Why do we use n+1/2 for finding the median of a number,(what is the point of adding the 1?) whereas with a cumulative frequency diagram, we just do n/2? What does discrete and continuous data have to do with this if sometimes cumulative frequency (of whatever) can be discontinuous?

Hi everyone,

I've been building QED because I found that learning proof-based math has a frustrating gap: getting explanations is easy, but getting enough structured practice is hard.

Most students end up with a mix of lecture notes, random exercises, and chatbots — but there is no clear overview of:

- What topics you have mastered

- What you should practice next

- Whether your reasoning is actually improving

- Which types of mistakes you keep making

QED is designed as a dedicated practice environment for proof-based math.

It includes:

• A growing question bank covering logic, sets, relations, functions, induction, graphs, combinatorics, probability, linear algebra, calculus, and more

• Learning paths that guide you from fundamentals toward harder exam-style questions

• Freshly generated questions at different difficulty levels, so you don't just memorize a fixed exercise list

• A personal library where you can save, revisit, and retake questions

• Exam-style grading that looks at the reasoning, not just the final answer (for example, identifying missing justifications in a proof or incomplete counter-models)

• A proper mathematical editor for notation like ∀, ∃, ∧, →, ⊨, truth tables, and formulas

The goal isn't to replace learning with an answer generator — it's to create the kind of deliberate practice environment that is usually missing in proof-heavy courses.

I'd love feedback from students!

- What features would actually help you practice math more consistently?

- How do you currently organize your proof/discrete math practice?

- What makes you feel like you're improving in a difficult math course?

If anyone is interested, you can try it here for free:

https://qed-math-trainer.com/

Thanks!

Boa noite, sou estudante do 1° Ensino médio e percebi que preciso melhorar em matemática, e gostaria de fazer isso do zero. Alguém pode me indicar livros para aprender de fato? (Isso incluí geometria também)

Solo dev, evenings only. It's a web game — no install, no signup, you're playing in 5 seconds: https://abako.games/?src=reddit_sideproject_v1

The pitch: mental arithmetic, but built like an arcade game. Neon CRT look, chess.com-style rating (every problem moves your ELO), a daily puzzle with one worldwide seed, and ghost duels: at the end of a run you get a challenge link, and your friend races your replay at your actual timings.

Start with ARCADE mode — that's the core loop, and it's what my two questions are about:

**1. The difficulty curve.** Does Arcade get hard too fast? Too slow? Just tell me the problem number where it stopped being fun (or started). One number = gold for me.

**2. Would you come back tomorrow?** The daily puzzle is my whole bet on day-2 retention. If after one session your honest answer is "nah", I'd rather hear it now than build the wrong thing for a month.

8 days in: ~120 players, decent activation, but almost all from my own network — so I genuinely can't see any of this from the inside.

Trade offer: reply with your project and I'll actually use it and give you the same kind of specific feedback. No drive-by "looks great!" — I'll tell you where I got confused or bored, with details.

I've seen a lot of posts discussing how Levent Alpöge (X: @__alpoge__ ) used Fable to find a counter example to the Jacobian conjecture. But I can't seem to find a satisfying answer to the question: why is this conjecture significant?

In other words: now this has been disproven, so what? What are the *concrete* implications?

I have enough maths knowledge to understand the conjecture. I know what a polynomial is, multivariate polynomial, Jacobian, matrix determinant. I read part of Terrence Tao's post [ https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/ ] linking this to the fundamental theorem of algebra, which is interesting: every multivariate polynomial function has polynomial Jacobian, and therefore polynomial Jacobian determinant, if this determinant is everywhere non-zero then it must be a constant (otherwise by FTA it would have at least one complex root). I understand that the interpretation of Jacobian determinant is local change in volume, and if this is zero at some point then volume "collapses" at that point. So a polynomial with non-zero Jacobian determinant basically has a constant effect everywhere on volume, it doesn't expand volume in some places and shrink volume in other places unevenly. And this counterexample basically says, a function can have a constant non-collapsing effect everywhere on volume, but still map 2 distinct points in the domain to the same point in the image. So although the function's *Jacobian* is everywhere invertible (because it has non-zero determinant), the function itself is not. But I don't understand why this is significant/what are its implications.

Scarlett is playing a video game. She spends \[900\] minerals to create \[18\] workers. Each worker costs the same number of minerals.

Write an equation to describe the relationship between \[m\], the amount of minerals, and \[w\], the number of workers.

The model answer is m=50w, but doesn't that mean one mineral gets you 50 workers? I put 50m=w (50 minerals for 1 worker, no?) into the equation, but it says thats wrong. Please help, thanks

I’m a rising senior and I’m starting linear algebra next year after doing calc BC junior year. I want to study ahead but don’t even know where to start or really what linear algebra even is and I fear the difficulty will consume my senior year..

