So I’m a second year undergrad Aeronautical Engineering student, about to have my second maths exam of the semester tomorrow afternoon.
One of the oft-quoted ‘facts’ in our department (along with “We study the third hardest degree in this university”, which I find dubious) is that we’re currently learning more maths for this degree than someone taking a mathematics degree.
Surely this can’t be right. Making things fly and whatnot is mighty complicated, but someone studying maths is studying nothing else.
I understand that we probably do go into more detail in some very relevant areas (although I’m struggling to see any applications of much of it), but a mathematics student must have a much greater understanding of maths in general, right?
Anyone shine any light on this?
Already tried to ask the few maths students that I do know. It was clear that they couldn’t help me with specific questions, and then talked about some very boring tangents (!) that I ignored…
In a US curriculum, the engineering program would probably go into more depth regarding the topics that are useful for the sort of problems you deal with, but there’s most likely less breadth. I don’t really know how that compares to a UK program, though.
I find it unlikely as well. An undergraduate degree in aerospace or aeronautical engineering will involve a significant amount of differential equations, including some amount of partial differential equations, linear algebra, and possibly some statistics, numerical methods, and complexity theory, along with the basic calculus and prereqs for that which all hard science and engineering students take. A mathematics undergraduate will have more general coverage likely including more partial differential equations, finite mathematics, topology, number and set theory, complex calculus, proof theory, et cetera. An advanced degree in aerospace/aeronautical engineering might require a more extensive depth of one or two areas of mathematics than are covered in a general mathematics M.S. or M.A., but still isn’t going to have the general breadth of what a math student covers.
The most math intensive curriculum outside of pure mathematics is probably theoretical particle physics and/or cosmology, with relativity theory coming up shortly thereafter. The quantum mechanics guys tend to use a bunch of esoteric mathematics as well, but they seem to make up most of it as they go along and do a bunch of things like dividing out infinities and whatnot, so it’s kind of questionable that they reallly know what they’re on about.
Don’t get me wrong; some areas of engineering, particularly nonlinear controls, continuum mechanics and fluid dynamics, and plasma electrodynamics are very mathematically intensive, and in studying these fields to the point of getting a doctorate in them one can easily cover enough material to have the equivilent of a Ph.D. in mathematics. (And possibly the converse; my instructor for first level dynamics had an undergraduate First in mathematics.) And if you tend toward classes that are mathematically rigorous, like thermodyanamics, statistical mechanics/fluid dynamics, controls, and the like, you’ll almost certainly have covered sufficient material to rate a minor degree in maths if your school offers one. But unless you’ve gone out of your way to incorporate some fairly unnecessary math classes into your curriculum you’ll have a significant lack of breadth of maths coverage. Saying otherwise is like claiming that having read X thousands of pages of engineering textbooks rates you a degree in Russian literature.
At my university, it was possible to get a “lesser degree” (BA) in math and take about the same credit hours of courses, maybe a couple less, than a BS-ME would. However, the courses required for the math degree were more progressive and difficult - but not by much.
At my school, a Math major required as a base three semesters of Calc plus Differential Equations plus Linear Algebra. Those five classes happened to be the same as the Math requirement as my Computer Engineering degree.
In addition, a Math major required 8 upper-level Math classes. So… they had more math.
OTOH, if you did Computer Engineering and picked the right courses, you could meet the Computer Science major requirements. (At very little gain, since most programming jobs didn’t care which one you had.)
Hmm. How do you quantify mathematics? How do you measure what’s more mathematics than what? Surely the math learned by a math major isn’t a proper subset of what you have to learn.
(By calling it “maths” rather than “math,” are you suggesting that maths are discrete entities? In that case, couldn’t you just count and see whether you’re learning more or fewer maths than a maths major? )
For a degree in pure mathematics, you’d have to do a lot more with theory and proofs and abstract reasoning than I’m guessing you’re exposed to.
Err, I am not sure how to disagree with this without making myself look bad, but I am walking proof that this isn’t always the case. I have a bachelors in math, and while I did have to study differential equations, linear algebra, some pretty advanced abstract algebra, real analysis and complexity, engineers can typically run circles around me when it comes to things like differential equations, series, transforms, etc. My knowledge might be more rounded, but there is not a single area of mathematics (excluding computability, formal languages, graph theory and other things I learned through CS) I had to learn to even remotely the same depth of practical understanding as an aeronautical engineer will have of, say, tensor fields.
I mean, maybe my university was just crap, but things like topology, complex analysis, partial differential equations, vector calculus, differential geometry, proof theory are typically not fixed requirements for undergrads in any programs I know of. They are available as electives and undergrads are encouraged to take them. However, a rather large number of people pursue a bachelors in math just to move onto a masters in math education and become teachers. You won’t see these people in those classes.
I took eighteen math courses, each half a year long, during my undergraduate honours mechanical engineering degree. We did a lot of math. Many of the courses were with the math and physics honour students. But no way did we do quite as much math as they did.
Maybe I can say something. I have a BS in Aerospace Engineering (US state Univ). While there, I did some work on a 2nd major in physics, but did not finish it (all that was about 25 yr ago). More lately I’ve worked on a MS in Math, but currently stalled in that effort.
