Hi guys. Since these are my vacations, I'm planning to study a bit more. Please suggest some pre-algebra or middle school to beginner high school free math courses.

Most people online instead of using metric or imperial measuring system say "that's {} Mount Everest, {} Burj Khalifa, {} empire state building {} Eiffel tower, {} statue of liberty tall"

Have you ever used a statistic to form an opinion or win an argument? If so, are you aware of how easy it is to misinterpret one? Some of you may have heard of the Prosecutor's Fallacy; other readers, fasten your seatbelts, because you are in for a shock.

The fallacy is confusing the probability of A given B with the probability of B given A (A and B are events). P(A | B) denotes the probability of A given that B has already occurred.

Suppose a disease affects 1% of the population, and the doctor uses a test that is advertised as 95% accurate. You test positive. What's the chance you actually have the disease? Most people say 95%. The real answer is about 16%. Out of 10,000 people, about 100 are sick and 95 test positive; of the 9,900 healthy people, about 495 also test positive, so only 95 of the 590 total positives are real. You've confused P(positive | disease) with P(disease | positive).

Okay big deal! This looks like another useless mathematical concept I'm not gonna use in my life. How does knowing about the prosecutor's fallacy affect my life? Because it is so, so easy to commit the prosecutor's fallacy.

Here's an example with real-life consequences. Per the U.S. Sentencing Commission, about two out of three people sentenced for robbery between 2021 and 2025 were Black. Some people let that color how they see every Black man they pass on the street. Same fallacy: confusing P(Black | sentenced for robbery) with P(sentenced for robbery | Black). The stat says nothing about what fraction of Black people commit robbery, which is tiny; almost none do. The statistic can be correct and the conclusion completely wrong.

This is just one of many statistical traps, alongside selection bias, Simpson's paradox, and mistaking correlation for causation. So how sure are you that every statistic you've used to form an opinion was interpreted correctly?

"I understand this," "my opinion is rational," "my worldview is supported by evidence." Once an opinion becomes part of our identity, we stop questioning how it formed. We accept statistics that support us and attack those that challenge us. A misunderstood statistic becomes a belief.

The lesson isn't that statistics are useless; it's that confidence doesn't guarantee correctness. Don't just question the information in front of you. Question the mind interpreting it.

Math over Biology ex biology addict who kicked maths to become doctor but physics showed him his place . Due to trading and doing stuff getting money maths especially statistics perm comb tables and lots of concept I can't term helping also today went for health checkup ...

It was same again eat this medicine you get fix or come again .

When I wanted historical pointers , discrete weightage and offcourse simulated correlation and variance because I ain't a liar - I wanted a option for that kinda treatment while clinical is addon for best case worst case only shit.

If I originally had planned to say the number 0 repeatedly forever, but all the sudden in the middle of my plan decided to say the number 1, would that be a truly randomized sequence?

i always thought i enjoyed maths and it’s my favourite subject at school. i enjoy learning new topics and i get excited when a solve a difficult problem that required a lot of thinking, it feel satisfying. but recently i’ve been wondering if maybe i just like maths for the logical process. i am the worst student in my class and i feel the others always ask better questions, questions that are more intriguing or that involve deeper thinking, whilst i’ve been questioning if i just enjoy it for the patterns and logical steps to get to the answer.🥲 i also want to continue maths at college but i feel like i’m just not capable. this school year has been difficult for me and i’ve struggled a lot but i have a solid plan to study maths at univeristy and my ambition is that i will get there one way or another. 💪🏻however, i always feel so fascinated by researchers and their work and i find academic lectures so inspiring. i especially admire those who absorb the new knowledge quickly and wish i could be like them. am i a fake maths nerd? do i just enjoy maths for the superficial part? 💔💔

I'm trying to calculate the probability that N people will have at least 1 evening free (For a meeting, or DnD or something)

You can assume that all people have x committed evenings already.

For Example, 2 people who have 3 evening commitments will have a 100% probability of finding 1 mutual night free, but what's the probability that 3 people who all have 3 evening commitments have at least 1 mutual evening free, or 8 people with 2 evening commitments etc.

