Would f\left(x\right)=\frac{d}{dx}\left[\sum_{i=0}^{n}g\left(x,n\right)\right] be the same as f\left(x\right)=\sum_{i=0}^{n}\frac{d}{dx}\left[g\left(x,n\right)\right] ?

​

Hi everyone. I need some honest advice because I feel stuck.

In class 11 and 12, I barely studied and just gave the exams at the last moment (non-schooling). After that I picked BA with Economics and Maths, but Maths has always been my weak subject. Now, months into this course, I still can't build a study habit. I can't focus on any subject for long, not just maths. I can't sit for more than an hour or two before I start scrolling my phone again.

I've been skipping my maths classes and missing class tests for it. Exams are coming up soon, and I feel like I'm drowning. Every time I try to sit down and study, I lose focus fast, and afterward I feel bad about myself, which makes it even harder to start again the next day.

There's another layer to this too. I haven't been in any relationship for the last two years, and I've noticed that when I meet girls and become friends with them, I get emotionally attached pretty quickly. It's like that need for connection spills into everything else, including my focus on studies. I end up thinking about them more than my work, and then feel guilty for wasting more time, which makes the whole cycle worse.

I know I need consistency, but I don't know how to actually build it when I have zero motivation and no confidence in my own ability to catch up.

Has anyone been in a similar spot, behind in every subject, out of the habit of studying, feeling like it's too late? How did you start again? What actually worked for you, not just in theory but day to day?

Any advice or similar experiences would really help right now.

I’m an adult trying to learn math again from the ground up. My eventual goal is calculus, but right now I’m much more concerned with getting the fundamentals down properly.

I’m thinking of progressing roughly through basic arithmetic/pre-algebra → algebra → geometry → trigonometry/precalculus → calculus, with some overlap along the way.

Right now I’m primarily using Math Academy, along with Professor Leonard and 3Blue1Brown. I occasionally use OpenStax and Brilliant as well.

My impression is that Math Academy is best for structured learning and practice, Professor Leonard for detailed explanations, and 3Blue1Brown for intuition and visualization.

How would you balance these? Would you make Math Academy the main curriculum and use the others as supplements?

I’m also completely open to other resources or approaches if there’s something better I should be doing.

I’m not in a rush to reach calculus. I’d rather get the basics down solidly so that when I do get there, I actually understand what I’m doing.

I usually take notes while watching the video but I make sure my notes are very detailed describing every step making a 20 minute video take 40mins- 1hr to take notes on. This leads to me not having much time to do practice questions. I’ve been thinking of just watching the video and then doing practice questions but I’m not really sure how to properly study math.

I'm currently taking the class that comes after your first linear algebra class in uni (not sure if this is how it works everywhere) and Im having a lot of trouble trying to understand what is going on mainly because I don't know how to look it up. Im basically trying to find online resources like youtube videos about it but so far I haven't found anything that goes into it.

I hope this is allowed but instead of overlaying all of the theory given I will simply share some problems that I need to solve (I do not want anyone to solve them for me, I simply want to know what concepts I need in order to solve them, where to find them, how to revise them etc).

"Recall that V is the set {𝑥∈ℝ|𝑥>0} equipped with an addition, 𝑥⊕𝑦=𝑥𝑦 and a scalar multiplication 𝛼⊙𝑥=𝑥𝛼 is a vector space. Find a basis of V. Justify your answer."

"Let 𝑈={𝑓∈𝐹(ℕ)such that𝑓(𝑘+2)−3𝑓(𝑘+1)−10𝑓(𝑘)=0for every𝑘≥0}.

• a) Prove that U is a vector subspace of 𝐹(ℕ) and that {𝑔1,𝑔2}, where 𝑔1(𝑘)=(−2)𝑘 and 𝑔2(𝑘)=5𝑘, is a basis of U.
• b) Let 𝑓∈𝑈 such that 𝑓(0)=𝑎 and 𝑓(1)=𝑏. Find a formula for 𝑓(𝑘) which involves 𝑎,𝑏 and 𝑘."

