Most of the math I do at work is related to compound interest. Of all the math I believe the general public should understand, the concept of how paying interest to others is a total screw would get my top vote.
I have a co-worker who took out a car loan last week at, wait for it, FIFTY THREE PERCENT INTEREST! No concept of what that was costing her. She could only see, "I can afford the monthly payment."
(1 + r)^n and its friend 1/(1 + r)^n have been the two most important concepts in work and personal life that I've ever learned and applied.
Stokes' theorem. Almost the same thing as the high school one. It generalizes the fundamental theorem of calculus to arbitrary smooth manifolds. In the case that M is the interval [a, x] and ω is the differential 1-form f(t)dt on M, one has dω = f'(t)dt and ∂M is the oriented tuple {+x, -a}. Integrating f(t)dt over a finite set of oriented points is the same as evaluating at each point and summing, with negatively-oriented points getting a negative sign. Then Stokes' theorem as written says that f(x) - f(a) = integral from a to x of f'(t) dt.
It's the most general form of Stokes' theorem that the integral of a differential form over the boundary of an volume and the integral of an exterior derivative of this form over that volume are the same. It covers a lot of classic formulas from the fundamental theorem of calculus to Green's theorem, Gauss' theorem and classic Stokes' theorem.
As an Applied Mathematician I feel both seen and attacked by this. At least I get to play with novel analysis because the company I work for is pretty niche.
It always gets mez the older I get I better realize how Jank my education was,
Elementary school taught me addition,
Middle School Taught me multiplication
Junior High Taught me pre-algebra
College is teaching me addition, but with common core
One day, maybe for my bachelor's I'll learn some of those funny math symbols.....but not today
I did advanced mathematics and chose physics as one of my elective subjects in school. Nowadays, I do a lot of work based around analytics and forecasting.
"We need to find the average of this."
"That's easy. I'll do some more advanced stuff to really dial in the accuracy."
"Awesome. What's the timeframe?"
looks at million row dataset "To find the average? Like a month. Some of these numbers are mispelled words... Why are all these blank?"
"Oh, you'll have to read this 45 page document that outlines the default values."
And that's how roffice maths works. Lots and lots of if conditions, query merges, and meetings with other teams trying to understand why they entered in the thing they entered. By the time the data wrangling phase is complete, you give zero fucks about doing more than supplying the average.
Yup this is every job now. Wrangling numbers. The actual job or calculation could be done in days if less. But dealing with dirty information and playing detective which isnt even part of it is the sink hole of every job right now.
Until it introduces a bunch of mistakes of its own. AI as a test has failed in several industries before now. It’s been around much longer than you’d think and has been tested in the BG for a lonnng time with much fail to the result of disgust if you even bring it up. It’s nothing more than a novelty in writing that doesn’t require the need to run on tight, non rational numbers. Something of which no binary based, household (and most industry) computer is capable of.
Look up the Ariane 5 rocket disaster. It is the summary of floating point error that can result in disaster. This is the limitation that is present in all standard computers you’d be accessing today since the 1930’s.
(Also referred to as round off errors or truncation errors in avionics because of how common irrational numbers are in spatial navigation.)
That's software development for you. Why is that weird value there? Because some guy, at some point, had checked for that and somehow it's still relevant.
I know of a system that churns through literally millions of transactions representing millions of Euros every day, and their interface has load bearing typos (because Germans in the 90s were really bad at the Englishs).
If Timmy has 45 pages to read on a bus traveling an average speed of 35 mph with an mean stop distance being 0.7 kms how many stops will Timmy pass before this fucking meeting ends ?
Oh, sorry the 45 page document is for something else. The only person who understands this dataset is Dave and he was made redundant 5 years ago. Anyway, can you get this done today?
Geez, that reminds me of a former colleague that, when asked for "the numbers," would just send screenshots of tables in the ERP system instead of exporting them to a spreadsheet. What's even worse, usually a lot of values were plain wrong, on one occasion more than half of them.
You mean mathematical examples? Or like examples of analytical outcomes? Keeping in mind the more analytics-heavy, the more it involves lots of sources, patterns, variables, and scenarios, but I could provide just a single example.
Edit: Oh, wait. If you're referring to just averages... In forecasting I prefer, as a minimum, to do weighted averaging. This is where I'll have a certain time period of cumulated historical data that provides a more stable base, however more weight is applied the more recent (relevant) the data is. This shows a more realistic average than a single snapshot of data that could be an outlier.
But speaking of outliers, I'd prefer to also apply weight to outlying data points that may skew the output, especially if sample size is low. Like 1, 2, 2, 76, 3, 2. That 76 obviously skews the "average".
