I was trying to get my head around Russell’s paradox and found the “who shaves the barber” example not very helpful, so I was trying to come up with a more contemporary phrasing that more directly involved sets. Here’s one I came up with:
“Is the girl who’s not like other girls a member of the clique of all the girls who aren’t like other girls?”
This seems to work, because if she is a member, she is like other girls in the clique, so can’t be a member, and if she isn’t a member, then she isn’t like other girls, so is a member. With the added bonus that the paradox applies to all the other girls as well, so clique membership becomes maddeningly arbitrary, just like high school.

Is this an accurate, if whimsical, version of the paradox?

Here is the screenshot to what I'm talking about: https://imgur.com/RZCWzw1

The passage is introducing trig equations and solutions, but certain details are not making sense. First it shows a sine wave graph and and says it's from -3pi/2 <= x <= 7pi/2. But the graph shows -7pi/6 to 17pi/6. Where is -3pi/2 and 7pi/2 coming from?

Also, it says to find the solutions in [0,2pi) the solutions of sin(x) = 1/2, the answer is pi/6 and pi - pi/6 = 5pi/6. I understand how it got to pi/6, but why is it subtracting pi/6 from pi to get the second answer?

Textbook is Algebra and Trigonometry by Blitzer

Hello,

First-year PhD student here. Officially since today, I am a PhD student, and my honest reaction is: I'm scared to death.

i'd consider you all as my big brothers and expect some advices from you, my field of research is Dynamical Systems and stochastic theory.

I’m so confused and I genuinely don’t know where to start. I have a few questions for those of you who’ve been through this:

How many hours a day/week should I realistically dedicate to research, especially in the beginning?

How did you go from “I don’t even know what I’m doing” to actually making progress??

How do you read papers effectively? I open one and feel like I understand nothing, i mean the right way to attack a concept, i usually try to prove theorems all by myself, but i fail.

How do you pick a problem to work on? Did your advisor hand you one, or did you find it yourself?

How long did it take before you stopped feeling like an impostor?

Any books, habits, or routines that helped you survive the first year?

Also, a more practical question: how do you all finance yourselves during the first months? My scholarship won’t kick in for a while, and in the meantime I still need to eat and pay rent. Did you take on tutoring, teaching, side gigs? How did you balance that with research without burning out? I’d love to hear how others managed that awkward gap before funding came through.

I know some level of confusion is normal, but right now it feels overwhelming. I’d really appreciate hearing from you all

​

Bellow is my answer

According to the normal curve model, the probability of a student scoring below average is 0.5000 (or 50%). Out of the sample population of 50 students, this mathematical model predicts that exactly 25 respondents scored below the class average.

For context we surveyed 50 student on their science exam score. N = 50, sum = 3,340, mean = 66.8,

sd = 13.14

I used ai to figure it out but I think im doing something wrong. I also don't understand why the x would be our mean and is it really just this? Im not really that good at math especially for problem types that im not familiar with yet and our prof only lectured about the usual z score, area to the left, between etc type of problems. Please help or is there anything I could use as reference for this type of problems?

Hi everyone.

I’ll be honest. I’ve never really been good at math and I was never a huge fan of it. But I’ve always enjoyed it when I actually understand something or solve a problem.

My math level is pretty weak right now. But I really want to improve and eventually become genuinely good at it. I’m also about to study Computer Science + Mathematics as a double major for 5 years.

I’m interested in AI, game development, and digital forensics. I’m not sure which one I’ll choose yet, but I know I want to build a strong math foundation.

These are the math courses in my university curriculum

Calculus I & II.

General Algebra.

Elementary Statistics.

Mechanics & Vectors.

Linear Algebra.

ODEs.

Discrete Mathematics.

Probability & Applied Statistics.

Measure Theory.

Advanced Linear Models.

My high school years were pretty messy, so I don’t really know how good or complete this curriculum is.

If you’re good at math, what free resources or learning roadmap would you recommend for learning these topics properly?

Also, are there any important math topics missing from this curriculum that I should learn on my own?

And for people already working in CS. What would you recommend learning alongside the degree that is actually useful in the job market?

I’m worried that the degree might be too theoretical and not give me enough practical skills for actual work.

Thanks

I understand the geometry of things which is pretty easy, but I am having real troubles when it comes to solving problems. I don't even know what I'm being asked. I've been working on this for 4 hours now, and I am exhausted. What made algebraic proofs click for you? For me, they are just symbols that express geometry of things — but I don't understand how they even do that.

In modal logic, we have quantifiers like “Possibly” <> and “Necessarily” [].
[]P := ∀x P(x) and <>P := ∃x P(x). Given this information, what do these statements mean intuively?
1. [ ](P → Q) Λ <> (Q → P)
2. [ ] (P → Q) Λ <> (Q Λ ~P)
3. <> (P Λ ~Q) Λ <> (Q Λ ~P)

we learned the cross product as the vector perpendicular to both inputs with length equal to the parallelogram area. in 4d though there's a whole plane perpendicular to two vectors so there's no single answer, and i get that part.

what i don't get is the 7d thing i keep seeing mentioned. apparently there's a cross product there too but it's weird. is it just that you need the right kind of algebra (quaternions in 3d, octonions in 7d) or is there a simpler way to see why those dimensions are special

I stopped studying maths at around 18 years old, I stopped at calculus 1 (not all), calculating derivatives using the power, quotient, product, chain rules, and indefinite integrals and such.