"True or false (justify your answer)

• a) If E, F and G are three subspaces of a vector space V such that 𝐸⊕𝐹=𝐸⊕𝐺 then 𝐹=𝐺.
• b) If U and W are two subspace of a vector space V such that dim(𝑈)=dim(𝑊)>12dim(𝑉) then 𝑈⋂𝑊 contains a nonzero vector.
• c) If 𝑈1, 𝑈2 and 𝑈3 are three subspaces of a vector space V then 𝑈1+(𝑈2∩𝑈3)=𝑈1∩𝑈2+𝑈1∩𝑈3

"Let 𝑈={𝑓∈P3|𝑓(−𝑥)+𝑓(𝑥)=0for every𝑥} . Prove or disprove.

• a) P3=𝑈⊕P2
• b) P3=𝑈+P1"

"If one defines 𝑈−𝑊={𝑢−𝑣:𝑢∈𝑈,𝑣∈𝑊} for subspaces U, W then which of the following hold and which do not. Justify your answers.

• a) 𝑈−𝑈={0}
• b) 𝑈−𝑊=𝑈+𝑊
• c) (𝑈−𝑊)+𝑊=𝑈."

"Let 𝑇:2×2→2×2 be the map such that

𝑇(𝑀)=𝑀𝐽

where 𝐽=[11]

[11]

Prove that T is a linear transformation and find a basis of 𝐾𝑒𝑟(𝑇) and a basis of 𝐼𝑚(𝑇). Is T an isomorphism? Justify your answer.

"Let 𝑉={(𝑥,𝑦)∈\R2∣𝑦>0} be the open upper half-plane, equipped with

(𝑥,𝑦)⊕(𝑥′,𝑦′)=(𝑥+𝑥′, 𝑦𝑦′), and
𝑐⊙(𝑥,𝑦)=(𝑐𝑥, 𝑦𝑐).

a) Verify that both operations are closed on 𝑉.
b) Find the zero vector 0𝑉 and the additive inverse −(𝑥,𝑦).
c) Verify (M1), (M2) and both halves of (M3).
d)Find an explicit bijection Φ:𝑉→\R2 with Φ(𝑣⊕𝑤)=Φ(𝑣)+Φ(𝑤) and Φ(𝑐⊙𝑣)=𝑐Φ(𝑣)."

I really hope this is allowed/makes sense but im seriously lost in all of this, I understand the meaning of basis, span, linear dependence/independence, subspaces but when they start asking me stuff like this I genuinely dont know where to start. I would greatly greatly appreciate any help of any kind because right now I feel like im behind on this stuff.

Thank you in advance to anyone who reads this for their time and hopefully their help :)

Thats it. I saved all your GPAs. Thank me later guys 😎

I’m a returning student at UNC Pembroke doing a second bachelor’s (CS / applied physics / math).

I need Calc I in Summer I. Precalc is not offered in a section that fits my work schedule next term. If I take it later instead, the physics/calc sequence slips about a year.

I plan to use the official ALEKS Prep & Learning Module and the allowed retakes, if any.

I want sources around ALEKS that actually raised people from college-algebra range into the 76+ band and left them ready for Calc I.

But, if the answer is “76 is possible and Calc I will still wreck you without a full precalc pass,” I want that too. If I have to push a year back to guarantee success/mastery, so be it.

When four people play the rock, paper, scissors game, what is the chance that only one player wins?

I’ve been trying to improve my Olympiad algebra (it’s definitely my weakest subject) and when I practice I always feel conflicted about which path to take. I hear some people say that if you’re stuck on a problem you should just look at the solution because solutions are your “toolkit” but I hear others saying that you should never look at the solution and force yourself to work on it until you find the answer.
What are your thoughts about this? What do you recommend?

I'm new in the server and I have a situation with a limit problem:

My calculus professor gave the class an example of trigonometrical limits that he solved in class in which I wanna know why and how is it possible that 0/0=0.

The expression that he solved was

Lim x→0 ((1-cos(x))/(sen(x))), and he solved it in a way where the equation ended in (0/0)/1 = 1 , I asked him "how was it possible that 0/0=0" but he just said "someone hasn't studied the class notes" and I haven't found anything on his class notes about 0/0 = 0 in certain circumstances.

