It seems to me we teach kids math in a way that prioritizes mass teaching and resource management over the actual learning of mathematical concepts.

We rely on paper and pencil, and maybe some limited manipulatives like unit blocks, and there’s 1 teacher for every 15-30 kids or so.

What are some methods that might work better to establish a strong understanding of math if we were able to approach it differently?

Or what are some methods that have been proven to work in other settings and why are they able to be successful?

I'm creating the concept for a story called The Little Differences. It's about an accountant that, one day, out of the blue, notices that a certain calculation is producing a slightly wrong result. Barely noticeable, nothing world-changing,

He runs it on the computer, tries different software, a physical calculator... everything gives a result that's a little off. When he checks on paper himself, he gets the correct result. But, to his surprise, everyone else tells him that he's the one that's off, and that the incorrect result is actually perfectly sound.

I need something that makes sense, mathematically. The weird result must be something that really is wrong, and not just something that programs sometimes get wrong (I don't want it to be explained at all... I mean, the reason why it is occurring must not be something easily reducible to some well-known malfunction). But it must also be minor enough for someone to miss, something that wouldn't really cause much trouble in the real world (is that possible? IDK).

Lastly: it must be something that I'm able to explain (on some level) to a non-math reader.

So, Tildes math wizzes, what you suggest? :D

So, I just listened to a This American Life podcast called Ghost in the Machine. In one of the stories, a man decides to calculate, every week, the Average Family Location of his family. By that, he means: once you add everyone's coordinates for every coordinate in which they've been in that period, what city/location represents the average point between them all?

I decided to do the same for my family, which will be much easier because there are no touring musicians among us. The one complication is that a good chunk of the family is on other continents, and I wouldn't want us to "meet" in the middle of the ocean. So some approximation might be warranted.

I'd be happy if someone could provide me the math, I'm fairly confident I would be able to do it with a calculator or maybe put into some crude Python. I don't think I need to make a weekly report, since we're not that mobile. Maybe twice a year, or once every two months.

Thanks!

Edit: I don't know much math

Edit2: holy shit this is not simple at all! Now I feel kinda bad for throwing this problem at you guys. I really thought it would be quick and easy!

Curious if there are movements within the governance or research pertaining to the field that act to promote or suppress certain ideas? Was watching the “Infinity explained in 5 different levels” and thought… maybe there are trends for or against interpretations and/or abstractions that get a rise in people…

Do we have any mathematicians in the house? I've been wondering for a while why math is usually focused around real numbers instead of computable numbers - that is the set of numbers that you can actually be computed to arbitrary, finite precision in finite time. Note that they necessarily include pi, e, sqrt(2) and every number you could ever compute. If you've seen it, it's computable.

What do we lose, beyond cantor's argument, by restricting math to computable numbers? By corollary of binary files and therefore algorithms being countable, the computable numbers are countable too, different from reals.

Bonus points if you can name a real, non-computable number. (My partner replied with "a number gained by randomly sampling decimal places ad infinitum" - a reply as cheeky as the question.) Also bonus points for naming further niceness properties we would get by restricting to computables.

I've read the wikipedia article on computable numbers and a bit beyond.

While pondering an off-grid microcontroller project, I got to wondering: A light sensor can obviously detect day vs night. So it could be used as a very cheap way to set a device's clock - but how accurately? To within an hour? A few minutes? How would you do it?

Questions that arose from this include:

• Should it detect dawn/dusk (light <-> dark transition), or noon/midnight (brighest/darkest time) ?
• How do dawn/dusk times relate to clock time? Does it depend on lat/long?
• If using dawn/dusk, what light level threshold to use?
• The same threshold for dawn & dusk, or different ones?
• Better to detect a darker threshold (start of dawn, end of dusk) or a lighter one?
• Some days will be lighter/darker than others, so how to manage averaging of times?
• How accurate could it be made?

My naïve first stab at this would be: Pick a light threshold. Record the dawn/dusk times according to that threshold. Average them, call that "noon", and gradually tweak the clock time over several days to bring it into line with the sensed/calculated "noon" - but a searching for graphs of sunrise/sunset times quickly showed that the midpoint of sunrise & sunset is not noon.

