Well, I will disagree with you regarding people not complaining about those other subjects. I think most of us have heard whining from “No one talks like that anymore” (Shakespeare) to “Why do we care what happened 300 years ago” (pretty much any history, really), to the exact same thing you hear about math except applied to chemistry. As someone who tutored and taught, I heard this even at the college level (“When will I ever use the Ideal Gas Law or solving an equilibrium problem?”). Same thing, except even harder to explain sometimes than using math.
I think many of the examples are satisfying, because they speak to a quality of life that even those that are complaining don’t realize they have because of the math they were taught. I was watching some of the sports today and ESPN had a segment of their Sports Science show. Now this works way better if you like sports a lot, but even if you don’t there are examples that can be substituted. Anyway, the show gets into all kinds of detailed measurements, calculations and explanations regarding amazing feats in sports. Certainly the appreciation level increases the more math and physics background you have.
But even if concepts like “moment of inertia” are beyond your educational experience, the basically math educated sports fan still is able to digest a show like that far more than they would have been able to without the standard math education. Hundreds, if not thousands of experiences like this every year add up to a quality of life that separates us from simple, relatively uneducated people who essentially lived at a subsistence level 24/7/365. Not to mention, naturally, the “specialized math” taught in high school and above that helped get us out of that existence which predominated for most of history on the grand scale. To not believe that is to think that leading an uncomprehending, vacuous life is all one needs to strive for as long as they can some live at some minimal level. I know that seems far fetched to people like @Rianthe who thought they were asking a more superficial question. But when you really think it through, it actually does represent the quality of life we lead now as compared to most of human existence.
Totally agree. Another way to say the same thing: human civilization is dominated by technology made possible only because of math. The technology ranges from an arch in a building to highways with traffic flow patterns to our most complex computers. For the portion of the population who is math-literate, all of the technology feels potentially understandable, and not like a black box that only other people know about. Why wouldn’t you want to be part of the cultural elite who understands how the world works?
My friend thinks I am a genius because I can figure out how to convert a brownie recipe for a smaller pan (exactly half the area of original pan). Yes I use math at work, but seriously? That’s a pretty simple math problem. I am glad, though slightly unnerved, that’s all it takes to impress someone!
While for many the balancing of a checkbook is a lost art, math is used frequently in everyday life. DS did a quick calculation to figure out if a mattress would fit in the back of a minivan, and DS#2 uses it when n Vegas. I recently booked a condo rental and did some quick comparisons of rates/tax/resort fees. Sure a calculator helps, but we don’t always have one, or our smartphones immediately at hand, and being able to think it through easily is a great tool.
Personally, I find the concepts I learned in calculus (not the tedious derivative or integral rules themselves but the concepts) useful in many professions too. The concepts of rate of change at a point, area under a curve, etc. can be applied to any process where one factor varies dependably on another, be it purchases of a product, the stock market, or pretty much anything in science; and experience in higher math will enrich any career–if not for the direct applications, then for the experience in logic and problem solving, as fallenchemist said.
It isn’t so much “where do you have to use math?” as it is “can I get more for my money, have more free time, and avoid getting ripped off as much if I know how to set up real life word problems and throw some math at them?”
While you don’t have to use much math in everyday life, being able to can be worth hundreds of thousands of dollars (or more) over a lifetime.
Just please, don’t every try to save more than 100% of something.
I once got something that, with all the sales and coupons, came down to $7.03, and then it printed a $10 rebate. So I did get more than 100% off!! They paid me to buy it!
And to @fallenchemist 's point … no knowledge is useless. Even Rocky and Bullwinkle is lots more fun if you know what is the “Ruby Yacht” of Omar Kayyam.
Even - or especially - in engineering, I think the real value added parts are in streamlining old processes and in new invention. Both of these call for clever juxtapositions of existing and original ideas - and the arts regularly confront us with the exactly that.
Wow, that jogged an old memory and story. When I took calculus in my senior year of high school (back in those days it was a big deal, not like today where many take AP Calc AB or even BC as juniors!), I didn’t do so well. Yes, there was a girl involved, what can I say. But it did mean that I took Calc 101 as a freshman at Tulane, i.e. started over when it came to calculus. Well, I came to class with my notepad and pencil all ready to go. But then the guy started the lecture, and I just sat back and listened. My test results the previous year notwithstanding, I had learned a lot more than I realized. Upon hearing it again, I was able to really focus on what was being explained, not just memorize formulas and problems. I not only completely aced the course, I only had to work about half the assignments since it just made so much sense now. That pretty much carried over to Calc 2 next semester, although I worked more of the problem sets, about 75% of them. Got in a bit of a tiff with my prof over that (I didn’t realize he was counting homework towards the final grade) but I prevailed since I got nearly 100% on every exam.
