10 ms·

> If you don't want to cough up the required rigor... Forgive me, but this sounds absurdly elitist. Mathematics is not a subject reserved for a select set of

by exergy 10y ago

> If you don't want to cough up the required rigor... Forgive me, but this sounds absurdly elitist. Mathematics is not a subject reserved for a select set of chosen elite. It is a very necessary tool for almost every scientific endeavour. And this is a huge problem because people in those fields aren't just studying maths. Case in point, I'm a mechanical engineer. I have to study thermodynamics, materials, structural analysis, mechanics and on and on. In the midst of all this, I needed to learn advanced numerical methods, but was flummoxed because it was taught by a senior professor, to a class of mostly mathematicians, with an inordinately huge amount of effort placed towards proving things etc. and not much thought spared for us non-applied mathematicians. I once heard maths described as something like "a person sees a category of something that exhibit a certain behaviour and then abstracts away the specifics to be left with a set of "general principles" that let the something exhibit it's behaviour". Thing is, it sounds like you start from the specific and abstract towards the general, but it is taught as a general and I am left to my own devices when dealing with the specific. All for good reasons I'm sure, but then who is making a case for how we lesser mortals learn it? I was nearly in tears by the end of the course, convinced of my own stupidity and incompetence, because it was as if the class was communicating in their own language, and I (and other aerospace guys) were the village idiots who accidently made it in. It was only after I took it upon myself later to learn using a lot of youtubing, "maths for idiots" type backtracking that I was able to learn just enough.

demonshalo 10y ago
>I once heard maths described as something like "a person sees a category of something that exhibit a certain behaviour and then abstracts away the specifics to be left with a set of "general principles" that let the something exhibit it's behaviour". Thing is, it sounds like you start from the specific and abstract towards the general, but it is taught as a general and I am left to my own devices when dealing with the specific. You made my point far better than I ever could. When I am faced with a general abstraction I have to conceptualize it in terms that I understand (the specific). Yet when the general case is presented, very little is said about the specific so I have to grind for months until I can finally maybe understand what was being meant. All of that could have been prevented had the concept been communicated in a more friendly, yet still mathematical, manner. >All for good reasons I'm sure, but then who is making a case for how we lesser mortals learn it? I was nearly in tears by the end of the course, convinced of my own stupidity and incompetence, because it was as if the class was communicating in their own language, and I (and other aerospace guys) were the village idiots who accidently made it in. That's how I felt constantly in college and it is actually part of the the reason I dropped out. It almost felt as if this alienation is intentional. Which makes me somewhat sad!
ska 10y ago
Most mathematics taught in universities at the undergraduate level is the mathematics for non-mathematicians. The typical calculus, ODE, PDE, vector calculus, complex variable stream taught for engineers and scientist is not at all rigorous, and misses a lot of the interesting details (for mathematicians) in order to speed up and cover more practical results. It sounds like you ended up in the wrong numerical methods course, which is unfortunate. But there is a lot of the system is actually oriented exactly at what you are asking for.
wayn3 10y ago
I see. What I'm talking about is mathematics for the sake of mathematics. Any training aimed at mathematicians needs to emphasize rigor. Otherwise, there will be a bunch of impotent mathematicians. Not what we want. I'm not opposed to teaching engineers "just the calculations". But such classes should be organised by their departments, not the mathematicians'. Your guys know better what you need to know. This has nothing to do with elitism, though. A mathematician needs to know how mathematics works. Most other disciplines do not. I wouldn't claim that engineers are only allowed to earn their degrees if they pass math classes, thats just how colleges organise their course requirements.
- kxyvr 10y ago
  As a counter point, I've a PhD in applied mathematics and I believe there's plenty of elitism in the field. Unless you're a logician following a very specific set of reduction rules that can be verified mechanically, a proof is largely just an argument that something is true or not. Just because something is true doesn't mean the argument for it is strong, nor comprehensible. Part of the elitism within the field is that, at times, the community places pride on being as incomprehensible as possible because we should be smart enough to fill in the "trivial" details. That's morally wrong and it turns people away from the field. Further, it locks out a huge number of people who are not specialists from accessing the material. Awhile back, I had a coauthor on a paper screaming at me in his office that it was condescending for me to include a full set of calculations for a proof that I authored. We had the room the paper for the result. I, as the author of the proof, couldn't follow the proof without the full set of calculations. We actually walked around the office and most people agreed with my coauthor. Although I ultimately prevailed and kept the calculations, it's an example of the underlying problem. Namely, yes, a large portion of the field is elitist. "I don't need these calculations to understand the result, so why should my readers?" Math is not so cut and dried that there is precisely the minimum number of statements to describe a problem or give a proof. I very, very strongly believe in rigor. We can be rigorous and not be a dick in how we write or present material.
  - demonshalo 10y ago
    Thank you! I am 100% certain that had authors of a lot of papers that I have read included some examples and perhaps even calculation results, I would have understood and perhaps even been able to reason about some of their publications a whole lot better than I currently can. Just the mere inclusion of a few examples makes a world of difference. The idea that X is clear to everyone and therefor we do not need to exemplify it for the reader is really back-breaking. Especially when you are not coming form a background that includes years of expertise within said domain!

