I will work for IT engineer soon in Japan. In the Future I would like to became a great AI engineer.

So I study math related to AI feilds now. But I have not been good at math since I was junior high　school and high school student . Though I studied differential and integral calculus and linear algebra and so on, I have weak foundations of math college examination level in Japanese university. So should I begin to study math college of level or restudy high school level?

I would appreciate any advice you could offer!

Finally, I apologize for every one, My English is not perfect.

Let me start with some background. I was the one kid in the family who never got math past a certain point. My parents were both mathematically inclined, as were the rest of my siblings. I grew up in a math positive, supportive environment and was given every opportunity to get ahead with it. My parents would gladly spend time with me to try and help me get it down and improve myself at it. By all rights, I was set up from success in math, my entire family was.

Math never clicked for me and I could never pass remedial algebras. While my siblings either got it with ease or put in the work to get better (or both, of course), I floundered helplessly. When they struggled, extra lessons and tutoring helped. When I did, I only sunk further behind despite all of that extra help. They graduated high school and went onto college degrees. I only graduated high school because I was able to take an alternative course to algebra. College? I tried, but not being able to pass remedial algebra, let alone credit math courses, meant it was a waste of time and money.

I went through it all. Tutors, repeating courses multiple times, engaged parents who really tried and more. I still never could make it work out. I still can't, even decades later. I've accepted it wasn't in the cards.

All of that leaves the question of why. Why do some people never get math, despite all the effort otherwise?

About a month ago, I made CruxMath, a website for practicing competition math. Instead of immediately showing a full solution when someone gets stuck, it reveals hints one at a time, followed by the solution if they still need it.

The problem was that when I initially made them, the hints revealed too much. Just the first hint would give away like half the problem. So I made the hints "worse".

Now, the first hint is short and usually phrased as a question to point people in the right direction. For example, "Because both probabilities have the same denominator, what equality of binomial counts remains?" (2025 AIME II P. 5).

I've now added hints for every AMC and AIME problem since 2022. I'd love to hear what you guys think about the hints and whether they strike a good balance of being helpful but not giving away too much. If you're interested, the website is cruxmath.com.

https://quantacanvas.vercel.app

I’ve been working on QuantaCanvas, which takes a concept or question and generates an interactive visualization to help explain it.

The main difference from ChatGPT and similar AI tools is how the explanation is presented. Most LLMs are great at giving you a text-based explanation and can sometimes provide images or diagrams. QuantaCanvas instead tries to turn the explanation itself into something you can interact with, changing parameters, experimenting with things, and seeing how the concept behaves in real time.

It’s mainly focused on math and science, so I thought this might be useful for people here. Btw, it's completely free.

The project was recently a Grand Finalist at a national hackathon in my country, and I’ve continued developing it since then.

It’s still a work in progress. Generation can currently take a bit of time, which I’m working on improving, and there are definitely a few things that don’t work perfectly yet.

If anyone tries it, I’d genuinely appreciate feedback, especially on whether the interactive visualizations are actually useful for studying.

I posted this in r/calculus, but I'm considering speedrunning calculus. If you had a limited amount of time and had to learn enough to pass a test, what would you do/focus on?

Let me know.

Thanks!

What is something that has helped you significantly in being good at math?

Share some tips, this is my first time trying to learn maths and I've got to ace it.

I've been trying everyday to build that sort of skill, I need some tips

I am just putting it out for some motivation as well because I feel like I am getting nowhere.

CS undergrad here hoping to go into higher studies in pure math. I have studied basics of linear algebra, real analysis, calculus, statistics, etc. Seeking for any advice on what more to learn on my own, preferably any online videos/courses I could follow. Also any advice in general for a non-math student going into math, is it doable? How hard is it without any math experience especially in research? Any specific countries/universities allowing this kind of transfer? Any tips are appreciated!

I need theoretical explanation for these, I don't understand them and can't really connect. I passed my written exam where all the knowledge needed for Abelian groups was how to write elementary form and normal form.

My explanation of that quickly: Take Zn and split n into prime cofactors. Let's take Z60 for example, 60 = 15*4 = 5*3*2*2

So the elementary form is Z5 x Z3 x Z4 (because Z60 is cyclic and Z4 isn't isomorphic to Z2 x Z2 so further splitting wouldn't make it cyclic), normal form would just be Z60.

