Depth of math in engineering disciplines

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generally, how abstract can engineering programs get? i thoroughly enjoy physics and calculus, but, i'm also taking an introductory discrete mathematics course and i find it excruciatingly dull to the point where i can hardly even concentrate on it.

what does this mean? if i go further into engineering, will i come across courses similar to discrete math more and more often?
 

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  • #2
SteamKing
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generally, how abstract can engineering programs get? i thoroughly enjoy physics and calculus, but, i'm also taking an introductory discrete mathematics course and i find it excruciatingly dull to the point where i can hardly even concentrate on it.

what does this mean? if i go further into engineering, will i come across courses similar to discrete math more and more often?
It depends on the particular engineering field you are interested in.

Most of the engineering curricula concentrate on calculus of a single variable, multivariable and vector calculus, ordinary differential equations with a little exposure to partial differential equations, and numerical analysis.

Are you taking a discrete math course because you are required to, or is it some kind of elective?
 
  • #3
jasonRF
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I would simply add linear algebra and probability theory to SteamKing's list. Different programs may differ a little on one or two of those requirements, but they will all basically be there.
 
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generally, how abstract can engineering programs get? i thoroughly enjoy physics and calculus, but, i'm also taking an introductory discrete mathematics course and i find it excruciatingly dull to the point where i can hardly even concentrate on it.

what does this mean? if i go further into engineering, will i come across courses similar to discrete math more and more often?
It can vary a lot how much math you'll call on. Some might get by with just basic ODEs and enough working knowledge of MATLAB. Others might very well require working knowledge of very advanced mathematics.

Philosophically, engineering is about the application of math and science to real-world problems. The wider your range of math and science knowledge, the more problems you'll be equipped to solve.

To answer the immediate question, discrete math is at the core of signal processing, some circuit analysis techniques are based on it, and it can also be important to software engineering and digital electronics.
 
  • #5
Discreet math is a plus, but you wont need to know abstract algebra, topology, etc, unless you get into a very specific topic. Where engineering math can get complicated is in differential equations, especially numerical methods.
 
  • #6
The intro to Diff Eq class is not representive of what you'll need to solve complex problems. I recommend take a second course in Diff Eq, numerical methods and linear algebra. FWIW I took a course in nonlinear dynamics. It wasn't what I expected, I wish I took a numerical methods class, but that maybe because the professor was substituting for a missing position.
 
  • #7
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The only individual in engineering I've encountered who was versed in convoluted mathematics was a control systems engineer, who discovered that this was mostly an academic artifact (actual industrial control systems engineers apparently don't care about differential topology or functional analysis). If you are majoring in a kind of computer engineering which is more computer science-ish you might encounter theoretical CS, which can get kinda abstract. Otherwise discrete mathematics is as abstract as it gets.
 
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When I began my work in engineering, I had discussions with my mentors about many things. Often this was over a lunch where there was a lot of hollering and laughing going on. They told me that if I was using anything more than a plain scientific calculator to get rough answers, STOP! I'm probably doing something wrong. Someone before me has probably encountered this problem and has a shortened rule of thumb that will get to the important conceptual notions.

And in 29 years of working as a Technician, Programmer, and Engineer, I have to say, they were mostly right. There were a few instances where I actually did find a use for the higher math classes I attended.

That said, the conceptual basis for what you're doing must still be learned. I may be able to work with the nulls of a Bessel Function using a calculator, but that's only because I know what a Bessel Function is. So, although you may be struggling with your math course work to understand what is going on, know that these concepts may show up in some unusual places. No, you'll probably never have to derive an equation more than half a dozen times in your career. If you are deriving equations, BE VERY VERY CAREFUL! Check your work in multiple ways, have some intuitive notions of where you expect the answers to be. If you don't know this or you can't imagine what's going on conceptually, walk away from the work.

This is not some abstract word problem for your math teacher to grade you on. Someone's life or limb may be at stake. You have an ethical duty to understand the fundamentals and the mathematics behind everything you design. You need to understand the forces, energies, and materials you use. You need to have answers for every design decision. As such, you do need to understand the concepts behind the math, even if you're not all that good at the precise derivations behind it.
 
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