicated. Similarly we study Maths in Engineering. Treat it as “just one of the subjects” in Engineering and you will stop worrying about it, this is my piece of advice.

Engineers use math to solve almost all engineering problems and to model the behavior of engineered products. If you are building a bridge, the load on the bridge is distributed to the supports for the bridge, and mathematics is used to calculate those loads. We use mathematics to determine the current in a wire under a specific voltage. We calculate the lift on an airplane wing due to airflow with mathematics. This list could go on and on. And - we then put all those mathematical equations together to model the behavior of complex objects (like airplanes, and computer chips, and much much more!)

Math is foundational to everything we do in engineering on the job. It comes into play in a variety of ways. It can be used to help verify analysis run by a computer to see if the results make sense. It can be used in the post processing of data and analysis to draw additional conclusions. It is also used for calculating time spent, dollars used with respect to budget as well as calculating savings for time, weight, money, etc. Sometimes it's something as simple as what percentage of a population knows or can do something. Math is everywhere in engineering in places we expect and some we may not initially think of.

As an Assistant Manager of Pipeline Integrity, I use math daily to ensure the safety and reliability of oil and gas pipelines. Math helps me:

• Calculate corrosion rates to predict pipeline degradation.
• Analyze stress and pressure to confirm structural integrity.
• Run simulations using ANSYS Fluent to model fluid flow and identify risk zones.
• Interpret inspection data and assess risk using statistics.
• Estimate costs and timelines for repairs and maintenance.

In everyday tasks, I use percentages to track wall loss, geometry to measure pipeline bends, and unit conversions to interpret flow rates. Math is essential, it transforms data into decisions and helps us design systems that are safe, efficient, and sustainable.

Like so many things in life and learning, fundamentals build to the next level of learning and application. You first learn letters to write, then you learn words, then sentences, then paragraphs, essays, etc. Perhaps you decide to be an author of a book, or maybe an editor. Perhaps you decide to learn French or German, you already have learned letters and will build in that direction. In any case, you started with fundamentals and built on it.

Math is similar. You learn numbers, then counting, then addition, subtraction, multiplication, up to algebra, geometry. Maybe you continue to calculus and move into engineering or physics, or maybe you go into accounting or statistics. It all builds from fundamentals and then going in the direction that interests you.

In the different fields of Engineering, math can be used differently - but in all cases it's a tool. Rather than going back to the fundamentals to solve a problem, you are able to use your advanced math tools to more quickly solve a problem. Think about how much quicker it is to use multiplication to determine the area of a 26 x 10-inch piece of material, versus if you had to only use addition (answer: 26x10-inches = 260 square inches).

How do I use math? I use it everywhere, sometimes at a fundamental level, sometimes using more advanced tools from calculus to determine power or energy in a more complicated system. So, an engineer takes the math classes first to learn [advanced] fundamentals, then takes the engineering classes and learns to apply these tools for the specific topic. When I apply the math tools, I don't think of it as math, I have learned to see it as a tool.

I am a civil engineering professor, studying the transportation-related choices that people make (for example, the choice to telework or not, the choice of how to get to work or school, where to live, etc.). To do that, I design surveys, collect data on people's choices and the characteristics that I think will influence those choices, and build mathematical models that predict those choices to the best of our ability, given what we observe people to do. So I use math constantly in my research, and what it tells us about which characteristics influence choices more strongly helps inform public planning and policy related to transportation systems.

But, you don't even have to use much math in your job for it to still be useful! Jordan Ellenberg, in the preface to his excellent and highly readable (albeit audaciously titled) book, How Not to be Wrong, makes an eloquent case for this.

He uses the analogy of all the "boring, repetitive, apparently pointless drills" that professional athletes undergo. He then points out that you won't see players actually performing those drills in real games, "But you do see players using the strength, speed, insight, and flexibility they built up by doing those drills… Mathematics is pretty much the same ... Math is woven into the way we reason. And math makes you better at things... Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world... With the tools of mathematics in hand, you can understand the world in a deeper, sounder, and more meaningful way... The problems we think about every day ... are shot through with mathematics. Understanding this gives you access to insights accessible by no other means."

Depending on the type of engineering, math is often the most important tool we have for making sure buildings, machines, and products are safe to use. Think about it—so much of what’s around us has to work without breaking or hurting anyone!

Take a car, for example. Engineers use math to check that the frame is strong enough in a crash, that the engine won’t overheat or explode, and even that the bolts holding your seat in place will stay secure if there’s an accident.

In general, engineers rely on standard calculations to pick the right materials, size bolts, and design the shapes of structures so everything works the way it’s supposed to. You could say math is our superpower—the thing we use every day to keep the world running safely and smoothly.