Googling threw up lots of results for sensor lights combining a clock and a photocell, but I couldn't find anything about using the photocell to set the clock. So does anyone know if this has been tried before? Is it a non-starter for some reason?

Edit:

Perhaps it's worth sharing the project I had in mind, which is a rain alarm so I can rush out and get the washing in from the line when it starts to rain. I was thinking how annoying it would be if I left it switched on and it rained in the middle of the night and the alarm woke me up. So I decided should automatically avoid triggering during the sleeping hours of night (say 10pm to 8am). My first thought was a photocell so it wouldn't trigger when it's dark. Then I remembered that it gets light at 3am at the moment, which wouldn't work. So it needs a clock. How to set the clock:

• Manually - Needs a user interface with buttons and a display. Seems overkill just for a clock.
• Serial port - Clunky to plug a laptop in just to set the clock.
• WiFi - Needs a username and password or WPS, and an ESP32 or similar - again seems overkill just to get the time.
• GPS - also overkill and expensive.

Does there exist a function that does not include any trigonometric function in its definition that has similar properties (periodicity, for instance) as trigonometric functions? I can't think of any, and this strikes me as a bit surprising.

Edit: I thought of a simple answer: piecewise functions can achieve this!

Hello Tildes,

I am currently taking DSA in college and struggling a lot with the math and algorithms. Recently had to solve Karatsuba questions and I don't even know what I wrote down on the paper. I have been trying to look for videos on this and only really came away with a vague understanding.

What I've noticed is that I struggle with solving the math part of the questions.

For example: "Describe a divide and conquer algorithm to compute the square
of an n-digit integer in O(n log3 5) time, by reducing to the squaring of five [n/3]-digit
integers"

I have zero clue how I am supposed to understand the latter half of the question. It makes no sense to me beyond I am supposed to be multiplying squared numbers. How do I even begin to turn this into an algorithm? What is the solution even supposed to look like?

Needless to say, I've struggled with math my entire life and I've been trying for years to be decent with it, and I have nothing to show for it.

So, do you have any recommendations that could simplify the math needed for DSA? Videos are preferred but I will textbook recommendations as well.

Thank you, and have a good day!

I suck at probability, so I thought I would ask here.

To clarify, given a population of size P, a sample size of K, and an arbitrary number of trials N, how do I compute the probability of having included each member of the population at least once in the experiment?

This problem is difficult to wrap my head around. It seems like it uses a combination of combinatorics and dependent events, which really throws me off.

Edit: This problem isn't the coupon collector's problem (please see some of my responses below). Think of the coupon collector's problem as being a special case of this problem where K = 1. My question is meant to cover an arbitrary K >= 1.

I would like to get slightly more educated in mathematics again - I took some basic calculus and linear algebra classes while doing my degree, but most likely forgot what I learned for the most part. Are there any good books that you guys would recommend for someone who wants to learn math again?

So, my 5-year-old nephew is obsessed with huge numbers, especially named numbers such as googol, duodecillion, and centillion. The other day I spent some time reciting these numbers to him, and trying (and failing) to describe them. What I need are some cool facts about these numbers, such as "there are 1 quadrillion cat hairs in the world", or "there are not enough stars in the universe to fill one googol".

Besides math, his main interests are super-heroes and, apparently, cars.

I'm not a math or physics guy, so hopefully you guys can help me cheat :P

I know those are easy to find on children's education materials, but the keyword here is simple. Anything kiddie, requiring too many clicks or that takes 3 seconds is off the table.

I kinda need to brush up on my super basic reasoning. In part, because a grown man should know the time table by heart, and in part, because I wanna convince myself that I did not get brain damage after being hit by a car (there's really nothing indicating that, I'm just paranoid).

I'm looking for something simple that presents me with the multiplication table and or simple calculations to answer under a time frame. The requirement for iOS is that my computer is broken.

And it really can be super simple, even something I open from a mobile web browser or transfer to my Kindle.

Additionally: there is no need for if to be an app. A huge list of exercises (with answers) would be greatly helpful.

Thanks!