by exergy 10y ago

demonshalo 10y ago

>I once heard maths described as something like "a person sees a category of something that exhibit a certain behaviour and then abstracts away the specifics to be left with a set of "general principles" that let the something exhibit it's behaviour". Thing is, it sounds like you start from the specific and abstract towards the general, but it is taught as a general and I am left to my own devices when dealing with the specific. You made my point far better than I ever could. When I am faced with a general abstraction I have to conceptualize it in terms that I understand (the specific). Yet when the general case is presented, very little is said about the specific so I have to grind for months until I can finally maybe understand what was being meant. All of that could have been prevented had the concept been communicated in a more friendly, yet still mathematical, manner. >All for good reasons I'm sure, but then who is making a case for how we lesser mortals learn it? I was nearly in tears by the end of the course, convinced of my own stupidity and incompetence, because it was as if the class was communicating in their own language, and I (and other aerospace guys) were the village idiots who accidently made it in. That's how I felt constantly in college and it is actually part of the the reason I dropped out. It almost felt as if this alienation is intentional. Which makes me somewhat sad!

ska 10y ago

Most mathematics taught in universities at the undergraduate level is the mathematics for non-mathematicians. The typical calculus, ODE, PDE, vector calculus, complex variable stream taught for engineers and scientist is not at all rigorous, and misses a lot of the interesting details (for mathematicians) in order to speed up and cover more practical results. It sounds like you ended up in the wrong numerical methods course, which is unfortunate. But there is a lot of the system is actually oriented exactly at what you are asking for.

wayn3 10y ago

I see. What I'm talking about is mathematics for the sake of mathematics. Any training aimed at mathematicians needs to emphasize rigor. Otherwise, there will be a bunch of impotent mathematicians. Not what we want. I'm not opposed to teaching engineers "just the calculations". But such classes should be organised by their departments, not the mathematicians'. Your guys know better what you need to know. This has nothing to do with elitism, though. A mathematician needs to know how mathematics works. Most other disciplines do not. I wouldn't claim that engineers are only allowed to earn their degrees if they pass math classes, thats just how colleges organise their course requirements.

kxyvr 10y ago
As a counter point, I've a PhD in applied mathematics and I believe there's plenty of elitism in the field. Unless you're a logician following a very specific set of reduction rules that can be verified mechanically, a proof is largely just an argument that something is true or not. Just because something is true doesn't mean the argument for it is strong, nor comprehensible. Part of the elitism within the field is that, at times, the community places pride on being as incomprehensible as possible because we should be smart enough to fill in the "trivial" details. That's morally wrong and it turns people away from the field. Further, it locks out a huge number of people who are not specialists from accessing the material. Awhile back, I had a coauthor on a paper screaming at me in his office that it was condescending for me to include a full set of calculations for a proof that I authored. We had the room the paper for the result. I, as the author of the proof, couldn't follow the proof without the full set of calculations. We actually walked around the office and most people agreed with my coauthor. Although I ultimately prevailed and kept the calculations, it's an example of the underlying problem. Namely, yes, a large portion of the field is elitist. "I don't need these calculations to understand the result, so why should my readers?" Math is not so cut and dried that there is precisely the minimum number of statements to describe a problem or give a proof. I very, very strongly believe in rigor. We can be rigorous and not be a dick in how we write or present material.
- demonshalo 10y ago
  Thank you! I am 100% certain that had authors of a lot of papers that I have read included some examples and perhaps even calculation results, I would have understood and perhaps even been able to reason about some of their publications a whole lot better than I currently can. Just the mere inclusion of a few examples makes a world of difference. The idea that X is clear to everyone and therefor we do not need to exemplify it for the reader is really back-breaking. Especially when you are not coming form a background that includes years of expertise within said domain!