C is for Calculus

August 14, 2015

You don’t need to be a math wiz to be an engineer. If you passed calculus with a C, congrats! You have met the bar. Now sell back those math books, because there’s a good chance you won’t be solving multivariable differential equations in your new day job. You can keep the graphing calculator if it makes you feel comfortable and you have a cool Tetris game loaded, but a ten-dollar four-function calculator is probably sufficient.

Most of that mathematics curriculum was meant to train your brain to perform logical problem solving. Oh yeah, and some stuff will be on the fundamentals of engineering exam, so don’t forget everything right away. In practice and life, you’ll still be able to apply algebra regularly. And if you are really into computational modeling, your linear algebra notes might come in handy. As for calculus, you can learn it again when your children start college prep.

If your C in calculus came at the expense of courses in your engineering discipline, leadership roles in ASCE, or participation in a project team like steel bridge or concrete canoe, you will not have regrets. As my career has progressed, I look back to my project team and ASCE leadership experience more and more as the training that allowed me to succeed in a dynamic engineering office environment.

Engineers in their natural habitat are there to solve difficult problems, by any means necessary. Those problems, by the way, are as likely to involve negotiating staff resources and budgets as a problem set. And real world problems rarely fit the structure of those carefully crafted textbook problem sets. If a colleague comes to me with an impossible solution, my best suggestion is to change the problem.

Interns often ask me what classes they should take in the coming semester. If truly interested in structural engineering, I assume they will register for the steel and concrete courses. If they’re lucky the school will offer wood and masonry as well (hello major university programs. We still use these materials.) Beyond those, I recommend courses in the architecture department, or maybe something in art history. They should develop a vision of the building design and construction industry that is far more reaching than the number crunching. To advance to the top of the profession, you need to understand the forces at play for your clients and the money-men. The most effective way to guide the design is by tapping into the needs and perspectives of the non-technical partners. Trust me, no one ever won an argument over design that included a calculus proof.

Sure, math is useful, in the way that learning to make fire prompted humans to establish civilization. But the skill set required to thrive in the 21st century is different, and complicated, and too often overlooked by our traditional education apparatus.  I believe an out-sized emphasis on classical mathematics in civil engineering education is erecting a barrier to otherwise gifted communicators and creative problem solvers that are vital to the profession.

I hope that I’ve been provocative enough in this post to prompt a spirited discussion. Please share your thoughts below.

  • Cherry Ann C. Reales

    I agree with what my dad and other engineers have to say about the “finance and human elements” which make their job more complex…. not only in the engineering line of work also in other professions… kudos for engineers!

  • About a half a cnetury ago when I was an engineering student one of my professors stated that BA students should be required to take basic engineering classes just as engineering students were required to take courses in humanities and social science. His point being that education should be well rounded.

    Although I would be hard pressed to pick up a calculus text and work through a dozen problems in an hour, that does not mean that calculus should not be a part of an engineering curriculum. It is like saying that training is not necessary to run a marathon and spelling is not necessary to write a letter.

    If anything, all engineering students should be required to pass a basic core curriculum as well as a set number of technical electives. And, because of the growing complexity in the fields of engineering, a BS plus additional classes may be required.

    Without a higher standard of education, our engineering profession may be reduced to technicians, or even machine operators who push a button to produce a widget.

    While interviewing graduating engineering students on a college campus about 30 years ago, I was shocked to met a upcoming civil engineering graduate who had not taken any transportaion engineering courses, no surveying, no soil mechnics or foundation design, no mechanics of materials, and no structructural design courses. I would hate to see that becoming the norm rather than the exception.

  • Ken Cooper, P.E., L.S., FASCE

    After 30 years since I graduated with a BSCE, I still remember how useless the calculus classes taught by the mathematicians were…theory…theory…theory…no value whatever. Shortly afterward, calculus courses for engineers were introduced at my alma mater that focused less on theory, and more on how and where to utilize calculus for problem solving. Complex problems in hydraulic design, sediment transport, structural dynamic forces, and growth and degradation rates in environmental problems all require calculus. Algebra may work for the everyday problems, but more mathematics is just the right tool at times. This said, I also wholeheartedly believe that four years of classes is not sufficient to learn what an engineer needs to learn in today’s world. Non-technical courses have become more important as engineers have moved away from being hunched over drafting tables.

    Going to college at age 31, I knew to take a course in technical (not professional or business) writing in addition to freshman English. Throughout my career I spent considerable time editing the work of engineers who were challenged by writing for other engineers, owners, regulators, or the public. Likewise, I knew to take a course in small-group communication because most work teams are 6-8 people…I didn’t need to know public speaking coming out of school because I wasn’t leading public meetings…that came later in my career. In order not to be one-dimensional, I also took courses in art and history…a person can never know too much. Consider this a plug for revamping civil engineering education and licensure to require a masters degree as the first professional degree and as the minimum strictly education requirement to sit for the FE exam.

    Having said all of the above, there is definitely a place within the large tent of civil engineering design and construction for persons without calculus and the above-mentioned masters degree. The civil engineering technologist provides a practical skill set that is valuable to address problems using mostly pre-engineered, algebra-based solutions. Calculus, when taught with a focus on how to use it for problem solving still has a place in tomorrow’s civil engineering education.

  • John P. Ruth, Jr. P.E. FASCE

    I can teach you how to communicate, but I cannot teach you math.

