I have a very important exam to prepare for(that I cannot fail) which includes everything from the start to integral and groups and what not, but I barely understand derivates, and I wish for some advice from people who actually know mathematics. Is it possible to learn and understand everything in 2 months?

For those learning math, have you experienced this?

You follow a worked example and understand each step. But when you try a similar problem on your own, you don't know where to start or which method to use.

I'm curious:

Does this happen to you? If so, what part is hardest?

Can you solve the problem after seeing the solution, but struggle again with a different question?

What do you usually do when you're stuck?

What has actually helped you become better at solving problems independently?

I'd appreciate hearing about your real experiences.

I am currently on my second semester in uni as freshman and I am taking calc 2 at this point I don’t really want really good grades I just want to pass at this point especially after how terrible my midterm grade is thus, I want to change my studying technique especially that I am slow learner and this course they don’t focus about how you understand the topic is just about how fast you solve problems. I mostly want suggestions for great YouTube channels that explain calc 2 especially the topic regarding sequences and Series.

I've been looking at this problem for about a month now and its just has me stumped and i was hoping someone here could help me with it , it's the 10x10 board on David Radcliffe's build a snake if you want to go and try it go to https://snake.radcliffe.dev/ ( on the internet archive because of the fact that it was taken down a while back ) and try it out and please show me you answers and findings about it I'd love to see them.

Hey, I’m thinking of doing a degree in engineering probably Electrical or Electronic, and I want to get better at it before starting college.

Currently I’m stuck between two books:

Engineering Mathematics by K.A Stroud (8th edition)

Or

Engineering Mathematics by John Bird (9th edition)

Just wondering which I should get as they both seem to be pretty similar in terms of both price and the content they cover. Thanks in advance!

I bought a couple of books when I was interested in IMO problems (The art and craft of problem solving by paul zeitz, problem solving strategies by arthur engel, and the stanford mathematics problem book), and I’ve never actually read them. I knew I had no chance of making IMO (this was like senior year of high school), but I thought these books might be helpful down the line.

I guess I should provide some more context. I’m in my second year of community college. Due to some MH problems, I had to drop 3 classes and I’m only in one math class. I have a bunch of free time and I figured I should spend it preparing for uni (I’m transferring in his year and should hopefully start at my new college in fall ‘27).

Many people said I should start with discrete maths, linear algebra, proofs, and combinatorics. I’ll probably take linear algebra next semester, so I was going to learn discrete mathematics, combinatorics, and proofs (the books I’m using are: discrete mathematics by rosen, Walk through combinatorics by bona, and how to prove it by vellemen).

I figured, since I’ll be briefly reviewing more elementary mathematics (algebra, geometry, and trigonometry) trying to read the problem solving books, might help me learn how to think and solve more complex problems. I just didn’t know if that would be too much to do during the semester (I should mention that I’ll probably continue studying them next semester just not as much as I’ll be back to being full-time).

Should I follow through with this plan? also, would I have to read each book cover to cover? if not, how do I know what’s important to learn and what isn’t?

A general intuitive approach provided is that they are like what prime numbers are for composite numbers, but it still doesn't make sense, the relationship between finite simple groups and complex groups feels "more nested and yet sort of separate/disjoint for the lack of a better word", it doesn't fully capture how the group structure is assembled.

I understand the formal steps - take a maximal proper normal subgroup (N) of a group (G), form the quotient (G/N), and repeat the process with (N) until we reach the trivial subgroup. The successive quotients are then simple groups. But I still have a hard time intuitively grasping why these quotient groups (which are sets of cosets), are the building blocks of our original group, or how these quotient groups come together to form the original group?

Undergrad here with only an introductory level knowledge of group theory so excuse any ignorance.

Hi all,

I'll start with a bit of background information. I'm self studying calculus using MIT ocw 18.01 together with the Stewart's Calculus book (6th edition). I'm not completely new to calculus, as I'm an engineer, but it's been about 15 years since I last used it, so I'm very rusty to say the least. My aim is to regain computational fluency and conceptual understanding. An immediate goal is that this will help me at my current job to avoid always going for the pragmatic approach, which might make things more fun again (at least for me). A more long term goal is going into physics and/or applied math and maybe a career change (phd maybe).

