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You beautifully sum up my experience with math at the university, as a CompSci student in Germany. The absolutely most frustrating thing for me, in the beginnin

You beautifully sum up my experience with math at the university, as a CompSci student in Germany. The absolutely most frustrating thing for me, in the beginning, were the basic math lectures (which I, as a disclaimer, still haven't finished). At first, of course, I did what most students do in their first semester: bitch about the apparent uselessness of the subject. That's about one and a half years back, now. I realized by myself that math is actually pretty useful. 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." Personal eye openers for me were my internship (and continued assistant work) at a department of the university that deals with image processing (which is basically a boatload of applied math), articles like Wolfire's excellent "Linear Algebra for Game Developers"[1], and plunging myself into a lecture about Fuzzy Set Theory and Artificial Neural Networks (which again is applied math). I actually like abstractions, generalizations and logic reasoning (I wouldn't study CS if I didn't). I still don't think that math is the only way to teach those, but it's arguably the largest field of science dealing with these things. I don't really think the problem is math itself, it's the way it is taught to most people - in the math way. Mathematicians teach math to do more math, which in turn is used to to even more math. And that's fine - for a mathematician. For literally every other field of science that needs math as a tool, it's highly frustrating to be subjected to what you aptly describe as "torture". [1]: http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-part-1/ http://blog.wolfire.com/2009/07/linear-algebra-for-game-deve...

impendia 15y ago
I am a math professor at a large state university in the US. A comment and a question: > Mathematicians teach math to do more math, which in turn is used to to even more math. That is true of some mathematicians, and of some subjects. But I think most mathematicians teach and learn math because they think it's cool, not because it's useful -- either to learn more math, or for the "real world". I might also add that I always appreciate it when teachers take a very long view of things. For example I have trained in the martial arts, and most teachers take the perspective that you want to master the art completely, rather than just learn one or two things. Some people don't like this, but I deeply appreciate it. > 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." As a math instructor I am always looking for ways to improve, but I'm having trouble extracting useful criticism from your remarks. "They throw it at you and expect you to deal with it" seems to be true of challenging lessons in anything. I would cheerfully welcome general advice and suggestions from you or any other HN readers. (But please keep in mind that both my interests and my expertise skew heavily theoretical!)
- worren 15y ago
  "They throw it at you..." I've the same gripe. Maybe, I can elucidate the parent's point. I can appreciate the mathematician's fancy for reducing numerical manipulation to an indivisible, atomic precision. Creating poetic abstractions is dear to many in applied sciences. Where it sticks in the craw, where it stops making sense, is where you have this beautiful construct and it's purpose is left a mystery. If it's a piece of art, fine. It's welcome to hang on the wall over there next to the others, but I'm not going to remember it in much detail without some context. If there isn't a concrete use, if there isn't a purpose, the idea won't make it out of short-term memory. "But it's the foundation for all of these other beautiful edifices of logic that we'll cover in the next chapter!" It's like being told, "This is red paint. This is green paint. This is burnt umber paint...", without ever being shown a Picasso, Renoir, or da Vinci. If you ground the presentation with messy, imprecise, real world numbers, the logical purity of the subject will not be lost or sullied, the esteem for it's power only more appreciated. Pull the pin, show us what it can do! You may not be a physicist or engineer, and that their respective topics will be covered in their respective classes. But those same physicists and engineers probably aren't mathematicians. So what business did they have teaching me math... better than a math teacher ever did?
- luke_s 15y ago
  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

impendia 15y ago

I am a math professor at a large state university in the US. A comment and a question: > Mathematicians teach math to do more math, which in turn is used to to even more math. That is true of some mathematicians, and of some subjects. But I think most mathematicians teach and learn math because they think it's cool, not because it's useful -- either to learn more math, or for the "real world". I might also add that I always appreciate it when teachers take a very long view of things. For example I have trained in the martial arts, and most teachers take the perspective that you want to master the art completely, rather than just learn one or two things. Some people don't like this, but I deeply appreciate it. > 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." As a math instructor I am always looking for ways to improve, but I'm having trouble extracting useful criticism from your remarks. "They throw it at you and expect you to deal with it" seems to be true of challenging lessons in anything. I would cheerfully welcome general advice and suggestions from you or any other HN readers. (But please keep in mind that both my interests and my expertise skew heavily theoretical!)

worren 15y ago
"They throw it at you..." I've the same gripe. Maybe, I can elucidate the parent's point. I can appreciate the mathematician's fancy for reducing numerical manipulation to an indivisible, atomic precision. Creating poetic abstractions is dear to many in applied sciences. Where it sticks in the craw, where it stops making sense, is where you have this beautiful construct and it's purpose is left a mystery. If it's a piece of art, fine. It's welcome to hang on the wall over there next to the others, but I'm not going to remember it in much detail without some context. If there isn't a concrete use, if there isn't a purpose, the idea won't make it out of short-term memory. "But it's the foundation for all of these other beautiful edifices of logic that we'll cover in the next chapter!" It's like being told, "This is red paint. This is green paint. This is burnt umber paint...", without ever being shown a Picasso, Renoir, or da Vinci. If you ground the presentation with messy, imprecise, real world numbers, the logical purity of the subject will not be lost or sullied, the esteem for it's power only more appreciated. Pull the pin, show us what it can do! You may not be a physicist or engineer, and that their respective topics will be covered in their respective classes. But those same physicists and engineers probably aren't mathematicians. So what business did they have teaching me math... better than a math teacher ever did?
luke_s 15y ago
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