Above that, depending on what's required, I'll use a proper method. Like if someone wants to know on average how many trucks they need a day, I'll utilise Poisson instead to get the number of trucks they need each day to meet service requirements, including acceptable queuing, during the day. Like how the popular Erlang formulas utilise Poisson distribution and can kind of handle 90% of BAU S&D loading in day to day operations with a couple clicks.
That's a basic example, but as data cleanliness increases, those better steps can be taken. Could be like 25 average last Wed vs. 20 weighted average over last month vs. 16 actually needed if optimised correctly.
Oh, and if there's data on each truck's mileage, capacity, availability, traffic density in areas over the day, etc..obbioisly it can be even more optimised. Though I'd only go that far if things were consistent/routine. Script it, automate it, set and forget and have the day's forecast appear in the warehouse each morning.
And yet such simple things are often incredibly hard to get done because of poor data governance or systems.
Linear algebra (ex: multiply the matrices A and B), multivariable calculus (example: find ∇F with F=[xy,yz,xz]^T ), or actual "multidimensional analysis" (example: define the norm of [1m,1m/s,1m/s^2 ] in a way that makes sense)? I can help with all three.
Sounds like fun! I'm going to bed soonish but I'm willing to answer questions about multivariable calculus probably when I wake up.
When I took multivariable calculus, the two books that really helped me "get the picture" were Multivariable Calculus with Linear Algebra and Series by Trench and Kolman, and Calculus of Vector Functions by Williamson, Crowell, and Trotter. Both are on LibGen and both are cheap because they're old books. But their real strength lies in the fact that both books start with basic matrix algebra, and the interplay between calculus and linear algebra is stressed throughout, unlike a lot of the books I looked at (and frankly the class I took) which tried to hide the underlying linear algebra.
Thanks for the offer! The exam is tomorrow (today is another) so there isn't a lot of time to prepare anymore. I'll just be writing a page of notes that we can take to the exam as a cheat sheet. Still, if something comes up, I might just ask you.
I was denied a mathematics education, for real. I can't even do long division, nevermind that squiggly F shit. I thought that stuff was only for astrophysicists.
I want to learn basic maths, but I'm in a 'learned helplessness' mindset where I can't even get through basic sums and equations intended for children (I'm old as fuck now).
I was diagnosed with autism a few years back, which kinda made no sense. I would have expected rainman powers, but numbers just don't jive with my cunt of a brain. Maths is as inscrutable to me as people's faces or social cues.
You might also have discalcula, which is a real but somewhat uncommon thing where you're absolutely shit at math. I have no idea how to get tested for it though.
If you actually want to learn maths (that is, if you're not just venting), you could try to ask for help in dedicated math or teaching communities.
The problem with teaching stuff you know, is to put yourself in a position of actually not knowing anything. I'm a software developer and had to teach some apprentices a few years ago, and it was really eye opening to me to see how much assumptions about the apprentice's knowledge I made even though I thought I made my explanation "basic".
It's quite possible that all the tutorials you've read are either for literal children, so they just don't work for your adult brain, or they're intended for adults and assume too much.
On a personal note: how did you get into that situation? Were you home schooled?
I transferred schools in the middle of 10th grade, and the new Algebra class I landed in was several chapters ahead. I never caught up, but the teacher passed anyone who turned in literally anything for homework so I did that.
Now in my 30's I'm getting into indie game design, and I need that gap filled so I can write the code I need. So I went to the local thrift shop and picked up a couple old textbooks (since it's safe to assume that nothing groundbreaking has happened in the field of basic algebra in the past twenty years) for fifty cents and I've been working my way through them. I don't understand everything that's happening, but I'm pushing ahead with the faith that somewhere along the line things will "click".
You might enjoy Freya Holmér's videos - I mostly know her for her excellent mathsy video essays, but she has loads of videos about "maths for game Devs" that might be useful.
Pretty much anything dynamics related. Starting basic displacements, velocity, acceleration integration for simple dynamic systems to more complicated equations for wind and spinning rotor interaction induced vibrations in wind turbines.
If you do not work with dynamics, for statics there are still a lot of encounters with deferential equations. Euler-Bernoulli Beam theory or plate and shell theories can be used for times when you want to solve more complex problems for which predefined equations do not exist and you do not have access to expensive fea software.
You can always try to pivot from project management to actual engineering. I am load engineer for wind turbines and everything is time dependant and dynamic. For past 10years i use every bit of math I learned is school and uni.
I recently had to do linear algebra for the first time ever irl. I’ve been out of school for ~15 years. I was trying to make a rotation matrix to transform some points in 2D space. It took me a very long time to remember how it’s performed yet alone “transformation matrix” which is something I’d never heard of before. I got my code all working and was so proud, then later found that one of the r packages I was using could have just solved it all automatically :/