My school doesn’t have any course guide or description for the class since it’s technically an elective advanced math, but if anyone can give some sort of unit guide that I can look into or something to help me figure out what this actually is that would be helpful.

also I plan on majoring in aerospace or mech engineering

that’s all. thanks

Any resources or advice that helped things "click" for you?

Hi everyone!

TL;DR:
I've written a proof on a very basic question and would love some feedback on it.

[EDIT: Users helped me rewrite my proof. Check it out here: https://www.reddit.com/r/learnmath/s/JdrurW60qW . Still, I'd appreciate your comments to help me learn more.]

The backstory:
I've recently started to relearn math (I have a biology BSc with a math-focused high-school training) and I decided to start with Serge Lang's "Basic Mathematics" for two reasons: (a) it's comprehensive on the precalculus side of things, and (b) English is my second language and I need to learn how to "talk math" (and I realized this book was very approachable for me).

Now, I'll get to my actual question.

In chapter 3 of the book (Real Numbers), section 2, exercise 4, this question is presented:
Prove: If a, b are positive numbers, then √(a/b) = √a / √b.

And I've proved it in the following way.

Proof [now edited to have the proper power: ^(1/2) instead of ^(-1)].
If a, b are positive numbers, then 1/b is positive and a × (1/b) = a/b is also positive.
Since a/b is positive, we have |a/b| = a/b and, therefore
√(a/b) = |(a/b)^(1/2)| = (a/b)^(1/2) = (a^(1/2)) / (b^(1/2))
which yields
√(a/b) = √a / √b
thus proving our assertion. ("Q.E.D." here, I guess?)

So, my actual question:
Does my proof follow the proper logical steps and rigor that a proof needs? Would this be considered a "correct" proof? If not, what do I have to focus on?

I realized that practicing to write a proof with these fundamental concepts (which are basically ingrained in my brain after 16+ years of school) would be a good place to start because I know the answers. That means I kind of have an internal compass that can help me correct a mistake.
If I'd started to practice proofs with higher-level math, I wouldn't know where to start and where to go (I'd become cotton-eyed Joe!), especially because I'm self learning and don't have any mathematicians within my circle that I can just "hit up" and have them answer my questions. That's why I'm here.
(Is this way of thinking solid?)

So, my questions, in summary:

1. Is my proof correct? Does it follow the proper "form" for a mathematical proof?
2. Am I missing something gigantic which I can't pinpoint because I'm relatively out of practice?

Thank you in advance!

P.S. I tried to provide screenshots of both the question and my proof, but Imgur seems to have some internal issues (at least in my region). Sorry if the math is hard to read.

P.P.S. Speaking of the hard-to-read math, I tried getting in-line math working here, but I couldn't write it in a LaTeX-looking format. Sorry for the inconvenience and I'd appreciate a resource that would help me write the math with LaTeX in my future post.

Apologies for this sort of semi-vent-esque post that i'm sure isn't uncommon here, but this has kinda been eating me up for the better part of my life. I promise it does have to do with how to work through math problems.

I'm in uni right now pursuing two humanities bachelors degrees, but as they're both a bit interdisciplinary (one requires statistics, the other just basic math) I can't entirely avoid math, though I've wanted to for a while. Right now I think I'd like to try being at least DECENT at math, but it's much harder than i thought. I failed a super basic unit conversion homework set in a gen-ed science class and am questioning how to get out of this.

I've always been someone who claimed to hate math since i was a small kid, as for whatever reason i struggled with it since elementary school. my childhood definitely didn't help as i got in trouble for grades less than an A, and therefore started to cheat on math tests in fourth grade to not get in trouble with my parents, as i'd typically score less on those and excel in other subjects. so. definitely missing something there...

i got put into advanced math later on as well even though i was definitely not ready for it (i have no clue how this happened) and i ended up failing. high school was a drag but i made it through, and simply did not take calculus like all of my friends. definitely felt insecure about that. got a c in precalc in college which i felt pretty shit about, but i at least dont need to touch anything like that for the rest of my degree now. statistics was OK, but it was a very basic level.

with all this context in mind, when i try to solve any math problem now- including BASIC multiplication or division at times- my mind goes blank and i'll start stuttering or panicking a bit. it's worse if it's among other people and they ask me to like. calculate splitting a two-item order or something. and the thing is, i know i CAN do math. i got everything right on a recent unit conversion homework, unlike the first one i failed. i was out studying with a friend that time, maybe the calm environment helped. (important note that i do have generalized anxiety lol so its prob related)

overall: if anyone has similar experiences as me with this sort of mental block or advice/steps on how to work through it and feel comfortable with doing math, i'd appreciate it. i actually do want to maybe take calculus later in life when im not so busy, and try and just learn it at my own pace without stakes. but for now i think i need to stop freezing up when i see simple problems on open-note-calculator-allowed-tests or when my friend just asks me to divide the cost of a simple order in my head. i think it's ultimately the fear of being wrong combined with not internalizing building blocks since elementary, but if anyone else had thoughts please let me know. this post is so long because i am sadly a bit embarrassed to talk to my friends in STEM about all this.

