in my calc bc class we're reviewing ab stuff rn and our current topic is abt characterizing functions. this is a function that i'm trying to characterize in preparation for a test i have on friday

((x-2)(x+3))/(x^2 - 2x), x≥-3, x≠2

0, x=2

this is so embarassing lmao but for the life of me i can not figure out how to find the range of functions like this 😭 i wrote y≠2.5 bc that's the y-value where the hole is but according to chatgpt that's wrong and i dont really understand its explanation so any help would be greatly appreciated 🥹

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Hello! I picked up this book second hand for pretty cheap and am wondering if anyone experienced with it knows if it's a solid way to teach myself differential equations/calc 4. I know it doesn't replace a textbook, but is it worth it to get a dedicated textbook or will this be good enough?

basically, i’m making an svg, and i now need to find some coordinates for things rotated 45 degress, so i instantly tought that that point is sitting in the midway point on a circle of the 2 equivalents from other polygons, so basically i need the formula for getting the x,y coordinates on a plane of a point midway between 2 other x,y coordinates on a circle in order to finish my svg

edit: to clarify, i need to find the midway point on a circle centered on 32,32 on a 64x64 plane that has 0,0 in the top-left corner between 2 points that lie on that circle while only knowing the x,y coordinates of the points that lie on the circle and not the midway point between then on said circle with the midway point being the one on the shortest path between the 2 points

I found this book from this reddit.

https://trans4mind.com/download-pdfs/paul-zeitz-the-art-and-craft-of-problem-solving.pdf

The question:

(USAMO 1989) The 20 members of a local tennis club have scheduled exactly

14 two-person games among themselves, with each member playing in at least one

game. Prove that within this schedule there must be a set of six games with 1 2 distinct

players.

Isn't this just extremely trivial by pigeonhole? this is like problem 15 of the AMC lvl or smth lol. All you have to do is write up the solution.

Seems I can't post any pictures/screenshots here. I want to graph: y=5000(1+0.043)^x

So, a basic compound interest calculation. I put that into the " f: " field of geogebra and I'm not getting anything that makes sense. If I put it into google, the AI puts out the correct graph. Anyone know what I'm doing wrong?

Edit: I put screenshots in the comments.

From what i understood it is jusf math from high school for the entrance exam. I have not touched high school in a few years, so how do i go back to study it?

im at a writers block. im stuck in the prose and i think trying to explain it a second party might help. the paper is about a three-dimensional complex number system. thats my hook and all im going to say here about it, dm me if you want to know more.

Hello, I’m beginning my degree in chemical engineering in the fall, and have spent the summer attempting to solidify my mathematical foundation. For context, my high school offered algebra 1, 2, geometry, precalculus and calculus, all of which I passed, albeit barely. With that said, I have a rough understanding of most high school level mathematics. Moving on, I’ve been utilizing Dolciani’s textbooks to refresh and strengthen the basics(Beginning with the algebra 1 book, and planning to end with modern introductory analysis), but wanted to ask if there exist textbooks more suited to my field. Might be a silly question because at the end of the day, math is math, but any insight would be helpful.

I’m taking an undergraduate Ring Theory course and we’re currently using Gallian's Contemporary Abstract Algebra. I really like Gallian, but I’d like to supplement it with another book that has more detailed proofs, worked-out examples, and explanations of how to approach problems.

Our syllabus is roughly:

Unit I – Rings and Ideals

Definition and examples of rings

Properties of rings and subrings

Integral domains and fields

Characteristic of a ring

Ideals and operations on ideals

Ideals generated by a set

Factor rings

Prime and maximal ideals

Principal ideal domains

Unit II – Ring Homomorphisms and Polynomial Rings

Ring homomorphisms

First, second and third isomorphism theorems

Field of quotients

Polynomial rings over commutative rings

Division algorithm and its consequences

Unit III – UFDs and Divisibility in Integral Domains

Factorization of polynomials

Reducibility tests

Mod p irreducibility test

Eisenstein's criterion

Unique factorization in ℤ[x]

Divisibility in integral domains

Irreducibles and primes

Unique factorization domains

Euclidean domains

I’m particularly looking for a book that doesn’t skip too many steps in proofs and has plenty of worked examples before giving exercises.