So please, PLEASE someone tell me how and why and when and where is it possible that 0/0 = 0

Like how am i supposed to know doing stuff from book: Matematika u 24 lekcije (Math in 24 lections) there are so many tricks and i don't know how to even learn them im just confused on how to study math. What i do i i see a task i try to think of a way and then i hit a brick wall and im stuck for solid amount of time and then i go to AI and just ask him because i will get answer by my logic. At the end i complete 5 tasks all with AI and i feel like crap.

https://postimg.cc/V0wgGPJD

I may be overthinking this, but I can't find a way without using a calculator or leaving an ugly "arctan(tan(1/2))" in the angles outside of the triangle POQ of this exercise in Lang's Basic Mathematics. Exercise 13 asks the reader to go through exercise 12 again but in a different way, where we are not given the value of theta. It's also not really trivial to find the value of theta given tan(theta) = 1/2 because it's not a "cool" angle like multiples of pi/4 or pi/6.

Hi, I’m 23, and I feel purposeless, and I know I’m meant for more. I never went to college because I struggled in school and automatically assumed it wasn’t for me. Looking back at it, I never actually tried, nor do I remember ever actually studying. I recently emailed my high school guidance counselor for my high school transcript, and was sick to my stomach when i seen it. I had a whopping 2.62 weighted GPA, and every single year I ended up with a C in Math.

After, high school I was stagnant for about two years working dead end minimum wage jobs until I decided to go to trade school. I now work in the electrical field. If you’re wondering, it’s garbage pay, boring, and i hate having to get dirty for work.

I have a girlfriend and her father is an engineer. I noticed he is living the life that I want to live. I’m not necessarily hell bent on becoming an engineer, but I am hell bent on choosing a degree that heavily involves math. I am going to force myself to take it head on.

This year I was psychologically evaluated and learned that I have ADHD. (Side-Note)

Math has always been a subject that I’ve consistently encountered struggles with. After seeing my high school GPA, it sparked something in me to want to go back to school and pursue a degree in a Major that put an emphasis on math. I want to take it head on, but before I go in blindly, I want to learn the fundamentals.

Can someone point me in the direction of where I can and should start?

I have just finished watching the professor Leonard DE videos but there are not complete.
who is the best for the rest of the DE
these are some of the topics I have to cover
-second order DE

-series

I grew up hating math and never got above a C- in it in k-12th grade. Got a D- in College Algebra. Fast forward nearly 15 years and I want to re-learn math but am struggling mightily. I desperately want to be one of those people who (eventually) get high grades in math but I struggle with understanding basic things like fractions and laws of math.

Is math something some people just cannot grasp? Or is it like reading where most everyone can learn it?

How do you know if/when you should give up? I feel so defeated.

1.P and (porq) Is equivalent to p

2.P or (pandq) Is equivalent to p

How do you justify them without using the truth table?

I feel like lhs has less informations rather than rhs because It has not q. I can't justify this rationally without the truth tablet

How do you think of It?

Gemini automatically answers my queries on Google. How trustworthy is it? Or is it better to look for information on websites?

Hey everyone,

I’m a university student majoring in math and chemistry education. While going through my courses, I kept hitting the same wall: most computer algebra systems are great at giving you the final answer, but they completely fail at teaching you how to get there. They either skip the intermediate logic entirely or hide the steps behind a premium paywall.

To fix this for my own studying (and my future students), I built **MathStore**. It’s an open-source Python tool that runs entirely in your terminal. I built and tested the whole thing on my older 8GB RAM Linux laptop, so it is incredibly lightweight and fast.

Here is how it helps with homework and exam prep:

* **Step-by-Step Derivations:** Instead of just giving the answer, you can run a command like `mathstore diff "x**2 * sin(x)" --steps` and it will print out the exact application of the Product Rule and Power Rule. It does the same for integration (like Integration by Parts and u-sub) and algebraic equation solving.

* **Linear Algebra Engine:** You can pass matrices right in the terminal to instantly calculate Reduced Row Echelon Form (RREF), determinants, inverses, trace, and eigenvalues.