Hello guys I am a second year bsc maths student from mumbai and have to submit a field project for the same to qualify for next sem is there any expert who can give me some ideas and guidance

A discussion I just read on a random thread:

He has 170 employees? That's a bloody massive number.

Not as big as 171

In fact, most numbers are bigger than 170

I think that there are more numbers smaller than 170 if we include negatives 

There's an infinite number of numbers less than 170, and an infinite number of numbers greater than 170.

Yes, but negative and positive infinities are equally big, but since we have moved the point to 170 negative infinity will be bigger as it will have all negative infinity plus some of the positive one. // I know that mathematically I'm wrong

This has made me think - are there actually "more numbers" less than 170 (or any other positive number) than there are greater than it? Or not?

3rd-year BS–MS student here!

My 5th semester will probably start in the first week of August. I'd love to connect with people taking similar courses so we can study together and discuss concepts.

The courses I'll be taking this semester are:

• Real Analysis I

• Elementary Number Theory

• Group Theory

• Advanced Linear Algebra

Looking forward to connecting with like-minded people for group study or for any discussion!

There are an infinite number of numbers. You can take those infinite numbers and slice them into an infinite number of infinite slices each of which can be sliced the same way ad infinitum.

i know that some of these are the same but which one(s) are worth my money even if i buy them more than once? also please tell me how you worked this out so i wont ask again.

context: starting a business and need 1cm wooden blocks as part of the business. need to save money by buying cheap and working smarter not harder.

Hey

I'm working on a spatial statistics problem in a social science context (electoral geography, small rural municipalities) and I've hit a gap in the literature I'd like a sanity check on before attempting to build something myself... or just taking a burn out mandatory break T-T

I'm computing local Moran's I on compositional vectors (vote shares across several categories, transformed via CLR/ILR to handle the compositional constraint) attached to spatial units of very unequal population size, some with fewer than 100 voters, a few with several thousand. Small units have much noisier vectors than large ones, purely due to sampling variance, which risks producing spurious "clusters" driven by noise rather than genuine spatial structure.

Assunção & Reis solve exactly this problem for a single variable: they standardize each observation using a population-dependent variance estimate before computing Moran's I, so small units are appropriately down-weighted in the significance assessment without ever altering the observed rate itself.

BUT IT IS UNIVARIATE !!!!

I need the equivalent for a vector (7 dimensions) variable (multiple correlated proportions per unit, not a single rate). As far as I can tell, no published or implemented multivariate extension exists... which is a bit of a problem

My rough idea : use the known closed-form sampling covariance of a multinomial proportion vector, propagate it through the CLR/ILR transform via the delta method, then "whiten" each unit's vector by its own estimated covariance before computing a multivariate local Moran statistic.

Ngl i'm 100% out of my depth. I feel like I don't understand what I'm doing anymore.

My current concerns :

• Covariance estimates become ill-conditioned near near-zero components (structural zeros handled via a population-anchored epsilon of 1/(2*pop))... and I have quite a few instances of this
• No existing implementation to validate against. I'd be building and verifying this alone... which would be a first for me
• Estimated at several days of work with real risk of subtle errors I wouldn't easily catch and since I don't have any bleuprint for it, I don't even know if I'll be able to catch my errors

My main questions are the following :

• Does a multivariate version of this kind of population-based empirical Bayes correction already exist under a name I'm missing?
• Is the delta-method/whitening approach above sound, or is there a cleaner formulation (maybe treating this as a multivariate GLS/Mahalanobis-weighted Moran rather than a whitening step)?
• Any known pitfalls in applying this to compositional (CLR/ILR-transformed) data specifically?

I didn't sing up for this when getting in my studies lmao (i'm not even in maths ! xD )
SOS

What would you do ? How would you answer this issue ?

I feel like I'm loosing my mind and I don't have the month necessary to build this as the thesis dead line is in september (yeah i'm late as f...)

