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Nobody Told Me This Was a Math Class

JAG Engineering LLC

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Since a lot of young people visit this forum I thought it could be of value repeat what I learned 40 years ago.

I did learn the following from one of my professors not in the classroom but during a meeting with her as my adviser. I did not fully appreciate what she suggested though I did follow her advice and it was the correct thing for me.

I was in a city community college (CC). The four year city colleges were somewhat prestigious. The CC prepared students to transfer within the city university system and planned the curriculum to match the methods at the four year city colleges.

I had the option to take mechanics (statics and dynamics) at the CC or wait until I went to a 4 year college. At that time I thought a class was class was a class.

My advisor suggested that I take statics and dynamics at the CC if I were to go to the 4 year city college. That would better prepare me for the more theoretical approach I will find at the city college. If I planned to attend a particular private college, which the adviser had attended and taught, that I was better to take statics and dynamics at the private school. Here the subject matter was taught on a more applied and practical bases.

I now appreciate how subject matter can be presented in different ways. This is important because not all people can absorb material the same way. If you are still in the planning mode for college or an advanced degree do some research about how the material is presented.

A coworker several years ago commented about his master’s degree from a famous college in the San Francisco Bay Area. He said "regardless of the tile of the class, the professors turned it into a math class. Only one class was of any practical value to me."



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I am afraid I have to take the contrarian position here.

It seems to me that much hinges on the word "practical." What does it mean to be practical? Does it not mean useful in practice? In the engineering context, does it not mean that which is useful for solving problems? To my mind, that is what is practical, that which enables me to do my job.

With that in mind, then I have to ask, "How practical is it to be unable to correctly describe the problem at hand?" If the mathematics and the  physics involved is beyond the understanding of the engineer, is that practical? Has his education enabled him to do the job, if he did not learn the necessary physics and math?

I think that mathematics and physics represent a hill to be climbed for most engineering students. Going up the hill, we wonder why we are doing this? Will we ever get to the top? What is the point? Many never make it to the top of the hill, often because they refuse to climb because they demand an answer to "why?" However, for those who do get to the top of the hill, much of the future is all down hill because the necessary tools are at hand. If you never get to the top of the hill, it is simply an obstacle; if you reach the crest of the hill, it is a great vantage point from which to survey the entire future.

Let me cite an example from my own experience. While I was an undergraduate, I took an EE circuits course after I had finished the differential equations math course. The EE course seemed to be very heavy in the use of Laplace transforms, a topic I had never seen before but it was obviously very useful for that class of problems. The semester after the EE course, I was back in the Math department taking a course in Laplace Transforms. Now, I rarely use Laplace transforms today, but I certainly know how to do so should the need arise. There have been times when I have used Laplace transforms quite a bit. It is one more tool in my tool box, available to use as needed. To my mind, that is practical.

If an engineer does not learn a particular bit of mathematics in school, when will he learn it if it is later necessary for his work? On the job? Not too likely! The whole purpose of the college education is to get the tools to prepare one for a career. Tools are much more difficult to acquire later, but during college tools are readily available to those willing to learn them. They will not be learned, however, by those who resist learning them.

There is another side too. Some students learn various bits of mathematics, at least well enough to pass their classes, but then they refuse to use those ideas when they get on the job. They say, "That's not practical." I suggest that, if you know a way to deal with a problem mathematically, but refuse to use that knowledge when you have no other means of dealing with the problem, that is certainly not "practical" at all. That is simple foolishness. To choose to guess when you have the means at hand to deal logically with a problem is just not too bright!

I would say to college students that it is simply wrong-headed to demand that the relevance of every course topic be demonstrated while you are in class. If you trust your teachers and believe them to be knowledgeable, then you should be prepared to accept their guidance as to what you need to learn. It will make college much easier and more productive in the long run. If you will simply learn what they try to teach you, you will receive the best they have to offer. If you demand to see relevance, you are placing your immature judgement over their more mature judgement; is that really wise?

Sorry to appear disagreeable, but I see things from a different perspective.

DrD

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Let me add two more anecdotes from my own experience.