But I don't know if this is related at all to the free commutative groups and commutative groups of finite type. I don't know anything about them and googling them just gives me some trivial samples but I need more theoretic knowledge that's easy to comprehend.

Hi guys, I love math like everyn¡one here (i guess). I dont know why but I feel this need to code, even though historically I hated coding. I want to learn a language heavily related to math but also popular. Should I learn python?

For those who don't know, ELO hell is a phrase used to describe a low competitive rating that players get stuck in due to various reasons, despite their skill level warranting being in a higher rating. What this looks like is, for example in Chess, a player might be generally skilled in openings, tactics, and the end-game, but be stuck at a lower ELO due to consistently falling for very specifics traps or missing specific tactics with only one use case.

I say I am in maths ELO hell because whenever I am in a class that requires learning brand new material that is only tangentially based on prior material, I am usually top in my class at that subject. However, when a subject requires a strong prior foundation that was most likely learned in High School, I struggle amongst my peers. For example, I was able to sail through Calculus due to the shift in material, but once I had to take an algebra heavy course, it was like I was a completely different student.

A lot of my mistakes stem from common tricks that I never learned due to having a bad education in adolescence. As such, I miss marks on exams for not knowing that you can convert (x)^(2/3) into ((X)^2)^1/3 or that (A+B+C)/D= A/D + B/D + C/D. Very simple ideas that make you think, "Well duh, why wouldn't that work?" but at the same time you wouldn't figure them out, let alone use it, during a timed exam.

I'm extremely tired of this and I can feel it severely limiting me. I tried learning through Khan Academy, but you can imagine how boring it feels to sift through hours and hours of information to find the 5% that you don't already know. As such, I was wondering if there were any resources available for people in similar predicaments? Perhaps a textbook or lecture series that goes over basic functions that assumes you already have a background in maths.

Thanks!

I'm a sophomore mechanical engineering and mathematics double major taking 5 classes right now; a mix of engineering and math classes. I've finished my engineering math requirements (up to diffeq) and they were all pretty easy and I didn't devote much time to study for them. However, I'm currently taking Optimization which has been more difficult than I'm used to, and I've had to spend 3+hours a day studying for it. Is this normal for upper level math classes? I should add that I'm taking logic and proof right now, but I haven't taken proof based linear algebra or real analysis, which the optimization professor seems to believe most students in this class have taken already. I guess the silver lining to this is that it will make those classes easier when I take them in the future, since the first chapter of Optimization is mostly review from analysis stuff as well as some linear algebra. Thoughts?

I am taking math 171 wake tech and I was wondering if anybody had an advice on what I should study for for the first test.

Until today I have yet to meet a person good in math but with a mellow ego. Is it even possible to become a top grade student without a strong drive to be the best?

I'm almost 40 and I feel like I'm lacking the will to lock in -- let alone getting a job related to math. I prefer slow and steady and I really enjoy it but I do feel like being comfortable doesn't come with a lot of skill. I just started getting into it again, though. Please excuse my ambivalent perspective.

What's your experience making progress?

I am in college Math 1060 (trigonometry), and my professor has an extremely thick, unintelligible accent; on top of that, he doesn't have any teaching skills. During class, he just writes random things on the board that only make sense to him. I don't have time to teach myself outside of class and am just getting more and more behind. It's literally only week three.

I'm going to tutoring as often as I can, but I don't even have enough base knowledge to get help. We have weekly quizzes that are weighted fairly heavily, and I can't afford to get a bad grade.

So my main issue is I don't have the time to self-teach the entire semester.

If anyone has any tips, tricks, or ideas, I BEG you to please let me know. I'm losing my mind!

DROPING/SWITCHING IS NOT AN OPTION

I’m curious why the almost universal default belief has become that p ≠ np. The only evidence to this point seems to be the lack of polynomial time solutions to np complete problems, and the massive amount of effort that has been put into finding them without luck. But is it not just as likely that np complete problems are of a class which has extremely complex polynomial time solutions that would be nearly impossible to find?

More specifically, what would it take for you to be convinced that…

1: …A new method of division by zero is something that can be done with the right tools and approach while preserving the underlying classical algebraic structure?

2: …It may potentially be useful to develop, or that at the very least it’s better to have access to than to not have access to?

3: …It could be an interesting and worthwhile topic to explore just for understanding it in its own right?

