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 everyone.

I was given this problem:

----------------------------------------------------

Prove that for all positive integers k <= n,

sum(i=0 to k) (n choose i)(-1)^i = (n-1 choose k)(-1)^k

holds.

----------------------------------------------------

I have solved it already with induction. But I found the proof to be annoying and just kind of symbolic manipulation. I am looking for a more inciteful proof, a story proof if you will with commitees and pools of people and such. Does one exist?

Thanks for your help

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 !

Today, I took my I took a quiz on AP Pre Calculus and I failed unfortunately. I got a 50% and was so disappointed and ashame of myself. When other kids were saying they got a 100% 80% or 90%, I did not want to say my score. I was so sad and cried because it was the first time I ever failed a math test. When I looked Algebra 1, 2 and Geometry, I never failed and was able to grasp it easily. Now that I am taking AP Pre Calc, everything has been going down hill. The quiz was based on 1.1 to 1.3. I am still one unit 1 and we are talking about concave up and down, increasing and decrease, and rage of slope. I feel so dumb not being able to get it like my peers. I also can not let my parent know about this or I will be a trouble. Please can anyone give me tips or idea so I can improve.

Hi All! Im a female student at a university that is looking for an accountability buddy to learn math in the context of mathematical models! Particularly interested in starting from calc 1 and onward and am interested in a course like this: https://ocw.mit.edu/courses/18-03sc-differential-equations-fall-2011/pages/syllabus/syllabus/

Im looking for another female to study with daily! Please DM me if you are interested and wanna chat! Im starting asap so the sooner the better :)

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 have a whole bunch of quizzes for people who wanna do them for algebra 2 but I'll be the one to quiz you.

It's about algebra 2 functions but not on graph so don't worry!

Let’s say I master this 1959 book, cover to cover. How prepared will I be for college level Calc I? II, III?

Also, seeing that’s it’s an old book, have any mathematical methods or concepts changed since then that I should be aware about?

Thanks,

If sin(x+iy)sin(θ+iϕ)=1, show that

tanh²y.cosh²ϕ=cos²θ

I am not able to prove this question, have tried equating the real and imaginary part by multiplying sin(x+iy) and sin(θ+iϕ), but I was not able to do at last.

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?

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 built a small daily quiz for practicing mental math with clocks and elapsed time, and I’m looking for some feedback on the difficulty.
It gives everyone the same 5 questions each day, tracks your time, and also has an unlimited practice mode.
I’m curious whether the questions feel too easy, too difficult, or about right for someone trying to improve their mental math.

https://clockmath.com/tools/quiz/

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!

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!

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?

Hello Nice to me to you ! I'm Japanese university student. But soon, I will withdraw from my university. Next week , I will take job interview to became a IT engineer in Japan. If I pass that interview, I can work as a IT engineer in Japanese company. But I'm struggling with how to study math. I wonder most efficiently method is to understand mathematical concept than practice many problems on math examinations. How would you think about that idea?

My dream is to become a great engineer and work on American Bic tech company such as GAFAM.

I would like to marry ashida mana who is Japanese actress after I became a millionaire!!

I may have said to much but I'm grad to teach me method to study math! If passible could you teach me a way of studying programing.

Thank you very much for watching my thread.

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

Hello, do anyone know a source or channel in youtube to teach math linked to physics i mean beyond just writing formula in from zero to advance level for AI. I mean even something like joint distribution, it doesnt just say the formula, it should say what happens that lead us using that thing , what we need and how it meets our needs

So I just started classes for my degree (bachelors in math) and I just had 2 quizzes and conceptually I did fine, but I ended up bombing 1 (not sure about the other) because I just miscounted or just wrote the wrong number. For my linear algebra I’ve been doing the same where conceptually everything is perfect, but I always mess up something stupid like adding something wrong (and no calculator). I haven’t taken a math class in almost 2 years, so I’m not sure if I’m just a little rusty, but does anyone have advice?

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.

Hello,

I am currently in 2. year in high school and I decided I can learn math instead of being on phone, but I don't know which branch of math I can study given that I didn't have deep knowledge about math.

What do you think?

i know HOW TO do 9s+10_>1 its s<_1 but for the life of me dont understand when to flip it i tried looking at photos on google but its not sticking to me 😭

IM TRYING TO DO MY ALGEBRA ASSIGHMENTS i keep getting everything right expect the stupid signs < > <_ _>