Optimization problems involving several constrained variables
Optimal path choice if we assign costs to each path (Very handy for logistics.)
Works really well with game theory and optimal strategies.
Quadratic programming builds on this and can be used to determine the optimal portfolio using Markowitz mean-variance.
That's all I can think of for now, but there are plenty more applications. Linear programming has to be one of the most handy areas of math and easiest for optimization problems.
The US dwarfs the rest of the world in production of IP. Hence, there should be little wonder in the rest of the world bitching about not being able to copy it.
Stop you're whining about not being able to copy Britney Spears CD's. Jeesh, we already subsidize research for your pharmaceuticals and sell them to you for cheap. Not to mention foot your defense bills.
"But no one has ever found evidence that calculating finer and finer values of pi will ever reveal an end to the string or that there is any regular pattern to be found within it."
I think the writer of the article is a little confused about what an irrational number is. For all of you that have been traumatized by a poor math education, irrational numbers cannot be written as p/q, where p,q are integers and q!=0. One of the implications is that if the decimal representation terminates or has a repeating sequence, it is rational.
Furthermore, pi is transcendental. This means it cannot be a root to a polynomial with integer coefficients. I believe Lindemann showed this and Lambert showed irrationality. The proof of these is beyond the scope of this thread.
IAAM and I've always thought of number theory as at best, some sort of a playground for the bored mathematician, and at worst, where the mathematician conjures up his or her mystical roots. Nothing too much practical going on, but it can be fun to just unwind thinking about how to prove something like this or Goldbach's conjecture. I think it's a bit of a waste to actually spend most of your time researching these things, but that's just me.
Before all you CS people jump on my shit, I know there are "practical" applications for number theory, but there are better tools to be found in number theory's bigger brothers: algebra, elliptic curves, commutative algebra, algebraic geometry, etc.
Forget bioterrorism applications. Who cares? I could market the shit out of this and make a market bubble that the dot bombs could only dream of.
First, imagine all of the cosmetic applications. e.Perfume, where bacteria customize your scent to the mood, time, place, etc. e.Make up, where similar changes happen with ladies makeup. e.Coli, for your customized smell in lavatory situations or those gassy days that you just need to let it out in a public place. e.Antiacne, where bacteria take the role of making you a teenager with nice skin.
Now, that you're the nicest smelling, great skinned, attractor of the opposite sex, you can use your e.birthcontrol to increase sponteneity and maybe even prevent unwanted STD transmission. Maybe even e.extrasensation. Well enough of that.
Now, we adapt this to yeast and give the brewmasters the ultimate in control of their fermentations. Want a perfect high gravity, never stuck fermentation, or other difficult beer done right every time? Use e.Brew.
They only serve to distract students. Don't give me the crap about computer skills being useful for the workforce. If you don't know basic math, reading, and writing, you're a moron and no one needs to read whatever the hell you are typing up in Word or Powerpoint.
The same thing goes on with textbooks. You don't need the 200th edition of the traditional subjects whose material hasn't changed at this level for 500 years. They load each textbook with distracting diversity crap about how some idiot halfway across the country uses math to distribute produce from their growing coop. Especially in the case of math texts. I use old school texts by the masters such as Gelfand, Spivak, Courant, etc. that are 30-100 years old and teach circles around today's math ed texts.
The whole thing is a plundering of resources that began at the administrative level. (Who deserves a several hundred thousand dollar salary for being a school district superintendant?)
Granted, there are problems with teachers and parents as well. Each of these groups of people need to get the kids to concentrate on learning and minimizing distractions. In addition, there needs to be increased discipline to get rid of people that don't want to be there and serve to be a distraction.
I don't think of Chris Rock as a topologist. I see him more as an analyst in a classic Richard Pryor sense. George Carlin would make a great algebraist kind of comic. I'm at a loss currently for a topologist comedian.
I think you could spend a better part of a weekend discussing different comics cracking jokes about different areas in mathematics. Anything to distract from studying for quals! lol
It'd be cool to take the memory of one of these guys and combine it with the insight of Einstein, the computational abilities of John von Neumann, and maybe throw in some Hilbert, Gauss, and Riemann. Now that would be one smart mother fscker.
I think mathematics and physics have an anti-memory effect though. It happened to me and others like the famously absent minded Norbert Wiener.
I think I learned a lot about history from Civilization and other strategy games. Games are basically what we scientists call simulation when we grow up.
For some subjects, it should only be a supplement. Mathematics comes to mind. I've found that teaching mathematics is super easy the old fashioned way. You don't pull any punches and have to be able to field any questions the students have. That means being able to focus in exactly where the student doesn't understand and dismantle the problem appropriately. Knowing algebra to the level of Herstein and Rudin is required. Otherwise, you have no business teaching math.
