Being an Engineer

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Main Question or Discussion Point

To be an engineer what kind of math skills do I need?
What math classes will need to take?
Do engineers need to understand mathematical proofs?
If so which ones?
Do I need to understand "proof by induction" really well?
 

Answers and Replies

  • #2
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Here is a list of the type math that I use frequently:

Calculus
Algebra
Geometry
Differential Equations both ordinary and partial.
Complex variables.

I don't really care too much about mathematical proofs, its important to understand math so you can understand where physical models come from and what they mean.

I dont even know what "proof by induction" means. :wink:

I am an aerospace engineering graduate student. My focus is on experimental work, so someone who is focused on analytics and computational methods would certainly use a lot more math than me.
 
  • #3
boneh3ad
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As an undergrad you likely won't go any farther than those mentioned by RandomGuy. Even at that, you likely won't NEED to go any farther into the math than I necessary to analyze the physics.

I you end up in grad school you will need to know the math at least well enough to understand the physics and, depending on your specific program of study, maybe deeper.

Proofs are usually not very important until grad school. Then they rear their head more but are still a pain in the ***, FWIW.
 
  • #4
As an engineering student you need calc 1,2,3, diffy q, and applied linear algebra for your undergrad. To actually work in the field? I dont know, im still a student. But if the engineers my company employees is any indication, you need some algebra. My main engineer who supports the tools i work with has a masters in management. Many of our engineers hold no actual engineering degree, they just worked their way up into a engineering position. I love holding it over their head that i know more about engineering than they do. Then they hold their paycheck over my head and I cry. I work for one of the largest semi-conductor companies in the world.
 
  • #5
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In my professional experience, most engineers don't need to know much beyond basic calculus. However, if you want to go into R&D then you will need/should/might want to know all of the above and then some. It really depends on what you're doing. Some don't use math at all, some use it all the time.

I am an aerospace engineering graduate student. My focus is on experimental work, so someone who is focused on analytics and computational methods would certainly use a lot more math than me.
Don't count on it. It depends on what you are doing. Someone who does theoretical work (CFD, EM, multi-physics) just needs to know vector calc, diffy-Q, and some linear algebra. Experimental oriented engineers (I'm in training to be one too) need to know more of statistics and probability theory, non-dimensional analysis, and similar but different knowledge of numerical methods. And if you're university experience is anything like mine, you will learn almost none of this in your classes.
 
  • #6
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Experimental oriented engineers (I'm in training to be one too) need to know more of statistics and probability theory, non-dimensional analysis, and similar but different knowledge of numerical methods. And if you're university experience is anything like mine, you will learn almost none of this in your classes.
Very true. Most of the stat and numerical methods I know I learned on my own while working in the lab.
 
  • #7
boneh3ad
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If you want to be a good experimentalist, you ought to understand the math every bit as well as a theorist. Most of the good experimentalists I know are phenomenal mathematicians as well. It isn't necessarily the same math, but it is still important. You have to know the math to design the experiment to the best of your ability.

To second what was mentioned earlier, you do tend to learn a lot of it on the fly rather than in a class. Thankfully, my university has a perturbation methods class (which owned me quite thoroughly by the way) that shed some light on that particular flavor of numerical method.
 
  • #8
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Here is my view.
You certainly need math, but don't necessary to be perfect to be a good engineer.
You should know that, "this xyz problem can be solved by doing an Integration (a math terminology, if you don't know), and should be able to write the initial integration expression, but its fine if you can't do the integration."
What i mean is, you need understand what maths can do, how things can be derived, but not necessarily remember all those confusing formulas and steps.
 
  • #9
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This is actually a very hard question to answer because it totally depends on what job you want after receiving an engineering degree....

I am an Electrical Engineer in a "Systems Engineering" position at a very large aerospace company... I rarely use any math higher than algebra. HOWEVER, it is still very important to learn the theories taught in calculus, differential equations and statistics so that if you come upon a situation where it needs calculus, for example, you can recognize that you need calculus to solve the problem. I think this is what "thecritic" was saying...

If it's been a while and you're a bit rusty on the specifics and formulas, then just head to Wikipedia or other websites as a refresher so that you can solve the problem. With calculators and MatLab, you really only need to know how to setup the problem(s) and Matlab or a calculator (such as a TI-89) will solve the problem for you... On the TI-89, you can enter in very complex formulas and it solves them, and even gives you the exact answer, not a decimal approximation (e.g. it will give you (√3)/2 as the answer to sin(2pi/3) rather than give an "approximate" answer of .8660254....)

However, other engineers I work with may use a lot of calculus in their daily activities. Like i said, it really just depends on the job you want to get (or can find)...
 
  • #10
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Take as much math as possible after considering credits/financial/student aids. It can't harm you. The better you are at math, the more comfortable you'll be at solving analytical problems and or any problem in life. Math is a tough subject that forces the brain to think hard. If you're finding yourself struggle with math, do what teachers have been trying to tell us all these years, do your homework even if it's not required. You can understand the material in class but by the time exam comes around you'll forget. If math is just boring and don't interest you, give it some time. A engineering degree is 90% math based so your going to have to be one with numbers to make it through. For me, math courses in general were very boring until Calc 3 when applications of electric flux, electric potential, curl and etc... were introduce. From calc 3, math became interesting because of the applications. Like I said earlier, math can't hurt you, it can only help and you never know, you just might be the next Isaac Newton.
 
  • #11
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I've only been an engineer for 4 years now, and I've been in design, test, and systems engineering. I also minored in math, and I think it was a good decision. Most engineering schools I know require calculus and differential equations but not all teach linear algebra or numerical methods (Both really important). I've used those two mathematics more than calculus.
 
  • #12
I would say it depends on what you are going into after graduating. If you're going into research, a solid theroretical math background is a must. If you're planning on going into industry, its less important to know advanced calculus and diff eq, but advanced algebra and trig are very important. In the industry, there is less theory and more application. Many of the concepts taught in diff eq go way beyond what you would need to know for a non-research engineering job. For non-research, physics skills are probably more important because a lot of what you do is finding stress in beams, shear stress, etc...which are known algebraic equations into which you plug the correct values. In some of my classes they even went as far as to show us how to calculate things that calculus would normally be used for, but they had it reduced to advanced algebra.
 
  • #13
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... Do I need to understand "proof by induction" really well?
Hmmm. Does this mean you do not understand it? Aside from the specific math applications discussed by others above (calc, trig...) I think it is necessary for an engineer to have a firm grasp of logic, and how to make a sensible 'argument' and how to spot shoddy reasoning. If you really can't understand why a proof by induction works, I think you should stop and get someone to explain it to you until you do understand it.

There's more to engineering than plugging values into stress formulas.
 
  • #14
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"Does this mean you do not understand it?"

I kinda do but kinda don't. I mean I could do the basics problems in my algebra book but I find them extremely annoying and pointless. I actually know a field engineer who doesn't know a lick of calculus and he constantly has other engineers with actual degrees asking him for help(even with math lol). I'm more concerned with the math because I plan to actually go to school and get a degree and from what I hear school is where most of the advanced math is actually ever used. Anyways thanks for all the help.
 

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