What do you work at???

As long as I got the gist of it, I'm happy :D I'll be honest- when I read your first explanation, as soon as I read algorithms, blood sampling, interferents, and contaminants, my eyes immediately glazed over:aargh:

Sounds like interesting stuff if that's your thing. Personally, I had a difficult time with pre-calc. It didn't help that it was useless in the capacity it was being taught, but that's another story.

Thanks for sharing! I would have to say I would not like your job! I am doing bootstrapping right now, and I ended up taking a stat course last semester. Put it this way, I thought stat was cool when I was working on my project, but after taking the stat class I started to dislike stat even more. It seemed to vague to me! I enjoyed the logic in numerical linear algebra far better!!!! I do like the application! Cool stuff.

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Originally Posted by wdhall

Currently, I'm using a version of linear regression called PLS (it's pretty much the popular favorite in the chemometrics world, probably because it's so much like ordinary regression that people are comfortable with the technique, and have good intuitions about what works and what doesn't); in the past, I developed [and then used] a non-regressive technique (HLA) based on a '98 Ph.D. thesis out of the MIT Physics Department; however, some spectacularly uncooperative data together with requirements of expediency nudged us towards PLS, where other folks in my team could contribute meaningfully. I'll probably get back to HLA eventually, but it'll take more time & effort than I have at the present.

Due to the hospital environment we're targeting, PLS requires a number of tweaks to do the job. Mainly, the problem is that ICU cases are by their very nature, custom jobs: no two patients have the same situation, doctors are pumping this and that into the patient to keep him alive, then to keep him stable while they figure out what is going on. The problem to me is that everything they do has an impact on the blood, specifically on the spectrum that I get to see. The blood samples one obtains can be markedly distinct form anything your training set wants to see, and regression can (and does) fail catastrophically.

To mitigate this effect, I have developed techniques to identify [probabilistically] the interferents most likely to be the cause of any spectral discrepancies (relative to the training set), and then to take a list of presumed interferent spectra and re-tune PLS to be relatively insensitive to their presence.

The interferent identification uses a Bayesian technique to estimate relative likelihoods for the various interferents from my library; the re-tuning is essentially an expansion of the training set to include the identified interferents as part of the background noise. The Bayesian technique works well enough for a modest number (< 5) of simultaneous interferents, while the retuning works exceptionally well for upwards of 15 simultaneous interferents.

That's enough of me rambling & bragging.

Dale

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I agree. Although I'm not a huge fan of algebra, it's something that seems logical and useful. I like stat to a degree, but calc is just a pain in the ass.

Having said all that, I feel embarrassed because I know people like wdhall and jockeys are math gurus that eat calc, etc. for breakfast. Darn smart people:rant:

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Originally Posted by Quick Orange

I agree. Although I'm not a huge fan of algebra, it's something that seems logical and useful. I like stat to a degree, but calc is just a pain in the ass.

Having said all that, I feel embarrassed because I know people like wdhall and jockeys are math gurus that eat calc, etc. for breakfast. Darn smart people:rant:

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I really think that people have a preconception that just because you can do math you are smart. I found that math is more learned than anything else, I think what sucks is that there are so few good teachers out there that people have a hard time getting down the basics.

One man band, boatbuilder/shipwright and carpenter and my wifes slave.

PuFF

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Originally Posted by fatpanda

I really think that people have a preconception that just because you can do math you are smart. I found that math is more learned than anything else, I think what sucks is that there are so few good teachers out there that people have a hard time getting down the basics.

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You raise some good points. I thought they deserved some response, and what I have ended up with is wordier than I had hoped. I'm not interested in hijacking this thread, so I'll just leave my contributions off at this article. If folks started another thread on the topic, I'd probably not be able to resist jumping in.

First, people DO give mathematicians a bit of a free "smart guy" card.

Frequently it comes from folks who've never had any mathematical training, but more often it's from people who've "hit the wall" with some math course they had in college. For instance, the CEO of my company will occasionally drop a reference to the three semesters of calculus he took. He's no dummy, but I can't tell whether he's bragging or admitting that his math education roughly matches my freshman year of college.

My experience is that it is rare for a practicing mathematician to have "only" average intelligence in certain areas (mainly having to do with dealing with logical arguments and manipulating abstract concepts). Mathematicians are trained to think carefully, and with precision. It's not uncommon to work on a single problem for months or years, and build up a sort of edifice of partial understanding that one alternately builds up and attempts to destroy. This training is rigorous, and when it takes, it is not unlike strength training: you do strength training correctly, and you'll get stronger. I believe that a similar effect holds with mathematics.

That intelligence doesn't always (or even usually) translate into other areas: for instance, money, dealing with people, or mechanical skills. Surprisingly, a fair number of mathematicians aren't particularly good at the sort of mental arithmetic that folks tend to expect. I, for one, have no ability to think clearly about finances. Money ties in to too many things I have emotional attachments to, and I can't get the clarity I need to be smart on the topic. I also tend to be poor at modulating my own emotions, and as a defense against my own foolishness I don't reveal emotion readily.

Second, there is a real problem in mathematics education (at least in the US), and my belief is that it comes down to college programs in education, which attract people who are somewhat math-phobic. This propagates mathophobia from one generation to the next. It has a more pernicious aspect, in that the teaching that DOES get done is aimed at the most mechanical aspects of mathematics, with the understanding of fundamental concepts getting short shrift.

This in turn snowballs into major hurdles for students as they progress, since mathematics may be the most cumulative subject around. I used to complain [to myself] in college that in the mathematics courses I took, it was impermissible to forget anything I had ever heard, and often it was not acceptable to be ignorant of something I had never heard in the first place.

Students in calculus who have weak comprehension of algebra (that is, a good comprehension of the concepts and a facility for manipulation) tend to have an especially hard time; calculus itself is (for the most part) fairly easy, but it's hard to know that until you've known calculus for a few years. You can't see the unifying structure without getting past the hurdles posed by the limit process and internalizing the associated intuitions, and some real mental flexibility is essential to get to that point. In the trade, it's called "mathematical maturity"; you need to be able to let go of some level of detail sometimes, just to get the gist of what's going on, and once you get the flow of some derivation or the basic outline of some extended calculation, then you go back and fill in the blanks.

Linear algebra, on the other hand, is deceptive: many of the things that appear obvious are notoriously difficult, if not plain wrong, while some of the things that one would expect to be nearly impossible turn out to be fairly simple.

Of course, mathematics takes off from there. The contemporary offshoots from those two areas (calculus and linear algebra) would be all but unrecognizable to a layman, and they account for maybe 10% - 15% of the area covered by the field today.

That's my rant.

Dale

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Originally Posted by wdhall

Frequently it comes from folks who've never had any mathematical training, but more often it's from people who've "hit the wall" with some math course they had in college. For instance, the CEO of my company will occasionally drop a reference to the three semesters of calculus he took. He's no dummy, but I can't tell whether he's bragging or admitting that his math education roughly matches my freshman year of college.

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I graduated as a Master in Engineering (electronics) and I was always fascinated by theoretical physics. After graduation I thought about going for a Masters in Science, (physics, esp QT) but after looking at the material, I decided not to.

My foundation in math was pretty solid (for example I was good at partial differential equations, laplace transformations, etc) but things like topology and group theory are just plain weird to me. It doesn't feel like real math at all and I didn't really 'get it'.

I'm a professional hermit.

I'm a finance manager at a large US bank. Which one? Not yours. :)

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Originally Posted by freebird

I'm a professional hermit.

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As long as it pays good. :w