I'm a bit rusty now (still able to calculate derivatives with ease), but will I be able to "catch up" if I returned to studying now that I'm 26? Will I reach the same level had I continued studying at 18 (I know it differs from one person to another, but, "typically")?

I made a scientific calculator app that has CAS (computer algebra system) capabilities, 2D plotting, 3D plotting, and complex plane plotting! Here is the app link:

https://play.google.com/store/apps/details?id=com.stimac.cascalc

I made a small game where you combine six numbers with +, −, ×, ÷ to reach a target. It’s been fun to see how different people approach it (greedy approximation vs. working backward from the target). Happy to share the solver logic if anyone’s interested.

please DM

Lowk i do need to hear some words if am i alright or utterly cooked, basically right now i go to math courses 1.5 hours / 3 days a week and it genuinely feels embarrassing to not remember basic stuff like finding common denominator when they are given in the form of expression in brackets. Once teacher explains me, it makes perfect sense and i understand it, but just as soon as i step on and try to solve/simplify other expression of the same level my brains kinda shuts off or sum and suddenly math makes no sense. I really need some help/words of wisdom of tf i shall do. Also will clarify that entrance exams will not be having any calculus just basically high school algebra

And suggest videos/tutorials, please.

I do pop-up books, and I have a tutorial I really want to follow. But the tutorial's shape and my desired is not the same. For one, the tutorial is based on a square; I need a thinner rectangle to fit into a notebook. So my question is, what's it called when you scale something up or down, and what's it called when you change its shape in addition to scaling it up or down? The problem with pop-up books, you have to keep some of the 'gears' the same while changing the areas for others. While retaining the same functions.

PLEASE suggest tutorials for this type of math

Hey guys I'm currently in my last year of high school and my math grade has been dragging down my overall average. The problem is that math is a prerequisite for some of the competitive university programs I'm applying to so I'm getting pretty stressed about it.

I've had 3 math tests so far and all my marks were right around the class average. The things that brought my marks down are always stupid mistakes (signs, degrees, missing points on a graph, etc.) and I just wasn't able to catch any of them during the tests. The frustrating part is that I put so much efforts in and genuinely understand how to solve most of the questions. So when I got my tests back, I would always be disappointed seeing the obvious mistakes I could've avoided. Is there a way to avoid this?

i am taking a quantative reasoning class as my last required credit for my associates. this class is absolutely destroying me and i dread doing another semester because i cant do math. please dm me and we can discuss details.

Had some ideas for advice on how to prove limit claims using the epsilon-delta definition, and decided to put it together into a blog post!

https://www.axiomtutor.com/new-blog/2026/10/27/how-to-make-a-rigorous-epsilon-delta-proof

Bonjour,

Quelles est la différence entre une application et une équivalence dans un raisonnement mathématique ?

Guys I am an high school student, and I have realised that I am quite interested in math, so can you please reccomend me some recreational mathematics( sorry for grammar I am not a native speaker)

So many teachers and professors say academic success often comes down to genetics. There are students who can show up to class everyday, ask and answer questions, do all problems in the textbook, go to tutoring, and more who still end up failing exams. Teachers say hard work just isn’t enough for some and they sadly can’t do much. I was one of those students growing up, and it frustrates me to put in way more effort than my peers to get worse results. Teachers tell me to give up on STEM, but I don’t want to give up. What options do I have?

Apparently I can't post on r/math for having insufficient community karma or something, and I was told I could try here-

Considering I saw someone make a post here asking how gamblers make money, I assume this kinda frustration is allowed here-

I read the Cat in Numberland as a kid- Perfect kids book to introduce the concept of an infinite hotel.

Throughout middle and and high school, I was praised at being the only person- students and teachers included- who actually understood the infinite hotel problem.

That being said, I never bought this whole: 'Uncountable Infinity,' thing.

Like, okay, fine- The diagonal decimal thing, it's impossible to count decimals because there's no end to them- They can't all fit in the Hotel.

Whatever.

So there's 2 versions of Infinity.

But then people just gloss over the rest and declare there's an infinite amount.

Huh? Since when was there more than 2? You can't just declare there's infinite because you proved there's 2.

I once saw someone give a presentation explaining the infinite and uncountably infinite hotel and he literally finished it by saying-

"There was one instance where even the Uncountably Infinite Hotel couldn't hold Everyone, but that's a Story for another time."

Huh?! You can't just end it like that! Prove there's a Third you coward!

My kid is struggling with math. Her school goes off of the Savvas curriculum. Any workbooks that are recommended to strengthen her math skills? I currently purchased the Kumon word problems workbook. We also have the Scholastics 1st grade math jumbo workbook.