See above, late night stoned BC musings

I recently started studying real analysis, and learning about Cantor has completely changed the way I think about infinity.
It's incredible how one person's ideas reshaped mathematics so profoundly. I'm genuinely fascinated and deeply grateful for his contributions.
The more I read about Cantor's work, the more I appreciate the beauty and boldness of modern mathematics.

I’m not sure I understand how undefined numbers work when applied to a level of confidence/certainty. Is it both as close to 0% as it is to 100%? Could you say you were 99% certain if your certainty was undefined?

The problem that gave rise to my question is “Even if you identified something you felt certain about, how would you verify that your feeling of certainty is reliable? You'd need to be certain that your certainty-detecting faculty works…” I was wondering if the value for how certain you are that your faculty is reliable is undefined.

Hey I have skipped or forgotten most of the maths i did in 11th and 12th for jee, somehow got in hech college and skimmed through it without even knowing proper integration, now I do genuinely want to get back from it to get into my masters so what all topics i must absolutely cover for me to get in ml and programing also some physics i want to get back in the game cause my dream was physics education.Now in covid i really messed up( it isn't Covid fault bit mine alone i could've studied by myself in covid times ) but please what topics can I study in 2 months in order to get back i know it's not possible to get very good but just want to cover everything I can.

Thank you.

⭐If you had a year in between A Level Maths and university maths⭐
I would really appreciate hearing about your experience!!

- I have a place to study a joint honours in maths and philosophy next year at uni, after taking a year out this year and taking a break from maths.
Im wondering how different the content is and what would be worth recapping as Im very aware I will have forgotten a lot of what I covered in A level maths last year.

This is causing me some anxiety as I dont want to feel behind my peers who will mainly have it fresh in their brains from year 13, and I want to give myself a head start so it will be more enjoyable to learn!
Thank you so much🙏
(message from my friend)

Any recommendations for good discrete mathmatics book to start learning from scratch

Hi, i'm 19, i'm italian (sorry in advance for any possible mistake) and in about 7 days i'll graduate from an economics school.

The fact is that, since i was 3, i LOVE maths, i almost always scored the maximum grade on maths tests (like either a 9/10 or a 10/10), but i have doubts about studying this subject at University because i never actually studied it at home, i just found it interesting during the lessons, adding the fact that i feel naturally gifted for these kinds of things.

Also, my maths teacher reccomended me to follow this path, since she understood my skills, and told me that i won't have to study by heart, and that i'll just have to figure out how to do certain things.

Basing on these things, focalizing on the fact that i never studied at home and so i still don't know how to do it, should i take the decision to study Maths at Uni? And if much study at home is required, is it more memory or logic/understanding based? Thanks.

There are 34 multiples only of 2, 17 multiples only of 3 and 16 multiples of both 2 and 3 (in another words 16 multiples of 6)

I know that the sum of differentiable and continuous functions is a differentiable and continuous fonction.

I also know that an infinit sum of differentiable and continuous functions may not be differentiable (Weierstrass function for example).

But can we have an infinit sum of continuous functions that is not continuous ?

so basically i am going for bsc physics but the real problem here is my maths cause i did not have maths in my 12th i did not studied it either much but we all know maths is kind of language in physics ...i like physics and the same goes for maths but i did not take it as my sub in 11th cause my father was kind of obsessed with doc ...so i used to be kind of ok ok in physics but after my 12th i had a drop cause my health worsened and all but now i am ok and i got in college for bsc physics on my 12th marks based but i do remember few things but i think i have to thorough of everything in physics too i have a whole month from now for free time or for to do atleast the basics and then i will try to continue it with my first year as it starts - my situation where i stands even though its underwater

so acc to what level should i even know like should i try to study

watching lect or books or teachers ...any advice suggestion please reccom here for this beginner like whatn should i focus on - Trigonometry ,Basiic algebra,Functions,Differentiation,Integration,Vectors

Does anyone have a formula sheet of different 3D and 2D shape's volumes, areas and surface areas? Would be much appreciated.