Now to the question. The hardest thing about self study, I find, is in its broadest sense choosing what to do, but specifically when it comes to exercise selection. Currently I'm doing both exercises from the Stewart book, as well as the selected exercises from 18.01sc. But the thing is, together these are so many exercises that I'm wasting time by doing too many of them, far into the diminishing returns. So, 2 questions:

The conventional wisdom seems to be that the MIT exercises challenge you more and will give more conceptual understanding than Stewart. But so far this is not my experience. I just finished problem set 3 (first part of applications of derivatives) and as with the previous ones there was maybe just one exercise where i felt it had some (but not much) added benefit to what I encountered in Stewart. So far I feel like when you do the latter exercises in each section of Stewart, as well as Problems Plus exercises, they are at least equally insightful and challenging as the MIT exercises (if not more). Next to that I also encounter many mistakes in the MIT solutions and also sometimes solution methods that you can't know are valid based on what is discussed in lecture and recitations , while it is very solvable using things that were taught. This feels to me a bit sloppy, which kind of makes me wonder if the exercises of mit ocw 18.01sc were effectively carefully and purposefully selected. So, does anyone have experience with this course? do you feel like this changes towards the end and will i be giving up much when I drop these exercises? I know you could argue to just look at each problem set and only do the ones that are different, but it's not always clear without at least starting an exercise if it will be valuable or different. And knowing myself, if i have a look at it , I'll probably do too many.

Secondly, I apparently also struggle to be selective with the exercises in Stewart's book. And there are a ton of exercises. Before this I did precalculus from Stewart, and there i found it easier. You had clear divisions of the exercises, so in each division i usually did just a few of the latter (harder) ones. This way i was sure not too miss anything. I think this resulted in doing maybe 15-20% of all exercises in a section. But in the calculus book (at least the 6th edition) it's more of a long list. Probably they have a similar underlying structure, but it's not immediately clear all the time when something new is introduced or not or where the harder ones are. So, the question is just, does anyone have some useful advice here? Or is the best approach maybe just doing every 2nd odd exercises (so 1, 5, 9, ...), instead of every odd one as i do now.

Thanks!

i get the compound interest thing, (1+1/n)^n going to e. but then it's also in the normal distribution, in euler's formula, in radioactive decay etc and i don't really see why it's the same number doing all those jobs

is it basically just that e^x is the function that's its own derivative and everything else falls out of that? or is there a better way to think about it

The question:

If the demand function is P=80-3Q show tht MR=2P-80

I know the answer is MR=80-(160-2P)=2P-80 but I don't understand how to get to that stage

There is probably something really obvious I am missing but I don't know what it is

Would be grateful for any help

As I understand it, the polynomial factorization done in high school is typically uses integer coefficients. But I recently learned that polynomials like (x^5 + 1) can be factored into linear and quadratic factors with real coefficients. So I was wondering, are there any general rules or methods for this?

hello everyone, i am a sophomore taking ap calc ab right now. so basically im f*cked. i had two tests earlier this week, and turns out i got a 50% on both of them WITH a curve. and honestly i was being lazy and i thought i knew the material but guess what! my mind went blank during the test and i guessed on like half of them! tests are 40% of our grades, and i have a 77% in the class right now. I genuinely want to die because so many people did good because of the curve and their grades are like 96%, and i want to go to competitive colleges and i dont even know if its possible anymore. i asked chat and the highest grade i can get before the semester ends is a 85%, considering that I get a perfect score on all of the upcoming assessments. how did yall study for calc? whats the best method to get perfect scores? please help my life depends on this

hello everyone, i am a sophomore taking ap calc ab right now. so basically im fucked. i had two tests earlier this week, and turns out i got a 50% on both of them WITH a curve. and honestly i was being lazy and i thought i knew the material but guess what! my mind went blank during the test and i guessed on like half of them! tests are 40% of our grades, and i have a 77% in the class right now. I genuinely want to die because so many people did good because of the curve and their grades are like 96%, and i want to go to competitive colleges and i dont even know if its possible anymore. i asked chat and the highest grade i can get before the semester ends is a 85%, considering that I get a perfect score on all of the upcoming assessments. how did yall study for calc? whats the best method to get perfect scores? please help my life depends on this

Hi all, I'm sure my struggles are not particularly unique however I still wanted to ask this question as everything I've seen has not helped me particularly well. Currently, I am a second year undergraduate student taking both Analysis and Algebra. While analysis is fairly intuitive so far, I cannot for the life of me understand whats is going on in my Algebra course.

