Does America no longer have any goals as a whole? Has our perception of being on top for so long made us lazy and complacent? What is driving the other countries to constantly improve?
My dad says that national security is a huge issue right now, so a lot of research and money goes into that. You need engineers and scientists for this, however, and if the US doesn't produce enough, we may have to start outsourcing national security projects.
That's a little offensive, Minstrel. You're referring to applied math. There are plenty if pure mathematicians who spend their lives solving problems that have little to nothing to do with science.
My apologies. It wasn't intended to be offensive. I'm an engineer, so I was trained in applied math. My bad. My main point, though, was about how we can get kids interested in math. It seems to me that they'll connect with what math is more easily if they see what it can do in the real world. That usually involves seeing how math can help solve problems in the sciences. When I was a kid, I was fascinated when I learned how to make a theoretical prediction, then do the experiment, and see that the results agreed with the prediction. That still seems a bit magical to me. It gives me a sense of confidence; a sense that there are certain (albeit limited) aspects of the universe that I can understand and even control. I'm well aware of pure math, though.
Ditto. It would probably take a pure mathematician to make pure math seem fun. I guess the nice part about it is you never have to worry about experiments?
Maybe the problem lies in the fact that kids in elementary schools are using calculators instead of writing out long division/multiplication. There is no reason to respect math from the beginning if you never have to learn it or apply it. I enjoy using mathematics to solve or explain problems, but that might because the TI-85 was the super-cool, state of the art, high school calculator. I remember being envious when my middle brother got his and my oldest brother never had one.
I remember, before war started, in my old country, we occasionally had kids who were born abroad to come back, as well as kids went as exchange students to other places. Kids coming back from America were just about better then kids coming back from places like Uganda. I had a friend in third grade, whose dad was an ambassador to Uganda. She was really smart, and she left at the end of fourth grade, and came back in the eight. She knew less then she did before she left, and another kid who came from the US was just about as bad a s her. They couldn't even follow the lessons (they both spoke the language well), whilst another guy who came from Germany was pretty much where we were, but his language was a bit worse so he struggled a bit, not with maths, though. And all of our high school students who went to the US, I knew at least five, basically said it was ridiculous, like being in primary school. I left for Australia when I was seventeen, my English was ok, for a school-learned English, but conversationally I was very shaky. In Melbourne, only those with 99+% were even considered for med school, and I went to government school where barely 20% made it to University, and nobody ever got into medicine before. Even though I could barely follow the lessons (I just couldn't understand Aussie accent for ages) it was the advanced maths, chem and biology that got me into medicine within the first year, no problem. None of my friends could believe it, and it was only the fact that their curriculum lagged behind ours by several years, that I got in straight away.
Speaking as an American student....who is well almost no longer a student (In high school anyway) I will say this I hate math with a passion and also enjoy it...well learning about it. Math has simply always been a thorn in my side even when I was in elementary school. I'm not sure why but my brain just wouldn't always work like the others kids it seemed. I even would have borderline panic attacks when I was called up to the board to solve a math problem. I would sweat and itch and breath heavy and look for any excuse I could to get out that situation. I'd sometimes just freeze like a deer caught in headlights and I still do sometimes. When people ask me certain math problems at the drop of a hat I get very panicked cause my mind goes blank and I can't spit out the answer. I'm better on paper doing problems but it can still take me very long to complete things that aren't the basics. And it just was always and still is a subject that has given me the most issues and I've always been good or even great at the other subjects. Just math has always been so hard for me to grasp but I've always been fascinated at seeing math geniuses work and solve problems and explain theories. Math is an amazing thing and despite me being probably below average at it for my age it is a key thing to learn in life. You just need it..... Even now despite my struggles with it I would like to be able to master it or at least be able to answer math questions without freezing. My math life has not been fun and it has caused me a lot of fear which has faded as I've gotten older a bit and come to get better at the subject. Now look I'm not sure if I was taught incorrectly or if I didn't pay attention or if I have some sort math disorder (if those exist) But My point is Math is one of the worst subjects to fall behind in and I urge anyone who is struggling with it that is still in school or not (well mostly for the people in) math is something that should not be taken for granted no matter how much it frustrates you.
