Well, there are the applicable parts and the inapplicable parts.
I’ll take that bet: $1,000,000, even money. I’ll PM you my bank info.
https://en.wikipedia.org/wiki/Category_theory
Category theory has practical applications in programming language theory, in particular for the study of monads in functional programming.
Busted, fair enough.
wow dude has a milly in his bank account. well done
your humor usually falls flat with me, but this is good. i chuckled.
Rotten teachers are undoubtedly part of the issue; however, I still think that in many instances the way math is taught to math students by math teachers puts too much emphasis on rigor too early, before elementary students have developed intuitive understanding of the subject. Some of the theorem proofs, even if a student can follow them, look like tricks out of a magic hat - construct a perpendicular bisector and extend it until it intersects that line, substitute this variable with some expression, etc. Where did that idea come from??
Nothing works better for developing a student’s ability than solving lots and lots of problems. In my opinion, at this elementary stage (i.e. non-PhD) it would be better if somebody just stated the theorems and said, “these are the tools in your toolbox now, let’s learn how to use them”, then go and start solving many, many different problems so that the student can get a context of how these theorems can be useful and what motivates their existence. A proof can rarely accomplish this at this stage of the game.
If there is an “elementary” math problem to be solved (i.e. one that doesn’t require PhD-level knowledge, so 99.9% of all problems in practice) and I have to randomly pick my team, I’d pick advanced physics and engineering students than math students - not because they are better or smarter but because they are more likely to be taught how to tackle the issue than start chasing epsilons and deltas on step 2 and get stuck…
Interesting.
I’d pick the math students, in a heartbeat.
That’s why there are horse races.
Well knowledge of math is very useful in general, because it teaches you how to approach and attack a problem in a systematic and disciplined way, and the usefulness of such skills go way beyond solving only math problems. One timeless classic on the subject is George Polya’s How To Solve It? - a great book about solving problems, the heuristics he develops there apply to many situations and not just math.
https://en.wikipedia.org/wiki/How_to_Solve_It
So studying math is good because it teaches you how to solve problems, unless you are a math major - then you need to try twice as hard because they’ll try to teach you all kinds of other stuff instead, and that’s what makes a math major difficult. It’s very similar to the situation with computer scientists - if you want to be a good programmer, you probably shouldn’t pick a CS major.
This thread pushed me to buff up on my linear algebra, and one perspective I learned is that one reason linear algebra is taught much more these days than when I took it in college is that there are so many applications of linear algebra that can be done with computers these days, whereas in my day, there was desktop computing power but not nearly as much data available in digital form (unless you entered it all yourself).
Much machine learning is basically linear algebra under the hood.
Although I did not learn statistics with a ton of linear algebra (my education was more in terms of how to use and interpret the statistics, rather than proving that particular linear algebra manipulation got the answer), a lot of it makes sense from a linear algebra perspective that I learned later.
I appreciated the emphasis on using the tools to check your intuition and to build on it.
There are certain things in programming that you would more likely get out of a CS type curriculum than a pure math curriculum. Mathematicians (and physicists, like my major) tend to prefer analytic (i.e. equation-like) solutions over numerical ones, whereas programmers often are perfectly happy to get a good enough numerical approximation. Also, software design patterns (principles that create more stable and reusable code) are really fascinating and useful and not so much (as far as I know) part of the mathematics curriculumn these days.
I would think a joint math and CS curriculum, plus maybe a class on investing and accounting would be an excellent way to go for someone finance oriented in this day and age, assuming that they aren’t doing the traditional finance route.
When I was doing warhead design I came up with a revolutionary (not exaggerating here: revolutionary) design methodology for a certain type of explosively-formed penetrator (EFP) warhead that relied heavily on linear algebra. In a nutshell, for each penetrator (of which there might be 7, 19, 37, 55, whatever), there are three design characteristics that need to be achieved: two orientation vectors (think of them as azimuth and elevation) and a mass. And for each penetrator there are three design parameters: an x-coördinate, a y-coördinate, and a z-coördinate. Thus, for, say, a 55-penetrator warhead, to get the correct parameters for each penetrator, we would need to solve 3 × 55 = 165 nonlinear equations in 165 unknowns. (Actually, it turns out to be much less, because of the symmetries of the design; nonetheless, it’s a lot of nonlinear equations.)
I approximated these nonlinear equations with linear ones, approximated the coefficients empirically, then used linear algebra techniques to iterate to a solution.
Before coming up with my idea, I created a design using then-state-of-the-art techniques. It was a disaster: so bad that the colonel in charge of the program planed to cancel it unless we could prove to his satisfaction that we knew what we were doing and could fix it. At our next meeting, I explained the idea I’d had, and demonstrated that if I had had that design analysis methodology available when I did the first design, it would have predicted exactly the disastrous results we saw.
The upshot was that the colonel allowed the program to continue, and my next design was perfect. Normally in these programs we’re given three design iterations; I went from a first design so bad that the program was on the brink of cancellation to finishing one design iteration ahead of schedule.
All thanks to linear algebra. (And a soupçon of creative brilliance.)
(By the way, my boss at the time had his PhD in physics. I was trying to explain to him how my methodology worked, using a single linear equation with one unknown. You know: a straight line. He didn’t understand it. At all.)
It’s kind of coold when you think how many people were killed by the new warheads.
These were specifically for use against heavily armored vehicles (tanks), and attack helicopters (e.g., the Russian Hind-D).
I don’t lose a lot of sleep over our guys protecting themselves and innocent civilians against tanks and attack helicopters.
Yea S2000 is a baaaaad mofo
I know it sounds stupid and all but what is the main difference between an anti tank rocket and an explosive one ? Is it just the penetration thing ? I have always been fascinated with the concept of using Anti-Personel Rockets on tanks and vice versa.Maybe it was due to my childhood dream of becoming an apache pilot.
Are math majors smart enough to know CO2 levels are at dangerously low levels? Plants are essentially suffocating. They thrive at 2000 ppm. We are at less than 400 ppm after millions of years of trapping carbon in the earth. All plants will die off below 150 ppm. It appears man is reversing the trend, but progress is being jeopardized. Does anybody care? Hydrocarbons are the ultimate store of solar energy. Ever compare the energy density of a battery to gasoline?
Rockets carry things that go Boom! Those things are warheads, and some of those were what I designed.
They are.
Whether they actually know depends on whether they have access to the data or not.
Thank God, if there is one. I’m starting to think I’ll be that outcast living in the woods thinking everybody is crazy but me.
No . . . you’re crazy, too.
That’s good news. I won’t sell everything just yet.