1) While I was still an undergraduate, I wanted a hi-fi sound system (this was long before the days of stereo). I saw an ad in the local paper for some hi-fi gear for sale by an individual, so I called and made an appointment to talk with him. He told me to come to his office.

As it turned out, he was the head of the Texas Highway Department, the state agency responsible for planning, building, and maintaining all the highways in Texas. He was a Civil Engineer by education, and I asked him about his work after we finished the audio equipment discussion. In particular, I asked if he used calculus very often, and he simply laughed. He said he never used calculus, and rarely used even arithmetic; someone else did all the calculations.

I thought a lot about that episode, and finally it became clear to me. Even though this man was educated as an engineer, and had engineering responsibility, he was no engineer. He was an administrator, and could just as well have had a business degree. From this I concluded that if your goal is really management, you probably don't need much math, just enough to look at a balance sheet. But there was no way this person could actually function as an engineer.

2) At one point in my working life, I found myself seriously needing to understand electrical machinery, motors and generators specifically. Now I had taken a circuits course and a field theory class in college, but that did not begin to give me the tools I needed to deal with my motor and generator problems.

I explained to my boss that I wanted to do two things:

(a) I wanted the company to pay for me to take an evening class at a local university in electrical machines. (Actually, I took two such classes concurrently at two different universities. This was really interesting because, although both classes used the same text, but the courses were utterly different)

(b) I wanted my employer to hire an EE Prof as a consultant to tutor me in electric machine theory.

The boss agreed to both, and I got in really deep into electrical machine theory. When I started working with the EE Prof, he was skeptical about my being able to understand electrical machines; after all, I was just an ME. I told him early on, go to it, use whatever math you need, and I will keep up.

A year later, when the whole effort was at an end, the EE Prof told me, "I didn't think you could do it. I was sure the math would overwhelm you. But you surprised me." That was only possible because I had taken a lot of math in college and never hesitated to use it wherever it fit. In the process, I learned quite a lot about electrical machines.

I have never, ever, found it to be a burden to know too much math, and it has often saved the day for me.

DrD

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I am a student who took 7 different Dynamics 1 exams to pass it. I had run out of puzzles, It only clicked when i could complete with reason,a scaled, pencil drawn, Acceleration Vector Diagram for Motion Relative to a Rotating Axis (i.e. including the Coriolis effect) that i realized all along I had been operating without the appreciation of the definition of a vector and the calculus involved to allow us to break the problem into small pieces, solve them and represent them Graphical form.

Mech Eng Class 

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Your disagreement does not surprise me. Aside from the professor who made the suggestion of when to take a particular class and the coworker who told me of his experience, I have discussed this with other professors over the course of 40 years, had other experiences, and read the opinions of others in academia that support my point. Even after 40 years recent articles sound like they discovered a new issue.

I think your perspective makes the case for my point that many in academia share the same perspective as you and that is the problem. I have never been in a class of yours, but some professors go out of their way to provide obstacles to learning because that is how they were taught or they are very bad teachers. I think this is the difference between those who have the title of professor and those who have the gift of teaching. These two are not the same.  As the cartoon depicts the judges narrow idea of a fair test. 

One other example, during my grad study, I took a math class that was presented over two quarters. About mid way through the sec quarter we were presented an example dealing with electrician circuits. I quote the instructor "one and a half quarters through the text and finally a practical problem." 

Forty years ago my Intro to Engineering Professor was quiet frustrated that the college did not allow engineers to teach math to engineering students. This professor provided insight into many practical things we would face as engineers. I believe he would have done a better job teaching math to the engineering students.

I think our disagreement may be our understandings the word practical. Perhaps a better but more verbose phrase would be "present the material in a manner in which the student can realize there is a top of the hill and provide some examples (in prose) of the situations in which learning the subject will help them solve problems when they enter the profession of engineering." That is a bit long winded but may better get to the point.

Some of the students you describe I know exist. I was not one of them. I hungered for understanding but without knowing there was a hill as you describe, it appeared as an an aimless wandering on a plain with grass tall above my eyes.

I strongly believe many are discouraged from any variety of professions due to the manner in which material is presented. I trampled in circles for the first few years of my career to flatten enough grass to see the hill. This is one advantage of getting some real world experience before going for an advanced degree.  

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