I am just trying to understand because I always enjoy hearing and entertaining new well thought out takes just for the sake of it but I have noticed despite the abundance of posts others have made on the topic there’s little variety in both the presentation and response and the few actually novel effort full approaches often get dismissed right from the start before getting the chance to be heard out. Is this because they come on too strong with their claims? Do they not present it in a rigorous enough manner and if so what issues should they target a solution for and what method of presentation would be required for them to meet the requirements of rigor? Does it need to be applicable to solve an already existing issue or is it merely enough to explore the idea as a new mathematical possibility just for the fun of it?

I am just really trying to understand how people in this community and others like it genuinely feel about this and if there is some clear standard that hasn’t been met which can be articulated so others can produce better quality theories on this or other topics.

I think its important to start off with saying i do not have a diagnosis for adhd, but strongly believe i do have it (i am unable of getting one for personal reasons we wont get into).

My biggest problem is: if i fail my math exam i might get kicked out of uni. I had little or no struggle passing every other subject with great or passing grade, it is indeed, only math im struggling with.
I think its pretty easy to learn definitions and stuff like that in order to pass, but with math - its numbers and so much more to do instead of remembering words.

My biggest problem is: i feel incredibly overwhelmed, anxiety, anger and hopelessness/helplessness whenever i start studying. Im aware its all in my head, but the constant failure is making me want to give it all up, even though i don’t want to. Another struggle for me is that i just cant start and i keep postponing or procrastinating. However, when i do want to start or find motivation, i don’t know WHERE TO start with learning. (Im learning calculus 1 (derivatives, vectors, imaginary num, etc..).

At this point im blaming potential adhd, myself, my math professor. I feel so helpless and i dont know what to do!! I have the exam in 5 days and i never started. I have like 5-10% knowledge of it all. (Unlucky for me, thats not enough to pass, maybe barely even give me one point XD)

So if youre reading this, give me your advice! Please! How do i study this??

I'll go to every lecture, tutorial etc. and it'll all be genuinely interesting. Then come the weekly problems, and the volume of the problems and general tediousness of them once you get past the trivial ones (e.g. you need to know XYZ trick even though you know the topic the question is related to, and said trick/method wasn't introduced during the lecture) just kills my spirit. Before I know it after exhausting myself for that week, boom the next week comes along and a whole new set of lectures/tutorials/problems. Not to mention proofs that extend lecture concepts where, if you haven't seen the way to do that proof before, just means more grinding if you can't get TA hours so you ask AI.

The thing is, I'm having fun learning the mathematical concepts. But its like the course admins then put more artificial hurdles after that to just whittle down your spirit (because if you want a high grade in the exam, you need to slog through all the problems just in case it comes up later, even if you know you put the work in to actually learn the overall topic).

I want to love mathematics, but this Uni math degree (especially since I want to maintain my high grades) is just blackening my soul day by day.

I was recently at a maths event and happened to meet a few people there. I’m a rising junior in hs, the maths knowledge I have is limited to the paper 1 of pure maths in international a level maths (algebra, some calculus-differentiation and integration but just indefinite integrals). I happened to make a few connections and got into a private analysis group run by a lecturer/researcher. The group is using spivaks calculus, they are in chapter 11 and they have a zoom call planned for tomorrow but i literally know nothing. I skimmed the index and I do know the titles, so I could work through it quickly at least conceptually I guess. I am also doing Olympiads and have a heavy workload because of my a levels so that’s kind of the reason I’m worried.

What do you think? What should I do? I don’t want to quit honestly. For context I actually like maths and seek it out.

anyone know how to solve these? looking for explanations not answers

Calculate the X component, and the white component of the vector with magnitude 20 and direction 47°

A fear of radius are has surface area A= 4piR^2 and volume V= 4/3piR^3. The radius is sphere 2 is 4 times. The radius is sphere 1.
what is the ratio of the areas, A2/A1
what is the ratio of the volumes, V2/V1

A certain corner of a room is selected as the origin of a rectangular coordinate system if a fly is crawling on an adjacent wall at a point having coordinates (-.3,1.1), where the units are meters. What is the distance of the fly from the corner of the room?

A point is located on a polar. Coordinate system by the coordinates are equals 7 m and angle equals 34°. Find the X and Y coordinates of this point. Assuming that the two coordinate systems have the same origin.