  • Stephen N Valero, PE

    Sorry, call me old fashioned (I proudly am), but lowering or “altering” classical mathmatics or any other technical standards to broaden the cross-section of people becoming Civil Engineers is not something this profession should support. Perhaps creative thinkers who can’t grasp math should look to other professions. There are far too many “engineers” already reliant on software for which they have no basic understanding. Removing standards related to mathmatics would only enhance this. Civil Engineers design things that hurt people if they fail. Let’s leave the “creative thinkers” who are satisfied with mediocrity (earning “C” ) to designing video games and playthings. We need to raise standards, not lower or remove them.

    • While I agree with your underlying message, your attitude is full of vinegar. “Playthings” …like the message board you are posting on, or your iphone. Mere “playthings”. Ha. maybe you should have skipped calc for some humanities courses.

  • I disagree with eliminating math requirements that are taught with reality in mind. I agree, however, that mathematics taught in an abstract manner sometimes miss the point. Having done well in calculus classes taught by engineers but poorly in math classes taught by “theoretical” mathematicians, I have seen problems get convoluted by abstract math that misses the point of engineering, as well as problems where basic economics are ignored by (even registered) engineers, sometimes with the feeble excuse of “designer preference”.

    A good solid seat of the pants ability to rapidly double check designs with common sense geometry or trig combined with knowledge of the principles of calculus can be very valuable in terms of a project’s cost effectiveness. There are situations at both ends of the spectrum – actually at all directions away from reality – where basic mathematical ability can see through the smoke and mirrors of “creative problem solving” and identify where basic economics have been ignored. Usually, even in these days of ever advancing computational paradigms, Occam’s Razor still applies.

    I will always remember the old adage that “an engineer is someone who can do with one dollar what anyone can do with ten”.

  • You are basically describing engineering technology programs, which only require calculus to the second level (skipping Calc III, IV and ODE) thus leaving room for more practical engineering courses. However this is in direct conflict with the positions of ASCE, NSPE and NCEES. The requirement for MORE questionable classes is in our future.

  • Much like Derek I am a practicing engineer working in a municipal setting. I agree with the thought process and conclusions but disagree with the “toss the baby out with the bath” argument. Many of the solutions to real world problems can be obtained through basic algebra but often times the cookbook scholarly algebra we learned to solve the problems often can have pitfalls we miss with regards to boundary conditions of problems. These conditions often become evident when you look at the problem from a “derivation” standpoint and work through the calculus to get to the algebra. I see designs presented to me often times with these or similar avoidable pitfalls from engineering firms.

    I also serve on an advisory board for undergraduate engineering at my alma mater and can tell you this approach in any engineering curriculum would lead your program to the front of the line to reapply to become ABET re-accredited. Your points are usually addressed in a well planned out holistic program that requires the inclusion of business and communication principles through design focused courses and accountable electives. These humanities of communication, pschology/sociology, Econ and finance should be required and included in an integrated curriculum to bring these points into the “math” based classes. That’s the model we followed as an undergrad and continues to be popular with the ABET accreditation folks. The real challenge then becomes continuing to require the electives without losing core classes when many state legislatures are passing hour limitations on undergraduate degrees (at public universities or risk losing funding) and requiring less than prepared students to be able to complete the degrees in a timely fashion including having to retake remedial coursework; all with hourly caps. It’s a fine balance but engineering without calculus is a cart without a horse. It may get you downhill, but it won’t carry you to the finish line in an uphill profession. Sure many engineers will never use calculus but there are many who will and do; and often don’t realize they do because it’s ingrained in their problem solving toolbox.

  • I agree that it’s the finance and human elements that makes engineering complex. The areas that would be of help to engineers are the knowledge of design and construction methods, for this will be needed in the reduction of cost. Major problems requires problem solvers with an overall knowledge in human relation and engineering. Often times the engineer has to get out of the textbooks to make a difference.

    With the advancement of computers and modelling the need for math seems irrelevant but in areas where this are not available, basic knowledge maybe necessary and a good background in math is a plus.

    For those employeed in industry and in the maintenance business sufficient knowledge in engineering and design will be necessary. Again finance is the major consideration with human relations. Math will be in the back seat but math will be useful in the material handling processes and equipments.

    The engineer needs math as a tool in problem solving and basically mastery is not for everybody due to the advancement of information technology.

  • Your comments sound good to me, too. I love and admire our profession and the people in it, but our education and preparation seem to assume a deterministic world that does not exist, and the limits of hard rationality are not appreciated enough. After all, human beings are emotional creatures first, and concepts like meaning and purpose that create a reason for them to even get out of bed don’t make much sense in a purely rational perspective. If we are going to be more than tools and help lead the world as we should, then we need to listen to people like Mr. Maschke and others that will help us look toward developing our critical thinking skills.

  • I whole-heartedly agree with this article. As a civil engineer working for a public agency, I have never used any math outside of basic algebra and maybe some trigonometry. Most engineering problems in the “real world” are fairly simple to solve. Its the finance and human elements that makes them so complex. The greatest design means nothing if you can’t afford to build it or you can’t get buy-in from stakeholders. In addition to the courses you recommend in your article, I always recommend communication or sociology classes to students as well as some basic economics courses. Understanding these areas as well as engineering, will take you to the next level as a professional.

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