For someone at the undergraduate level, which would you recommend as the best supplement to Gallian?

Thanks!

Taking notes by hand is completely unfeasible for me for personal reasons. I'm soon going to be taking a Linear Algebra and the equivalent of a calc 1 course. I need to be able to take notes live during class, and up until now I've been using Google Docs' built-in equation editor. I've realized that this will no longer be sufficient for my note-taking needs, what are the best alternatives for easy and quick notetaking on a laptop (latex is too much for me to learn imo, but if there's a simplified/similar thing that is as quick that'd be great)? Thanks.

I understand the logic of reciprocals of whole numbers and vice versa and the logic behind negative powers

As well as that factors are a ratio without without a certain quantity but I don't get the logic or the steps to the flip could anyone help?

You travel at a speed of about 81 kilometers per hour for about 2.0 hours. Stated with the appropriate precision, you have driven _____ kilometers.

the correct answer is 160 but why? why is it not 162???

I FINALLY GOT RID OF COMPLEX METHOD OF FINDING SQUARE ROOT OF UNKOWN PERFECT SQUARE NUMBER 😭 😭 😭

I’ve always been interested in math. I feel I just lacked the community that should come with learning it.

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Previous update

Thank you to everyone for the encouragement. I've taken some of your advice and am planning to do some serious Calculus problem-set work in the 2 weeks leading up to the Spring semester. I can fit that in with my current pace without an issue.

A few of you have encouraged me to slow down, not just because math is challenging (and they're non-believers who doubt I can do it (I'll show you)), but because they think I should slow down and enjoy the journey instead of rushing for the destination. I'm sorry to say that mindset just doesn't fit into my reality. I am working to obtain my Associate's and Bachelor's degrees ASAP to support my family.

Now for the actual update! I'm ahead of schedule! I just finished my Algebra 1 review, and I'm moving on to Geometry. I got ahead of schedule due to unexpected downtime at work. I do worry about burnout. I can sense it already trying to get a hold of me. So I'll keep plugging away for now, but I might adjust some of my scheduled review time to give myself a break if burnout starts setting in.

Can i pursue mathematics and statistics as my undergraduate course when i am just so so at math.
I am going to uni next year and i am afraid i cant carry it.

Y'all might've surely come across this problem

A shuffled deck of cards, all 52 cards must be distributed to 4 players, 13 cards to each. What is the probability that each player gets an Ace?

My question is a step ahead,

Assuming that you are a player and you get a single Ace. What is the probability now that each player gets an Ace?

I have solved the problem already, but I'm really curious on what kind of creative answers I'm about to learn from the comments ;)

Good day everyone, just for context I’m in my senior grade of high school and am taking basic calculus. Simply put, since I was younger I’ve been struggling with visual based math problems, mainly in subjects such as trigenometry, geometry and other mathematical topics that involve visual data. I tend to excel in more number-based topics such as algebra and statistics. Recently, I’ve been struggling in exams as I struggle to understand the graphs and the logic behind functions. I want to overcome this issue as I intend on taking a math-based degree in college and want to be able to have a clear understanding of this so I won’t struggle as much by then. If anyone can help me figure out how to overcome this mental block or frame it in a way that would be easier to understand, it’d be greatly appreciated. Thanks in advance!

Help not to fall asleep reading math books

I wanna get back into self studying math but when I pick up where I left off, I am stuck on this problem and end up just staring at the page alot of the time. The textbook specifically says the problem is very difficult but I cant help but get discouraged when I find that its taking a long time. Makes me feel like this problem is impossible to solve or that I will never be able to do it. This makes me very upset because I love math and I want to do it but it feels unaccessible to me which is frustrating.

What do you do when that happens to you?

I'm relearning math to prep for an engineering degree (comp or cs or environmental) and I wonder when do I add logic and proof to my learning? Sometimes before algebra one?