I can believe that an Aero E might take more math than a math major who is working on an educational math degree. Teaching elementary math doesn’t seem to have much use for partial differential equations. OTOH, someone looking to go on to higher math degrees would probably take more than the Engineer.
In resuming math courses after many years as an engineer, I gained a new perspective on the subject. As an engineer, math was a “means to an end” whereas taking math for the sake of math alone is very enlightening.
Reminds me of an old joke - A drunk guy is looking for his keys at night, under a streetlight. A friend comes along and asks “whereabouts did you last see your keys?” The guy says “over there” and points to a dark area many yards away. The friend says “if you thing you dropped them over there, why are you looking here in the street?”
The drunk says “the light is better here”
That’s how I thought about math majors as an engineer - it always seemed that they worked on problems that were “easier” to solve, rather than productive. But I now have a better appreciation for the depth that Math majors go into.
I assumed he was just attempting to make the title both Brit- and American-friendly. Instead, he’s just confused all of us :).
Another vote for: you may study some areas in more depth than a maths undergraduate would, but they will cover many more areas. For instance, most of real analysis and number theory isn’t going to help you fly your plane, so you won’t study them.
Anybody who would think the undergraduate mathematics degree is harder than the aeronautical engineering one would most likely not pursue a mathematics degree.
It is possible for major A to have “more hours” or “more credits” or “more courses” in an area than major B without actually studying it any deeper.
My school (Chem Eng) had less Organic Chemistry courses than the guys doing Chemistry down in Central. We had Orgo I (9 months, 5h/wk theory plus 4 months, 15h/wk lab) and Orgo II (9 months, 5h/wk theory plus 2 months, 15h/wk lab). They had Orgo I, II, III and IV: all of them were 4 months, 3h/wk theory plus 1 month 15h/wk lab. They didn’t have Synthetic Chemistry (completely Orgo, 9 months, 5h/wk theory plus 20h/wk lab).
They had more Orgo courses and since Spanish Universities moved to the credit system, more Orgo credits.
When I taught engineering mathematics, we certainly covered topics that math majors are not normally taught unless they take a specialized course in partial differential equations.
That said, I should mention that I would have found a program in aeronautical engineering much harder than a math major. For one thing I would have to study (in UK: revise), which I never did for math courses. (There were courses it would have done me good to have studied for, but I got my A’s without studying and was too dumb to understand that marks were not the point.)
Well, I don’t disagree with you, and in fact, this is the point I was (apparently not clearly) trying to make. A maths major will cover more fields of mathematics, and spend more time on pure math, than an engineer. And, at least on the (American) undergraduate level, the amount and depth of maths that an engineer will typically study will be limited at most to some basic matrix algebra, linear systems and other applications of differential equations, basic statistics and probability, vector calculus, perhaps some discrete math or numerical methods, and one or two limited areas of partial differential equations. A graduate student in engineering might get thick into tensors (especially if he’s doing work in continuum mechanics or statistical mechanics) or broader areas of partial differential equations and numerical simulation, and be far more versed in those areas than a maths major (particularly a math education major, which I don’t equate to having a degree in pure or applied mathematics), and thus run circles around even professors in math in those areas, but that’s a result of focus of studies in one particular area. I guess by “more” maths I’m thinking in terms of coverage of different areas, which an undergraduate maths major will certainly do.
I’m not sure that’s even a reasonable question. A math degree would be harder for someone who lacks an aptitude for more abstract mathematics, and an aeronautical degree would be more difficult for someone who doesn’t have a good intuition for mechanics or an interest in flight dynamics. I considered mechanical engineering and physics much easier than chemistry and metallurgy (which I always struggled with because they seemed largely arbitrary and required memorizing so many rules rather than deriving equations from first principles) but those areas of study require significantly less mathematics, and someone disinclined to bury themselves into differential equations and tensor calculus would probably disagree.
I assume that Cunctator is asking what two degrees the people at pretend’s school consider harder than Aeronautical Engineering when they say “We study the third hardest degree in this university”. And not which is harder between math and aeronautical. (Although they still could list math as one of the two that are harder, I don’t know.)
Oh, it’s not questionable at all. There’s no doubt that physicists don’t know what they’re on about when we do things like divide out infinities. The funny thing is that it works, so the mathematicians have to scramble to figure out why ;).
I received an engineering degree from U of Illinois (2 years in Aero and the transferred to Electrical to finish up) and if you followed the basic route of Aero you would have had enough math credits to get a Minor in Mathmatics… but they didn’t let us since we were all required to take it. So, if you took those classes as an Economics major, you could get a minor in Math… for us, nothing. And as I recall, it was only 4 or 5 more classes you had to take to get a true double major in Engineering and Math. But those were much more of the ‘theoretical’ type of math rather than the ‘practical’ type of math an engineer would take. That, I think, dissuaded alot of us from doing the double major. So, for that University, at that time, it was close to the original premise of the OP, but not quite.
To sum up what most people are saying: your program probably does teach far more of what most people (including those in your program) think of as “mathematics”. It teaches far less of actual mathematics. Don’t believe the hype.
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