This is a good point, and one I've been trying to make to science outreach coordinators. There is math outreach at the local level, but it doesn't seem to be very effective. I've heard that anywhere between 25% and 40% STEM majors change their major to something in non-STEM fields. I wouldn't be surprised if this number was higher at some colleges. Part of the reason students drop out of physics and engineering is because of the math involved. Like you said, everyone loves hearing about physics, but no one likes hearing about the math involved. It might have to do with the way it's currently taught. Even good high school students have trouble once they get to the college level. Professors tend to forget that most students are seeing the material for the first time, so going into more detail might be one way to get students to better understand what's going on. There are some good math channels on YouTube, but their goal isn't really to attract more students to STEM fields. They just do general outreach to inform the public about various math topics. That's essentially what DeGrasse Tyson and Kaku do when they talk about astronomy and physics. There isn't a lot of math in their videos.
Do all engineers and physicists need to be good at math, though? For those who do nothing but run computer simulations, the program is doing the math for you.
Computers can do the drudgery, yes, but we have to understand the math so we can mentally predict how systems are going to work, estimate what's going to be required (power, component sizes, etc.) and make reasonable guesses about costs and time before we even build a computer model. Besides, it's a bit scary to have a computer doing something you don't understand yourself. At least it is for me. I'm happy to use a calculator to do a tedious long-division problem, but I like knowing how to do it myself so that I know the answer the calculator gives me makes sense. If I'm not able to do that, a typo can sink a whole project.
But isn't that what the programmer is for? He/she programs the actual math the software uses, and users simply run the software without completely knowing what's going on behind the scenes. Take a simple calculator as an example. From what I understand, it uses some advanced math techniques to calculate square roots and exponents. How many users understand these math techniques? As long as we have an intuition for the answer, do we really need to know how the calculator does the actual math?
As I said, I understand these math techniques. That's why I feel confident about leaving them up to the calculator. I'm confident about leaving them up to a computer. If I don't understand what the computer is doing, how can I know whether the answers it gives make any sense? I work in control systems engineering. I deal with things like feedback loops, motors, hydraulic actuators, transducers, sensors, and so on. I understand what I'm doing mathematically, and over time, I've also developed the ability to see what my systems are going to do before they're even built. The theory gives me the ability to do that. I can watch a defective system operate and tell what's wrong with it (though my roommate/partner is much better at that than I am). In other words, through the mathematics, I've internalized the systems theory in my head. If I left everything up to the computers, I wouldn't have the first clue what to do when designing a system. I wouldn't have the first clue what's going wrong when I see a system misbehaving. That set of skills must be in the engineer's head; the computer is simply an aid that helps put the accurate numbers to engineering intuition.
Engineering and physics IS math. It's just applied math. If you want to plot electric field in COMSOL, for instance, you still need to figure out things like boundary conditions. Even chemists who run simulations need some basic understanding of dfts (density functional theory). And by the way, Mathematica was developed by a physicist.
By intuition. My roommate, who's a mechanical engineer, uses software all the time, and for many of the simulations he runs, he has to rely on intuition and experience. He has no idea how the software is actually computing the answer because there are techniques involved that he hasn't learned about. But he's still able to get accurate answers and do his job. To go back to my calculator example, if you want to find the square root of a number, how many of the methods calculators use do you know? It's probably not very many. When you calculate the square root of 12, for example, you know it's between 3 and 4, and by doing small checks like that, you can tell whether the calculator is on the right track or not. Yeah, sure. But that's not what I'm talking about. I'm talking about how software actually solves equations.
No, I mean like knowing every single mathematical algorithm used by programs. Taking the link I posted above as an example, I wouldn't expect many scientists or engineers to be familiar with all the methods on that Wiki page.
