Importance of algebra in engineering.

[ickby]

I work in the field of ulta high precision mechatronics, and there both are essential.

Algebra and general physical equations are the only way to understand your system and to derive a system architecture. You need know your main parameters, and how they influence the result. You need to understand how things interact (between thermal, electromechanics, system dynamics, optomechanics...) and for that require a describing set of equations that result in coupled systems. Usually you find some clever way of doing things if you look long enough on your equations. However, I think the algebraic math skills required are low, as you deliberately want simple system descriptions, the more important skill is system modeling.

After the architecture phase comes the simulation analysis. There is no way around. The real system will be much more complex than your algebraic model, with many parts you omitted. There are different reasons dependent on field. For thermal analytical models are usually bad, as there are no real isolation materials. For system dynamics you omit 90% of parts in your analytical model which influence the result, for optomechanics it's impossible to derive exact numbers for complex geometries etc. So the numeric optimisation loops are very long and require a ton of analysis. It is improved by your analytical model, as you understand the relations and can give guidance on what to change. But the real outcome will be only determined by a good set of numeric analysis and simulation. Note that this is not FEM only, often a combination of FEM and MATLAB and multibody etc., and combining those tools for complex systems comes with hard challenges in itself. So you need very good mathematicians for this step, imho more talented ones than for the algebraic part.

So for your query it IMHO depends where your position is in the general engineering loop i descried above, are you a system architect or a designer or a FEM specialist etc. All will give you vastly different answers. I'm a system architect, but try to answer whith a view on the full system design loop:

1.
-> Algebraic Analysis (System modeling): 48
-> Numeric Calculation of equations: 4 (mostly solving or optimizing your algebraic equations when one is to lazy to find a analytical solution)
-> Simulators: 48 (FEM, Matlab etc.)

2.
--> I keep names, as I usually want to see fundamental relations between all parameters, to see how I can influence the calculated value

3.
--> Analytical model for the general goal, after wards numeric optimization loop to get as close as possible to this in reality (you never really achieve it)

[jruiz]

I work in the field of ulta high precision mechatronics, and there both are essential.

Algebra and general physical equations are the only way to understand your system and to derive a system architecture. You need know your main parameters, and how they influence the result. You need to understand how things interact (between thermal, electromechanics, system dynamics, optomechanics...) and for that require a describing set of equations that result in coupled systems. Usually you find some clever way of doing things if you look long enough on your equations. However, I think the algebraic math skills required are low, as you deliberately want simple system descriptions, the more important skill is system modeling.

After the architecture phase comes the simulation analysis. There is no way around. The real system will be much more complex than your algebraic model, with many parts you omitted. There are different reasons dependent on field. For thermal analytical models are usually bad, as there are no real isolation materials. For system dynamics you omit 90% of parts in your analytical model which influence the result, for optomechanics it's impossible to derive exact numbers for complex geometries etc. So the numeric optimisation loops are very long and require a ton of analysis. It is improved by your analytical model, as you understand the relations and can give guidance on what to change. But the real outcome will be only determined by a good set of numeric analysis and simulation. Note that this is not FEM only, often a combination of FEM and MATLAB and multibody etc., and combining those tools for complex systems comes with hard challenges in itself. So you need very good mathematicians for this step, imho more talented ones than for the algebraic part.

So for your query it IMHO depends where your position is in the general engineering loop i descried above, are you a system architect or a designer or a FEM specialist etc. All will give you vastly different answers. I'm a system architect, but try to answer whith a view on the full system design loop:

1.
-> Algebraic Analysis (System modeling): 48
-> Numeric Calculation of equations: 4 (mostly solving or optimizing your algebraic equations when one is to lazy to find a analytical solution)
-> Simulators: 48 (FEM, Matlab etc.)

2.
--> I keep names, as I usually want to see fundamental relations between all parameters, to see how I can influence the calculated value

3.
--> Analytical model for the general goal, after wards numeric optimization loop to get as close as possible to this in reality (you never really achieve it)

Cool!. What a complete answer!. Thanks a lot for taking your time.
Each answer makes the picture clearer and clearer.
Thanks again.

[drmacro]

Lot's of thoughts in this thread. And all correct that algebra is important to engineering.

I'd say math (all branches) are essentially the language of science, and thus since engineering ultimately is based on science, it is essential to speak some level of most, if not all, branches.

[jruiz]

Lot's of thoughts in this thread. And all correct that algebra is important to engineering.

I'd say math (all branches) are essentially the language of science, and thus since engineering ultimately is based on science, it is essential to speak some level of most, if not all, branches.

Thanks. (Would you mind telling me what engineering do you do?)
Now I cannot pinpoint the reasons for determining why I had the impression that most engineers were inclined to numerical solutions in the first instance, giving little thought to algebraic aspects. (Please forgive my ignorance) Maybe this was because (I imagined that) one of your main tasks was to solve specific problems, where many parameters (it was my impression) had fixed values, and perhaps you would have not too many reasons to spend time on more general solutions.
Judging from the responses received so far (thanks to all who have shared their opinions / experience / points of view)
Apparently ( ) I was completely wrong in my assessment.

I hope other engineers on the forum are encouraged to give their answers.
Regards.

[ezzieyguywuf]

I had the impression that most engineers were inclined to numerical solutions in the first instance, giving little thought to algebraic aspects

Consider the following analogy: what if children were only taught how to use a calculator, but not how to actually add/subtract/multiply, etc.? Do you think they would ultimately be any good at their chosen profession?