I focus on math, since it will probably be the first to be replaced by computer instruction for numerous reasons.
Derivatives used properly aren't gambling or malicious. In fact, they are a way to sell off risk to make sure you don't assume risks you don't have to. For example, a farmer will be guaranteed a fixed sum of money upon delivery of a crop. That way he can feed his family and not have to worry about flucuating market prices.
On the other side, hedging can take these instruments and create new instruments to simulate the returns of the S&P 500 with minimized variance.
If the math is done right, there's no problem. If the math is done wrong or not done at all, you're on your own. Much of the basic stuff works the same way as classical actuarial and ruin theory. Imagine living without insurance, it would suck basically. If you don't have insurance (auto, home, life, disability, medical, long term care, umbrella, and others), you are a fool.
Ideally, these instruments should smooth everything out financially. They could be used improperly, but I think the effect of one bank's f*ck up should be able to be absorbed in the grand scheme of things. I doubt there will ever be a failure as spectacular as 1929. While I don't think a single bank could cause it, failure of a country (US in particular) could cause world crisis.
Since I brought up the US, something to keep in mind is that the fundamental constant so to speak is the yield of the 30 year treasury bond (some operations use the shorter term US debt obligations though). When SS starts dumping it's share of gov't debt in 2017 or so, I'm wondering what kind of chaos this will cause. Don't mind what you've heard about the lockbox not existing and crap, it's all in book entry and the end result is the same.
Same sort of idea with Medicare. The present value on that bad boy is $75 trillion I've read. $75 trillion could create a serious Great Depression type situation.
I'm skeptical that the amount of derivatives is $300 to $600 trillion. The entire net worth of the US is $50 trillion or so. If anyone has a link, I'd like to see it.
I agree that 1 is still the biggest materials engineering hurdle, but I'd imagine that it could be real after a couple of years and some financing.
As for the other two, the guy that was working on this said that dodging space debris was realistic and easier than it sounds and that repairs could be made every now and then. I guess the being hurled part doesn't actually happen, because as long as the elevator wasn't in transit, the nanotube rope could be cut and it'd still be fine. I really wish I had a link to the article but it was in Scientific American a few months ago.
That's true but there's always going to be a rather large lower bound to your costs using chemical propellents to put something into orbit. I don't think the mass market will be able to be had in this way. Something totally revolutionary will have to happen to put folks like me and you into orbit.
I agree. I think the legal and insurance reasons are the hardest to overcome. Personally though, if I had the opportunity to be an investor in this project, I'd consider the reward to be worth far more than the risks. That being said, I think it could be possible to round up enough investors who felt passionate enough and/or willing to take the chance if the right guy was behind it.
Because there isn't a project that government can't do for less than 10 times the original cost. Besides, imagine if Bush would call a press conference today and said he wanted to do this. Everyone would either:
1. Laugh and call him a space cadet
2. Say the money could be better spent elsewhere
3. Say it would rob other projects in the sciences of their funding
All of that being said, if I had the money or finance it, I'd do it in a heartbeat and I'd own space. I'd yell, "I'm rich, biyatch" a la Dave Chapelle the whole way to the top of my elevator.
If we wait for terrorism to go away, we'll never do it. I've also read from the main guy thinking about the problems, that it would be easy to fix once the whole operation is up and running. He was thinking more in the way of hurricanes, etc.
I believe the article is in Scientific American and the guy worked for some part of NASA.
I don't know why everyone gets all worked up over these things. Science allows itself to be challenged and I'm rather confident that science can withstand some silly stickers. Besides, how many of us use Evolution or Creationism in our day to day lives?
It would be much more constructive to argue about the piss poor math abilities of our school kids. I think that above average kids could come out of high school at the level of the Lebesgue integration but they waste years on basic arithmetic in elementary when they should be doing algebra. Of course, the less skilled kids would be somewhere less than that and we'd need better math teachers for the Lebesgue stuff.
Building a stupid little ship to put a couple of rich people into suborbit for a few minutes gets us no where in the grand scheme of things. I'm rather dumbfounded as to why none of these guys are trying to bankroll a space elevator. That's when you can do some serious space stuff and become richer than Bill. I've read various places that it could be done in the very near future for as little as $10 billion. When I read that someone isn't dicking around with suborbital vehicles and is behind this, I'll get excited. Otherwise, all this has already been done for the past 60 years.