The physical reality of what the math described really took hold. That not only made all the other math courses I had to take much richer and easier, but it allowed me to do much better in physics as well. The capper on the story is that my physics prof sophomore year threw in a question every weekly quiz designed to be at the very edge of what had been covered, to see if people really understood the concepts instead of strict memorization. Often that meant being able to set up the solution because you understood how the whole thing came together in the real world, and solve it for the correct numerical result using calculus that everyone was supposed to know because by then everyone was supposed to be through at least Calc 2 and into Calc 3. But most stumbled on that part and only got partial credit for setting it up right, if they did that. I picked up at least 100 extra points during the semester because I was able to apply the right math to the problem at hand and get the correct value at the end. Took me from a B to an A-. It was a tough course.
Was it ever something I personally had to apply outside of school, per the OP’s question? Admittedly rarely in a very direct fashion, since my career didn’t involve those sorts of physics or engineering issues. But as I stated earlier, I sure do appreciate the work of others at a much deeper level than I would otherwise, and that really is quite satisfying. Anyway, thanks for the shove down memory lane. My kids now hate you just a little bit.
@fallenchemist I’ve had the opportunity of directly applying calculus in physics as well in the lab where I work. Sometimes I have the rare privilege of applying something I learned in physics or calc right after learning it! So learning the concept behind all the tedious math is really important.
The main reason I went into structural engineering was that I loved the idea of using math to create buildings! The field is a good mix of using theoretical math and practical skills. Whatever I draw has to be proven to be correct by mathematical calculations, but it also has to be buildable! Very challenging at times.
I have a brother who was raised in the era of calculators and never had to memorize times tables or really understand the way numbers work. He’s really bad at it. He could never figure a 15% tip, so always leaves 20%, or about that. He can’t tell if something isn’t right with a bill, so just pays it. I have a daughter who isn’t great with numbers either, and when we were Christmas shopping couldn’t figure out which coupon was best to use. Is $15 off $50 better than 20% off?
Either will pay just about anything someone tells them to and they have no idea if they are being overcharged or getting a deal.
Our minds use math even when we don’t realize it. There is a reason musical notes are in quarter notes and eighth notes. And think of great works of art: so many of them use that golden point of one third, where the focal point of the picture is one third of the way on the right or left of the painting. Look at a great work of art and count the focal points, divide the painting into triangles: it’s not an accident.
In home decorating, our eye approves of the artwork in the space over a fireplace or sofa if the art takes up about 2/3 of the space.
Most people who part their hair part it one third of the way over from ear to the other or they part it exactly in the middle. (A man who parts his hair 10% of the way up his head is probably trying a comb-over.)
And lastly, odd numbers. Most things grouped together look better as groups of 3, 5, etc. Look at a flower arrangement that you like and count the focal points.
Our minds recognize that everything is numbers in one way or another - sure, science and engineering. But also music, art, and philosophy. I had a professor who said God had to be a Trinity - it wouldn’t make sense otherwise!
@Rianthe I’ve been asked this question a lot. Besides what’s been stated above (granted, I haven’t read all of the posts), here are some applications:
You basically need to be familiar with working in other bases (particularly 2 and 16) to study CS, as a low and a high voltage encodes 2 values (hence, binary).
Linear programming (sometimes introduced in Alg2 or Pre-Calc) is a huge question in computer science, and lots of algorithms have been developed for solving LPs (simplex algorithm, ellipsoid method). Finding the best solution to integer LPs is NP-hard.
Building/bridge/road design calls for plenty of algebra, trig, calculus, and physics.
Using vectors and vector-valued functions when designing video game animations.
Oftentimes when writing a program, instead of repeating or hard-coding stuff, using recursion saves you a lot of time.
5a. Sometimes solving the recursion leads to an easy solution.
Notes on a keyboard follow a logarithmic scale. For example, A above middle C is tuned to 440 Hz, while the notes one octave higher and lower carry frequencies of 880 Hz and 220 Hz. A lot of professional musicians I know know this.
Modular arithmetic and the concept of an inverse modulo m is used in RSA encryption. Note that factoring large numbers is still hard.
