- #1
Elbobo
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[I'm more concerned with how mathematics is taught in university in this topic]
I'm a junior Mechanical Engineer and have taken Differential & Integral Calculus, Multivariable Calculus, Differential Equations, and Linear Algebra. Just from these classes and talking with a variety of peers in STEM majors, it's pretty clear to me how poorly mathematics is introduced and driven into us.
At least for the non-mathematics major.
Just because we're engineers or scientists doesn't mean the mathematical theory shouldn't be expounded upon. I'm not necessarily talking about proofs (which engineers and scientists usually DO hate), but more about the consequences of some theorems, how a theorem came into conception and what it enabled, what it actually means versus being just some formula, etc.
My Linear Algebra instructor took the route of skipping formal proofs and instead tried to get us to understand the subject and theory itself rather than just solving rote, systematic problems (though we did do some of that, of course). By elaborating on concepts in class, he took our thinking to a deeper level and my interest piqued, and thus I strove to do better in the class and get a better understanding, which ultimately led to a very satisfying Math class that I haven't been able to have in forever. Just because I didn't major in Mathematics doesn't mean I don't appreciate math.
My only gripe is that he would seldom relate the many applicable concepts to engineering or the sciences, such as bases or eigenvectors.
Differential Equations was by far the worst. I learned the methods. I learned how to use integration factors, Fourier series, Laplace transforms to solve different problems. But did I learn why I did what I did? Did I ever learn what a Wronskian truly meant? Or that the the conception of the Fourier Series enabled the heat equation to be solved because it turned complicated oscillations into sines and cosines? Or what the hell "s" was in a Laplace transform? NO.
This shouldn't be optional for the curious student; it's pivotal in understanding why a certain method is used and why it's used the way it is. If you understand that, you have a much better chance of retaining that knowledge, a deeper grasping of the theory, and possibly an ability to apply it creatively to unknown territory.
I can now say I have a firm grasping of intro Linear Algebra, while I can't say the same for Differential Equations. A lot of my friends who took the same LA professor will say the same. DE was a worthless class because it consisted of crunching out God-given methods without a good theoretical understanding.
So in essence, this is an engineering student's plea to anyone who sets up Math curricula for engineers/scientists or teaches it:
TEACH US THE THEORY. Get us to appreciate it. Get us to understand it from an abstract, qualitative perspective rather than just part of the problem-solving drudgery. That doesn't necessarily mean make us do a formal mathematical proof, but rather make us see mathematics in a meaningful light.
[sorry, I may have rambled a bit. Just trying to get people to understand what is wrong with mathematics in university today.]
I'm a junior Mechanical Engineer and have taken Differential & Integral Calculus, Multivariable Calculus, Differential Equations, and Linear Algebra. Just from these classes and talking with a variety of peers in STEM majors, it's pretty clear to me how poorly mathematics is introduced and driven into us.
At least for the non-mathematics major.
Just because we're engineers or scientists doesn't mean the mathematical theory shouldn't be expounded upon. I'm not necessarily talking about proofs (which engineers and scientists usually DO hate), but more about the consequences of some theorems, how a theorem came into conception and what it enabled, what it actually means versus being just some formula, etc.
My Linear Algebra instructor took the route of skipping formal proofs and instead tried to get us to understand the subject and theory itself rather than just solving rote, systematic problems (though we did do some of that, of course). By elaborating on concepts in class, he took our thinking to a deeper level and my interest piqued, and thus I strove to do better in the class and get a better understanding, which ultimately led to a very satisfying Math class that I haven't been able to have in forever. Just because I didn't major in Mathematics doesn't mean I don't appreciate math.
My only gripe is that he would seldom relate the many applicable concepts to engineering or the sciences, such as bases or eigenvectors.
Differential Equations was by far the worst. I learned the methods. I learned how to use integration factors, Fourier series, Laplace transforms to solve different problems. But did I learn why I did what I did? Did I ever learn what a Wronskian truly meant? Or that the the conception of the Fourier Series enabled the heat equation to be solved because it turned complicated oscillations into sines and cosines? Or what the hell "s" was in a Laplace transform? NO.
This shouldn't be optional for the curious student; it's pivotal in understanding why a certain method is used and why it's used the way it is. If you understand that, you have a much better chance of retaining that knowledge, a deeper grasping of the theory, and possibly an ability to apply it creatively to unknown territory.
I can now say I have a firm grasping of intro Linear Algebra, while I can't say the same for Differential Equations. A lot of my friends who took the same LA professor will say the same. DE was a worthless class because it consisted of crunching out God-given methods without a good theoretical understanding.
So in essence, this is an engineering student's plea to anyone who sets up Math curricula for engineers/scientists or teaches it:
TEACH US THE THEORY. Get us to appreciate it. Get us to understand it from an abstract, qualitative perspective rather than just part of the problem-solving drudgery. That doesn't necessarily mean make us do a formal mathematical proof, but rather make us see mathematics in a meaningful light.
[sorry, I may have rambled a bit. Just trying to get people to understand what is wrong with mathematics in university today.]
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