I would argue that they would not. Over-reliance on a machine to solve your problems for you is a fallacy - the machine cannot think. Therefore, it is the machine that relies on you, not the other way around. The machine relies on you to understand the problem fully enough so that you can feed it the appropriate information for it to compute.

This applies to calculators in the same way that it applies to numerical analysis.

Just like ickby said, it takes a very educated and specialized individual to utilize a numerical analysis software properly. Anybody can be taught to run a simulation. But to fully understand all the inputs and their interactions in order to produce a quality output is an intricate art indeed.

[jruiz]

I had the impression that most engineers were inclined to numerical solutions in the first instance, giving little thought to algebraic aspects

Consider the following analogy: what if children were only taught how to use a calculator, but not how to actually add/subtract/multiply, etc.? Do you think they would ultimately be any good at their chosen profession?

I would argue that they would not. Over-reliance on a machine to solve your problems for you is a fallacy - the machine cannot think. Therefore, it is the machine that relies on you, not the other way around. The machine relies on you to understand the problem fully enough so that you can feed it the appropriate information for it to compute.

This applies to calculators in the same way that it applies to numerical analysis.

Just like ickby said, it takes a very educated and specialized individual to utilize a numerical analysis software properly. Anybody can be taught to run a simulation. But to fully understand all the inputs and their interactions in order to produce a quality output is an intricate art indeed.

I am very pleased that engineering in general is being handled in the way that you have been exposing. Many of us outside of this area are unaware of this reality.
Although, I did not want to present my opinions yet, I dare to comment that although a specific solution is sought for certain conditions, a general analysis of the problem can help in an optimization process.
Now an additional curiosity that is emerging is to want to know about the strategies you use to optimize {time, resources, efforts} to obtain tangible solutions to a specific problem.

[openBrain]

I'll second previous posts saying algebra is a (the?) prime knowledge of engineer. Your engineering skills directly links to how fluent you are with algebra (and mainly how easily you can "mentalize" how the variables are linked to their real meaning in the studied system).
As others I always keep named variables (even for known values) till the end. Because it helps visualizing the impacts. Also because engineers rarely process a single set of data.
Algebra is probably the main reason why I still have a paper and a pen on my desk (the other is to quickly draw sketches to explain/exchange with the colleagues).
I think however engineers aren't physician. This is generally 'simple' algebra, but it merges with knowing the basic rules of your engineering domain, choose the useful ones in the studied situation, and use all this smartly. There are a lot of cases where we don't need the exact result, we want just to ensure a condition is asserted.

Now an additional curiosity that is emerging is to want to know about the strategies you use to optimize {time, resources, efforts} to obtain tangible solutions to a specific problem.

There you'll touch another pillar of engineering (a less technical one). Basically from this perspective, all engineering is always risk management. Everywhere.
And especially the risk of failing. You will always analyze, assess and mitigate the risk. Depending on your product / market, the acceptable threshold will vary but not really the approach.
The base is to use a development process, that will generally design the product from the whole down to its components, then verify it the other direction. Then where risk mitigation is needed, engineers have a wide range of tools. From a theoretical systematic approach (as FMEA or QFD) to empirical method (mock-up, "look where it heats"), from former products feedback to standard verification.
That's a wide topic.

[ezzieyguywuf]

Algebra is probably the main reason why I still have a paper and a pen on my desk

I think however engineers aren't physician. This is generally 'simple' algebra

Basically from this perspective, all engineering is always risk management

If I was a hiring manager and needed an engineer I'd offer you a job right now

[jruiz]

I'll second previous posts saying algebra is a (the?) prime knowledge of engineer. Your engineering skills directly links to how fluent you are with algebra (and mainly how easily you can "mentalize" how the variables are linked to their real meaning in the studied system).
As others I always keep named variables (even for known values) till the end. Because it helps visualizing the impacts. Also because engineers rarely process a single set of data.
Algebra is probably the main reason why I still have a paper and a pen on my desk (the other is to quickly draw sketches to explain/exchange with the colleagues).
I think however engineers aren't physician. This is generally 'simple' algebra, but it merges with knowing the basic rules of your engineering domain, choose the useful ones in the studied situation, and use all this smartly. There are a lot of cases where we don't need the exact result, we want just to ensure a condition is asserted.

Now an additional curiosity that is emerging is to want to know about the strategies you use to optimize {time, resources, efforts} to obtain tangible solutions to a specific problem.

There you'll touch another pillar of engineering (a less technical one). Basically from this perspective, all engineering is always risk management. Everywhere.
And especially the risk of failing. You will always analyze, assess and mitigate the risk. Depending on your product / market, the acceptable threshold will vary but not really the approach.
The base is to use a development process, that will generally design the product from the whole down to its components, then verify it the other direction. Then where risk mitigation is needed, engineers have a wide range of tools. From a theoretical systematic approach (as FMEA or QFD) to empirical method (mock-up, "look where it heats"), from former products feedback to standard verification.
That's a wide topic.

It really is highly pleasant to read the comments around this topic here. I am imagining how beneficial it would be if these types of conversations were read by the students who are getting trained in the different areas of engineering.
But in addition, it would also be very useful for teachers who, without being engineers, would have to give some material to these students.
Thank you very much for sharing your ideas.