It was National Socialism if I recall. It has a lot more in common with the left than the right in America ever has. Remember, the Holocaust was a government program. Of course, America will probably try something similar soon called National Health Care. Imagine, soulless, incompetent, unaccountable bureaucrats making decisions about your healthcare, while the elite go to some offshore cash only second to none healthcare.
Slashdot Mirror
Optimal path choice if we assign costs to each path (Very handy for logistics.)
Works really well with game theory and optimal strategies.
Quadratic programming builds on this and can be used to determine the optimal portfolio using Markowitz mean-variance.
That's all I can think of for now, but there are plenty more applications. Linear programming has to be one of the most handy areas of math and easiest for optimization problems.
Stop you're whining about not being able to copy Britney Spears CD's. Jeesh, we already subsidize research for your pharmaceuticals and sell them to you for cheap. Not to mention foot your defense bills.
"But no one has ever found evidence that calculating finer and finer values of pi will ever reveal an end to the string or that there is any regular pattern to be found within it."
I think the writer of the article is a little confused about what an irrational number is. For all of you that have been traumatized by a poor math education, irrational numbers cannot be written as p/q, where p,q are integers and q!=0. One of the implications is that if the decimal representation terminates or has a repeating sequence, it is rational.
Furthermore, pi is transcendental. This means it cannot be a root to a polynomial with integer coefficients. I believe Lindemann showed this and Lambert showed irrationality. The proof of these is beyond the scope of this thread.
Before all you CS people jump on my shit, I know there are "practical" applications for number theory, but there are better tools to be found in number theory's bigger brothers: algebra, elliptic curves, commutative algebra, algebraic geometry, etc.
First, imagine all of the cosmetic applications. e.Perfume, where bacteria customize your scent to the mood, time, place, etc. e.Make up, where similar changes happen with ladies makeup. e.Coli, for your customized smell in lavatory situations or those gassy days that you just need to let it out in a public place. e.Antiacne, where bacteria take the role of making you a teenager with nice skin.
Now, that you're the nicest smelling, great skinned, attractor of the opposite sex, you can use your e.birthcontrol to increase sponteneity and maybe even prevent unwanted STD transmission. Maybe even e.extrasensation. Well enough of that.
Now, we adapt this to yeast and give the brewmasters the ultimate in control of their fermentations. Want a perfect high gravity, never stuck fermentation, or other difficult beer done right every time? Use e.Brew.
I better stop. I could go on all morning.
The same thing goes on with textbooks. You don't need the 200th edition of the traditional subjects whose material hasn't changed at this level for 500 years. They load each textbook with distracting diversity crap about how some idiot halfway across the country uses math to distribute produce from their growing coop. Especially in the case of math texts. I use old school texts by the masters such as Gelfand, Spivak, Courant, etc. that are 30-100 years old and teach circles around today's math ed texts.
The whole thing is a plundering of resources that began at the administrative level. (Who deserves a several hundred thousand dollar salary for being a school district superintendant?)
Granted, there are problems with teachers and parents as well. Each of these groups of people need to get the kids to concentrate on learning and minimizing distractions. In addition, there needs to be increased discipline to get rid of people that don't want to be there and serve to be a distraction.
I think you could spend a better part of a weekend discussing different comics cracking jokes about different areas in mathematics. Anything to distract from studying for quals! lol
That's easy, just expand the infinite series of arctan 1 and multiply by 4.
That's the funniest thing I've read all day.
Now that would be hilarious. I'd love to see Chris Rocks routine generalized to Banach spaces and arbitrary metrics.
It'd be cool to take the memory of one of these guys and combine it with the insight of Einstein, the computational abilities of John von Neumann, and maybe throw in some Hilbert, Gauss, and Riemann. Now that would be one smart mother fscker. I think mathematics and physics have an anti-memory effect though. It happened to me and others like the famously absent minded Norbert Wiener.
For some subjects, it should only be a supplement. Mathematics comes to mind. I've found that teaching mathematics is super easy the old fashioned way. You don't pull any punches and have to be able to field any questions the students have. That means being able to focus in exactly where the student doesn't understand and dismantle the problem appropriately. Knowing algebra to the level of Herstein and Rudin is required. Otherwise, you have no business teaching math.
I focus on math, since it will probably be the first to be replaced by computer instruction for numerous reasons.
Nonstandard notation bothers the hell outta me. You statistics and finance people need to be brought into line.
In measure theoretic probability we define a random variable X on the probability space (Omega, F, P).
In partial differential equations, Omega is usually the the open subset of R^n within which a given PDE holds.
Sorry to be a mathematical notation Nazi, but I'm a bit of a follower of Bourbaki. Shit's hard enough without bad notation.