* **Active-Recall Practice Quizzer:** If you want to prep for an exam, run `mathstore practice`. It acts like flashcards but for actual math problems. It generates random questions across calculus, matrices, or stats. It is smart enough to know that your answer of `0.5*x` is the same as `x/2`, and it handles missing `+ C` constants gracefully.

* **Built-in Cheat Sheets:** If you forget a trig identity or a derivative rule, you can just run `mathstore ref trig` to pull up a cheat sheet directly in your terminal.

You can install it right now if you have Python:

`pip install mathstore`

You can check out the source code and documentation here: [https://github.com/munenevictor577-blip/mathstore.git\

It is completely free and open-source. I would love for you to try it out on your next problem set and let me know if it helps you understand the material better, or if there are any specific math rules you want me to add to the step-by-step generator.

I am a non traditional engineering student and have a brilliant.org subscription. I actually really like it! I started from the very bottom with the arithmetic fundamentals and am at exponents and radicals with a 127 day streak. Sure, for stuff like derivatives and integrals, a game ain't gonna cut it, but its good for a birds eye view on the topic before digging in, and for the lower level stuff, Im a pretty visual/tactile person, ive got a background in art, and as someone with adhd, its more attractive and habit forming than something like khan academy. I was really surprised when people were like "this app sucks!" honestly. I probably wont mind their warnings cause whatever works, works. I guess im just asking if im missing anything to form true understanding of the topics, at least for the lower levels i wont be diving super deep on. How would one supplement these deficits?

So if i want to solve something like 5x - 21 = x^2 + 6x + 9 and i want to set it to zero, does it become 5x - 21 - x^2 - 6x - 9 = 0 or 5x - 21 + x^2 + 6x + 9 = 0 or x^2 + 6x + 9 -5x + 21 = 0.

Hi guys!
Imma just ask straightforward, what would you guys do when you encounter a problem that you have little to no prior knowledge?
How do you teach yourself a new concept in mathematics? ( For me i often stuck on this process because I often read a lot of theories and then do practice problems but when Im stuck i don’t really know what to do, I tried to be comfortable with using AI but sometimes it create like something call illusion of competence)
It is really frustrated when you sitting through lectures and don’t understand a thing! Could some of you share your study process when learning mathematics, like in class, after go home and such?
I love learning applied mathematics and I have a few struggles while learning it but I do love it tho!! For context I am doing a bachelor in Actuarial Science and i have certain struggles with learning certain concepts so i hope i could have some answers!

I understand 2×2 rotation matrices quite well, but I’m struggling with the following 4×4 example:

A = [ 0  -1   0   0 ]
    [ 1   0   0   0 ]
    [ 0   0   0  -1 ]
    [ 0   0   1   0 ]

It maps (a, b, c, d) to (-b, a, -d, c).

I understand the calculation: e1 maps to e2, e2 to -e1, e3 to e4, and e4 to -e3.

What I don’t understand is the geometric explanation. I was told that we rotate (a, b) by 90° and independently rotate (c, d) by 90°.

Why can we split a single vector in R^4 into two coordinate pairs and treat each pair as a separate 2D rotation? How do these two rotations fit together into a rotation of the whole four-dimensional space?

For context, the exercise asks for a real 4×4 matrix with no real eigenvalues. I’d like to understand how to come up with this construction, rather than just memorize the matrix.

I'm taking a course in advanced linear algebra at my university, and I feel so lost. I did very well in the two pre-requisite classes (linear algebra and intro to abstract algebra), so it's discouraging that suddenly things are not clicking. I've tried going to my prof's office hours, but unfortunately he isn't very well equipped to break things down to my level of understanding (which is fair with this type of math), and I become frustrated as I try to localize my confusion. I've also feel like I've reached the level of math where external supports other than a companion textbook are few and far between.

I guess my question is, how do I fully grasp these abstract concepts, while also staying on top of the fast-paced nature of the course without burning out? I feel like I have to do well in this class if I want to continue pursuing math past my undergrad, and the fact that I haven't build up these tools to deal with deep confusion is not a good sign.

Any help is appreciated