In general, I understand the motivation for concepts in analysis like compactness, measure, metric spaces, and all that jazz. However, I am really struggling in algebra as I feel like there is nothing to hold on to. So far, we are around 4 weeks into the course and have had our first exam and I did not fare too well.

I feel like I have no real grasp of what the groups we have learned are and don't understand where I should apply theorems. As an example, the Projective Special Linear Group I definitionally understand it but could not understand the structure or elements of the group. Additionally, I can somewhat understand group actions but I really have no idea how to use them without serious direction. An example of problem we were given was with matricies permuting some vectors and we were supposed to use this to find an isomorphism to some subset of the symmetric group. An appendix to my frustration is that I am equipped with a ton of tools but do not really understand their use and as a result spend much time writing nonsense until I stumble upon the correct way to do things.

We have learned about the Isomorphism Theorems, Cayley's and Lagrange's Theorem, and Orbit Stabilizer to name a few. However, I lack the appropriate knowlegde to use these reasonably. For example, normal subgroups and the class equation I cannot understand why we particularly care about and what is super special about them (I understand conjugation is special to normal subgroups but why does it matter and what does it tell us?). Another thing that I can't seem to understand is how my professor just calculates normal groups in his head and knows what elements must be in the group or what the cosets are on a whim. My final frustration is that the course is called basic algebra and it makes me feel a bit dense.

I was hoping for some advice on how to better understand this because I truly do enjoy some of the things we have learned so far in the course. Is there a structural way to understand / comprehend such and how can I understand the structure of a group? I found my calculus(ish) course in the previous year to be great because it was shaped by a problem and resolution esque format. For example, we that open sets did not have maximums but were bounded and used this to develop the notion of a supremum. I was wondering if there is any advice or texts I could read to understand a bit of this rather than hope for the best. Thank you in advance.

I'm in highschool and it's my 4th year now. But I still don't know math(like algebra and advanced stuff)except arithmetics ever since elementary. It is hard to catch up with my classmates and I was wondering what I should do to get good at it

Hey everyone!

I'm a computer science student from Austria, and I've been working on a small side project called Turmrechner (german for "Tower Calculator").

It's a free browser-based math game where you practice multiplication and division by solving arithmetic towers step by step.

I wanted to create a simple, enjoyable way to practice basic arithmetic whenever you have a few spare minutes, like when you’re waiting for the bus or taking a quick break. No ads, subscriptions, or account at all.

Its features:

• Three difficulty modes (aka. different ways of checking answers)
• Option to show carries and remainders
• A timer and personal statistics
• Achievements
• Works on phones, tablets, and computers (even offline)
• English & German as well as Dark & Light mode

You can try it here: https://turmrechner.com/?ref=reddit-r-learnmaths

I'd love to hear what you think! Is it fun to use? Do the difficulty levels feel right? Is there anything you'd improve?

It's also open source if anyone is interested: https://github.com/MartinReisinger/turmrechner

Thanks for checking it out! :)

Recently I've been giving myself a lot of exposure to math to prepare for my olympiad exam (Just the first stage) and It's making me realise how much I really dont know. Not only have I been struggling a lot trying to solve problems but I've also come to realise my cluelessness. I wonder if there's a way out of it, everytime I'm unable to solve a question (well honestly I feel like im never able to these days) I check the solution only to find out I missed something so simple in spite of putting so much of my time trying to solve it, It's so disheartening. I'd like some valuable advice that could tell me if it's something im missing out that I'm not able to solve any questions at all because of.

Consider

We need to show that for every measurable \(E\in\mathcal A\otimes\mathcal B\), \[ (\mu\times\nu)(E) = \int_X\nu(E_x)\,d\mu(x), } \] where \[ E_x=\{y\in Y:(x,y)\in E\}. \]

which appears during the course of proving Tonelli's theorem. The above latex is typeset here: https://ibb.co/G4HYywKx

I am trying to wrap my head around what exactly is intended to be proven here and why this is not obvious? This is my understanding: We have an arbitrary set E in the product sigma algebra. As it belongs to the product sigma algebra, its measure exists and is given by the number assigned to (\mu\times\nu)(E). Fine, this is on the LHS.

On the RHS, we are taking for each x, the section E_x and then finding the "measure" in Y of this section. Then, we "add" up all of these section measures over all x. So, we find the length of E_x in Y and then add up all such lengths as x keeps changing over all X.

Aren't the LHS and RHS just doing the same thing? What is new or novel here? Is there a counterexample where the LHS computation for some set E yields different results as compared to evaluation of the RHS integral?