Derivatives used properly aren't gambling or malicious. In fact, they are a way to sell off risk to make sure you don't assume risks you don't have to. For example, a farmer will be guaranteed a fixed sum of money upon delivery of a crop. That way he can feed his family and not have to worry about flucuating market prices. On the other side, hedging can take these instruments and create new instruments to simulate the returns of the S&P 500 with minimized variance. If the math is done right, there's no problem. If the math is done wrong or not done at all, you're on your own. Much of the basic stuff works the same way as classical actuarial and ruin theory. Imagine living without insurance, it would suck basically. If you don't have insurance (auto, home, life, disability, medical, long term care, umbrella, and others), you are a fool. Ideally, these instruments should smooth everything out financially. They could be used improperly, but I think the effect of one bank's f*ck up should be able to be absorbed in the grand scheme of things. I doubt there will ever be a failure as spectacular as 1929. While I don't think a single bank could cause it, failure of a country (US in particular) could cause world crisis. Since I brought up the US, something to keep in mind is that the fundamental constant so to speak is the yield of the 30 year treasury bond (some operations use the shorter term US debt obligations though). When SS starts dumping it's share of gov't debt in 2017 or so, I'm wondering what kind of chaos this will cause. Don't mind what you've heard about the lockbox not existing and crap, it's all in book entry and the end result is the same. Same sort of idea with Medicare. The present value on that bad boy is $75 trillion I've read. $75 trillion could create a serious Great Depression type situation. I'm skeptical that the amount of derivatives is $300 to $600 trillion. The entire net worth of the US is $50 trillion or so. If anyone has a link, I'd like to see it.
I agree that 1 is still the biggest materials engineering hurdle, but I'd imagine that it could be real after a couple of years and some financing. As for the other two, the guy that was working on this said that dodging space debris was realistic and easier than it sounds and that repairs could be made every now and then. I guess the being hurled part doesn't actually happen, because as long as the elevator wasn't in transit, the nanotube rope could be cut and it'd still be fine. I really wish I had a link to the article but it was in Scientific American a few months ago.
That's true but there's always going to be a rather large lower bound to your costs using chemical propellents to put something into orbit. I don't think the mass market will be able to be had in this way. Something totally revolutionary will have to happen to put folks like me and you into orbit.
I agree. I think the legal and insurance reasons are the hardest to overcome. Personally though, if I had the opportunity to be an investor in this project, I'd consider the reward to be worth far more than the risks. That being said, I think it could be possible to round up enough investors who felt passionate enough and/or willing to take the chance if the right guy was behind it.
Because there isn't a project that government can't do for less than 10 times the original cost. Besides, imagine if Bush would call a press conference today and said he wanted to do this. Everyone would either: 1. Laugh and call him a space cadet 2. Say the money could be better spent elsewhere 3. Say it would rob other projects in the sciences of their funding All of that being said, if I had the money or finance it, I'd do it in a heartbeat and I'd own space. I'd yell, "I'm rich, biyatch" a la Dave Chapelle the whole way to the top of my elevator.
If we wait for terrorism to go away, we'll never do it. I've also read from the main guy thinking about the problems, that it would be easy to fix once the whole operation is up and running. He was thinking more in the way of hurricanes, etc. I believe the article is in Scientific American and the guy worked for some part of NASA.
Dude, eat your cheerios and try to smile, it's Friday!
I don't know why everyone gets all worked up over these things. Science allows itself to be challenged and I'm rather confident that science can withstand some silly stickers. Besides, how many of us use Evolution or Creationism in our day to day lives? It would be much more constructive to argue about the piss poor math abilities of our school kids. I think that above average kids could come out of high school at the level of the Lebesgue integration but they waste years on basic arithmetic in elementary when they should be doing algebra. Of course, the less skilled kids would be somewhere less than that and we'd need better math teachers for the Lebesgue stuff.
Building a stupid little ship to put a couple of rich people into suborbit for a few minutes gets us no where in the grand scheme of things. I'm rather dumbfounded as to why none of these guys are trying to bankroll a space elevator. That's when you can do some serious space stuff and become richer than Bill. I've read various places that it could be done in the very near future for as little as $10 billion. When I read that someone isn't dicking around with suborbital vehicles and is behind this, I'll get excited. Otherwise, all this has already been done for the past 60 years.
It was National Socialism if I recall. It has a lot more in common with the left than the right in America ever has. Remember, the Holocaust was a government program. Of course, America will probably try something similar soon called National Health Care. Imagine, soulless, incompetent, unaccountable bureaucrats making decisions about your healthcare, while the elite go to some offshore cash only second to none healthcare.