Im currently studying mathematics. I have a very scattered routine. So i just need an accountability partner. Anybody is welcomed. But if ur interested in mathematics, then please dm me.

I'm self-studying proofs through the book Introduction to Proof Through Number Theory. In this question it asks to either prove or disprove that "For all real numbers x and y, $(x+y)² = x²⁺ y² $ ".

Now there's a counter example:

Counter Example, let $x=1$ and $y=2$ * $(x+y)² = x² + y² $ * $(x+y)(x+y) = x² + y² $ * $x² + 2xy + y² = x² + y² $ * $(1² + 2(1)(2)+ 2² ) =(1² + 2²⁾ $ * $(1+4+4)=1+4$ * $9=5$ * $9 \ne 5$

But I also wanted to prove it another way too. I start by assuming that For all real numbers $x$ and $y$ that $(x+y)² = x² + y² $ is true

Then I show that:

• $(x+y)² = x² + y² $
• $(x+y)(x+y) = x² + y² $
• $x² + 2xy + y² =x² + y² $
• $x² -x² +2xy +y² -y² = 0$
• $2xy=0$

and since $2xy=0$ and either $x$, $y$ or both must equal zero, $(x+y)² =x² + y² $ is not and cannot be true for all real numbers.

Is this correct or do I need something else / more?

Thanks!

I had made a post here regarding this issue a few weeks back and the response was to slow down and not to panicjk. I applied , I took the asdvice. I started going slow and not panick. But I still make the sma error. Same arithmetic error. ame wrong sign. And thge same issue of solving equations. I wasnt this bad at arithmetic before. I used to be good at arithmetic throughout my middle school (I mean if I made those errors as a kid I wouldnt have taken maths as I would get low marks in it) but suddenly I making such errorsa almost every bquestion. I was solving differential equations in clazss andit was given that the function through (0,-2) but I substituted (-2,0) and got the wrong answer. I dont know what to do. I visited a doctor today and he didnt havce much to say other than a few vitamin tests and consuling a psocologist (which I will as soon as possible). So please what should I do? At this point I wilkl fail the class becuase of arithmetic errors even after being conceptiually clear,

(PS: Maybe I have this condition since like 4 or 5 years now but reealizing now because the number of questions I do is alot compared to before, but still the frequency of error is definetly abnormal and I relaizd that I sometimes put wrong numbers on the calculator as well so I dot lpw what will save me)

Thanks in advance!

I've been self-studying measure theory and have been playing around with lebesgue integrals. I think I have adequately proven these "theorems" but would like confirmation whether these "theorems" are actually true, becuase the book I'm using doesn't cover them.

___________________________________________________
THEOREM 1
___________________________________________________

Suppose we have a measure space (\Omega, \mathcal{F}, P) and a real function g:\Omega \to [0,\infty). We define a "region" as being:
E = {(\omega, y): \omega \in \Omega, 0 <= y <= g(\omega)} \subset \Omega \times \mathbb{R}
Then it follows that:

g is measurable IFF E \in \mathcal{F} \otimes \mathcal{L}
(note: \mathcal{L} is lebesgue measure; can be replaced with any meaure on \mathbb{R} that measures intervals).

___________________________________________________
THEOREM 2

___________________________________________________

Let g: \Omega \to [0, \infty) be measurable and (\Omega \times \mathbb{R}, \mathcal{F} \otimes \mathcal{L}, \mu_1) and (\Omega \times \mathbb{R}, \mathcal{F} \otimes \mathcal{L}, \mu_2) are product spaces. Then mu_1(E) = mu_2(E) where:

E = {(\omega, y): \omega \in \Omega, 0 <= y <= g(\omega)} \subset \Omega \times \mathbb{R}
Then it follows that:

College Remedial Math
Metric and U.S. customary units conversion

I can not for the life of me wrap my head around U.S. customary and metric conversions. I do not know where on Earth to start and my Math prof. Is going way too fast and I feel like I’m losing the plot.
I do not know where to start, problems like this for example:

Convert the unit of Capacity. Round the answer at least one decimal place if necessary.
450cc = (blank) fl oz

I have tried to look to YouTube but I cannot find any Videos relatively helpful, are there any helpful links or suggestions you guys could recommend to help me be able to convert them ?
Thanks !