How can I motivate myself to do math exercises? Because Im really lazy

hi. i’m currently working my way through calculus stewart (9e) and i’m enjoying it a lot. i can do the problem sets just fine, it’s the “problems plus” sections where i get humbled hard. i can do a couple of them, but with the majority i just get stuck. do you have any recommended readings, strategies or tips to be able to tackle these problems?

Hi, I'm at 11th grade and want to participate in a local math olympiad. My goal is to have alternative career opportunities in the future. The problem is, I've always been better at humanities, and now I feel lost, not sure where to start. The program is huge, and it's nothing like what I'm used to being taught. What would you suggest? What kind of structure should be followed?

The problem starts with (N) balls of n different colors. At each step, two balls are chosen at random, and the first ball is recolored to match the second ball. The process continues until all the balls are the same color, and the goal is to find the expected number of steps this takes.

The solution focuses on one particular color and lets (i) be the number of balls currently having that color and uses a transition graph, and I understand that transition equation. But I don't understand how they calculate the transition probabilities:

They condition on which color eventually becomes the final color and use symmetry between the colors to calculate certain conditional probabilities.

In particular, I don’t understand how I’m supposed to know the probability that a particular color eventually wins given that the next step changes its count from (i) to (i-1). The solution seems to derive this using Bayes’ rule and the fact that all colors are symmetric, but I’m not seeing the logic behind setting up those probabilities.

Could someone explain what exactly is symmetric here, what events Bayes’ rule is being applied to, and why the resulting conditional probability has the form given in the solution? I’m mainly trying to understand how someone would come up with that result rather than just following the algebra after the fact.

Edit: college student getting an AA degree in Electrical Engineering. I've done college algebra, stastical method, trigonometry, and pre calc so far.

I'm planning on taking the fall off to pretty much focus on my declining health and save up money for my final year. But I would also like to prepare myself for calculus and physics during the mean time.

Do you guys have any books that I could buy that would provide a substantial review of everything needed for calculus?

I'm confident in my math skills but afraid that I'll lose a lot during the time.

Hi everyone's I wanted to ask how can I get help for learning 6th Grade Math as an adult I did graduate high school.but since I had an IEP and I also have Autism I felt like I was just rushed through school without knowing some of the material. I Almost failed 6th Grade due to not passing Math but I still progressed due to my IEP I am great at English but terrible at math . Right now I am using Khan Academy and I am ordering an IXL Workbook from Amazon but are there any other resources than can be beneficial for me ?

Hi everyone,

I’m a data engineer with a degree in computer science. Over the past few years, I’ve become increasingly interested in understanding AI at a deeper level—not only as a programmer using existing tools and APIs, but as someone who may eventually be able to understand and contribute to the mathematical and research side of the field.

It has been quite a long time since I last studied calculus at university, so I’ve decided to start again with Stewart’s *Calculus*. Over the next three or four years, my goal is to build a solid foundation in linear algebra, calculus, and probability.

I have already completed more than half of a linear algebra textbook, and I plan to continue studying it while also working through calculus in parallel, since some of the later topics require it.

The main reason I’m making this post is to create a sense of commitment and accountability for myself. I want to stay focused and study at least a little every day. Since I work full-time as a data engineer, I cannot dedicate as much time as I would ideally like, but I hope that consistent effort over the long term will allow me to achieve something meaningful.

I’d also be happy to connect with anyone who is studying similar subjects—or even working through the same book—and would like to stay in touch and set small study goals together. Feel free to leave a comment below, and any advice or suggestions about studying calculus alongside a full-time job would be greatly appreciated.

Hello friends I was a commerce student and didn't had maths back in school, because teacher made it look like only a genius can solve maths , you must solve them fast, you must learn these formula etc. blah blah and because of this fear and self doubt (because I am a slow learner) I didn't choose maths but nowadays I am fascinated and excited about maths I love to solve questions and logic behind them but I don't have proper guidline like how to progress ahead, what roadmap to follow and I don't want to waste more of my time.

Please guide me

This year, I'm starting my first year of university.  im going to take calc 1 linear algelbra im not good at math can you give advice how to learn math to be good at it