Slowpoke's comment really resonated with me, so perhaps I can provide some concrete examples.
8 years ago, I graduated from my Software Engineering degree at Swinburne University in Australia. As part of my degree I had to sit through 3 years of engineering maths.
In our first programming tutorial we were taught how to write a program to display “Hello world”. It was immediately obvious to me why we might want to write a program that displays messages on the screen and what sort of problems this would be useful for solving.
In our first maths tutorial we were taught how to add, subtract and multiply complex numbers. To this day, I still do not understand why I would need to do that. Where do my complex numbers come from? What do they represent? When I add them together, what does the answer mean? The only problems that I can apply my maths education to, look exactly like those on the tests: what is (-3.5 + 2i) + (12 + 5i) ?
It is possible that in my job I am besieged daily with problems that I could use complex numbers to solve. But if so, I am totally incapable of recognizing them!
Fourier series were a particularly egregious example – the subject started, when the lecturer came in and wrote up 3 boards of dense maths, and said something along the lines of “… and this is the formal derivation of a fourier series!” It was as if somebody had tried to teach programming by explaining the algorithm a complier uses for translating source code into machine code. Then expecting the students to just figure out how to write actual useful programs, all by themselves! I believe this is what Slowpoke was talking about when he said: “The problem, as I still see it, is that nobody fucking tells you why. They throw it at you and expect you to deal with it. No further explanation - "It's math, we ain't gotta explain shit."
The way we were taught fourier series particularly hurt. Years later, I found out by myself, that the things are actually incredibly useful. As it turns out, that there are these things called fast fourier transforms, that programs use all the damn time, to do fantastic stuff!
So, to give a very concrete example of how maths education in universities could be improved: If only the first lecture on fourier series had instead explained what they are used for, and why they were so important that we were going to spend 5 weeks on them. Then perhaps I would have had a much better understanding of what they are and how to use one. It helps so much, to be able to think as the lecture is writing boards filled with formulas: “Shit! Now I can use this to do X!”
Thanks for taking the time to listen. It’s such a shame that maths is being taught this way, because mathamatics is both so very useful and very important…
Edit: Actually I reflection I sat through 3 years of maths, not 4
If you had enrolled in electrical engineering then by half way through second semester of first year you probably would have been having lots and lots of light bulb moments. Complex numbers and fourier series and transforms rapidly become like oxygen for EEs. Essential but consumed almost without noticing.
You suffered from the university's lack of bandwidth -- only so many lecturers, only so many lecture theatres, many other competing classes. They try to find efficiencies where they can -- e.g. by giving all of the engineering departments a common mathematics curriculum.
That curriculum is almost certainly driven by the needs of the EEs and ME/CivE's much more than chem and software, and I'd guess software engineering is looked at is if there's really no maths required. After all, software engineers just program and write documents, don't they? The truth is of course that there is just as much scope for maths, if not more, in a software engineering or computer science course, it's just a whole other type of maths that's needed.
Hmmm ... It is entirely possible that the EE's went straight out of that maths tutorial and into an electronics class that used complex numbers for a practical application.
To be honest all us software engineers understood that we didn't make up the majority of maths students. I would have been perfectly happy to hear about how I could have used complex numbers to design circuits or build bridges. But I guess the maths classes were designed to provide the pure theoretical foundations upon which other, more subject specific classes would build. It just so happens that for software engineering there were no subject specific classes which made use of the maths.
However, after reading your comment I still don't know what to do about it. As far as applications I'm familiar with... well, they are typically to other areas of math, as Slowpoke was complaining about.
Since you mentioned Fourier series, please imagine that I am about to teach an undergraduate course in the subject, and I want to follow your advice. However, I don't know jack shit about EE or any other practical application of Fourier series. What would you do in my shoes?
Hmmm, well its a very interesting question. I'm not entirely sure what I would do in your shoes, but some places start looking may be:
Why are Fourier series on the curriculum? There must be a reason why they are so important that a whole undergraduate course would be dedicated to them.
How and when were Fourier series first described? I understand Joseph Fourier made some pretty major contributions to maths. What was he trying to achieve? Did Fourier series help him do it? Why did other people pay attention, and how was the idea popularised?
Finally, if you really don't know anything about EE or any other applications for it may be a good idea for you to lean a bit more about the various fields that are built on top of yours. Having a better understanding about how your area of interest relates to others is always a good thing.
I know from a software point of view, even though they are hidden from day to day coding, Fourier series are hugely important. Fourier series allow us to compress audio and images down to sizes where they can easily be transferred across the internet [1]. Almost every single digital image you see, song you listen to and movie you watch will have had a fourier transform applied to it. Did you know that movies on netflix account now account for 32% of north american internet traffic? Without the fourier transform its safe to say the world wide web as we know it would not exist.
Furthermore, because it is actually practical to transfer movies and songs across the internet, mass piracy of media is possible. Millions of people are sharing (fourier transform compressed!) movies over sites like the pirate bay. This has lead to a backlash from established media corporations demanding stronger copyright protections. Currently a huge legislative battle is being fought, which will have a impact on such disparate areas as the future of censorship, what rights people have over the things they create and the role of money in politics.
All because of what the fourier series lets us do!
8 years ago, I graduated from my Software Engineering degree at Swinburne University in Australia. As part of my degree I had to sit through 3 years of engineering maths. In our first programming tutorial we were taught how to write a program to display “Hello world”. It was immediately obvious to me why we might want to write a program that displays messages on the screen and what sort of problems this would be useful for solving.
In our first maths tutorial we were taught how to add, subtract and multiply complex numbers. To this day, I still do not understand why I would need to do that. Where do my complex numbers come from? What do they represent? When I add them together, what does the answer mean? The only problems that I can apply my maths education to, look exactly like those on the tests: what is (-3.5 + 2i) + (12 + 5i) ?
It is possible that in my job I am besieged daily with problems that I could use complex numbers to solve. But if so, I am totally incapable of recognizing them!
Fourier series were a particularly egregious example – the subject started, when the lecturer came in and wrote up 3 boards of dense maths, and said something along the lines of “… and this is the formal derivation of a fourier series!” It was as if somebody had tried to teach programming by explaining the algorithm a complier uses for translating source code into machine code. Then expecting the students to just figure out how to write actual useful programs, all by themselves! I believe this is what Slowpoke was talking about when he said: “The problem, as I still see it, is that nobody fucking tells you why. They throw it at you and expect you to deal with it. No further explanation - "It's math, we ain't gotta explain shit."
The way we were taught fourier series particularly hurt. Years later, I found out by myself, that the things are actually incredibly useful. As it turns out, that there are these things called fast fourier transforms, that programs use all the damn time, to do fantastic stuff!
So, to give a very concrete example of how maths education in universities could be improved: If only the first lecture on fourier series had instead explained what they are used for, and why they were so important that we were going to spend 5 weeks on them. Then perhaps I would have had a much better understanding of what they are and how to use one. It helps so much, to be able to think as the lecture is writing boards filled with formulas: “Shit! Now I can use this to do X!”
Thanks for taking the time to listen. It’s such a shame that maths is being taught this way, because mathamatics is both so very useful and very important…
Edit: Actually I reflection I sat through 3 years of maths, not 4