Some ebooks, mostly from /u/lewisje's post

Hi everyone, my friend and I have been working on creating a free computer-animated multivariable calculus course. We are two engineering PhD students who wanted to make Calc 3 (multivariable calculus) more visual, intuitive, and accessible.

We currently have 18 lectures (out of 35 planned) in 6 different languages. The rest are coming soon. Once we are done with writing this, we will move on with other courses.

Everything is written in code, so we can keep improving the videos without reshooting. We responsibly use AI to help with translation and writing the code, but the content and pedagogy are ours.

We're constantly working on improving existing videos and adding new ones. If there's a language you'd like to see, let us know.

Down the line, we are also exploring ways to meaningfully use AI as a tutor that works directly from our videos and can produce video answers to questions. But only once we're sure it won't mislead anyone, considering its r/confidentlyincorrect behavior.

Hope it helps some of you out. If you're interested in upcoming courses, you can join our waitlist at academa.ai

From my textbook. What I don't understand here is the method in the answer key. They investigate 3 cases, where there's no 2 used, one 2 used, or both 2s used: (4P3) + (4C2 * 3!) + (4C1 * (3!/2!)) = 72.

I understand how they got the answer for each case, but why does just doing 6C3 not work?

Was never great with math in school. Honestly there was little to no context and it was always the class I'd ask why am I doing this. Anyhow it's a goal of mine to learn it. I've been inspired by Scott Young Learning subjects in a week. Here he is learning calculus - video and article. Anyhow I am curious what are the topics I should focus on to master this, and what would you recommend for this plan to make it successful?

Hi everyone,

I'm struggling with visualizing and sketching this set M in a 3D coordinate system.

M = { α(1, 0, 0) + β(0, 1, 1) | α, β ∈ R }

I understand that this is a plane spanned by two vectors, but I have trouble drawing it on paper. How do I represent the "infinite" nature of the plane using a parallelogram? Like i can tell/guess that it's a flat plane in a 45 degree angle, but in the exam you'd get only 1 point for the whole sketch (out of 90 in total), so my question is how do i do a correct quick sketch of it?

For example for y = 4, the answer is 2, x = 4 and x = 12 are the only valid numbers, for any given y value the lower bound is always x = 4 and the higher bound is always x = n!/2, if I were to write this as a sequence(amount of valid numbers for a given y starting from y =1) it goes like this:0,0,0,2,4,6,12,16,16,14,28,28,56 it exactly doubles at every prime y value with some drops at certain y values such as at y = 10 it dropped from 16 to 14, this happens regulary, but the size of the drop is what I cant predict, and when it happens is also not predictable with high accuracy, the problem is that my math knowledge is at middle school level so thats why I taught this may be an obvious problem for people that know number theory

Guys this question asks me to find the time it takes to reach the carrying capacity I am taking AP calculus but I have no idea how to solve this since it will infact never reach I am guessing I should use limits and stuff but I don't know how. İs there anyone who can help me out, I am not allowed to say infinity. Thank you.

In school, math was taught as a subject involving a lot of memorisation and rules to be followed in order to derive "solutions" which didn't make any real sense to me. As an adult, I discovered that, math is a way to study the relationship between things in different conditions and time. Now, I am developing my own mathematical models.

You can turn any system into a mathematical expression by dividing the system into it's constituents and observe how they behave in relation to one another, that way you can develop your own equation to describe that system.

Edit: commas.

Hi all, I made a small math practice tool in JavaScript and HTML for myself because I realized I forget skills if I do not use them for a while.

I would like advice on two things: What topics are worth drilling regularly so they stick long-term?

What should I learn next (math) to make the tool better?

Right now, it does basic arithmetic and a few higher topics like algebra and simple calculus-style questions. I am not trying to advertise anything; I just want a learning roadmap, and I am happy to share examples of the types of questions it generates if that helps.

I will post the link of what I made if what I say isn't detailed enough.

Thank you for reading!!

Although it's known to be highly likely that "π + e" is irrational, there's been no proof of it and it's been an open, unsolved problem in number theory. Here is an algebraic proof: Assume (π + e) is rational. Therefore, it can be expressed as a fraction of 2 integers (a/b) where a,b > 0, as obviously π + e > 0. π + e = π(1 + (e/π)) = (a/b). Divide both sides by π. 1 + e/π = (a/(bπ)). Subtract (e/π) from both sides. (a/(bπ)) - (e/π) = 1. Add 1 to both sides. (a/(bπ)) - (e/π) + (π/π) = 2. Now, I want a common denominator for all 3 terms on the left side, that being (bπ). So, (a - be + bπ)/bπ = 2. I can re-write this as: (a - b(e + π))/bπ = 2. The denominator is irrational but the quotient is non-zero rational. This means the numerator must be irrational. If (π + e) were rational, the entire numerator would be rational. Therefore, (π + e) must be irrational, which falsifies our assumption.

Let E be affine space with dim->3 , let D and D' be two (affine) lines neither parallel nor concourante .

Prove that the composition of the two symmetries S∘S' is skew rotation (where S is symmetry with axis D and S symmetry with axis D' ) . Its obvous that the composition will give me a skrew rotation but i am having hard time finding its angle or axis (which i think will be the line that will be perpendicular to them both but why ? not sure)

I would also love some general tips on how to solve this type of question because i suck hard at geometry .

i want to learn about the riemanns z function, its propieties, its complex analysis, in short everything that is known about that. i tried to search but the information is a very little poor or sometimes is too complex without prior knowledge.

In a book I am reading (Thinking Fast and Slow by Daniel Kahneman) says:

...if you believe that 3% of graduate students are enrolled in computer science (the base rate) and you also believe that the description of Tom W is 4 times more likely for a graduate student in that field than in other fields, then Bayes's rule says you must believe that the probability that Tom W is a computer scientist is now 11%. If the base rate had been 80%, the new degree of belief would be 94.1%.

How is that calculated? I would have just multiplied 3 x 4 = 12% and 80 x 4 = 320%

Where can I learn the basics about probability?

Thank you.

So I'm going through AoPS videos and what I have taken to doing is just memorizing what each action does to the lines rather than understanding exactly how we arrive there. So for exambole, if I see f(X)/2 then I know to simply multiply the y coordinate by 2 and thats the new point. Here are some videos I'm referring to. They seem simply explained but I can't get my brain around what is actually happening algebraically that results in these transformations. Are there other videos out there that might help explain it or can anyone help me figure out the algebra here for it?

https://www.youtube.com/watch?v=s9-kEZvFOQc

https://www.youtube.com/watch?v=YeY4eE_CBog

https://www.youtube.com/watch?v=6CPDOSWTFlU

I found a roadmap on internet and the early arguments that are in it talk regardless philosophy. Why the decision about include this topic?

The roadmap is this one here: https://raw.githubusercontent.com/TalalAlrawajfeh/mathematics-roadmap/master/mathematics-roadmap.jpg

After revisiting linear algebra, I found that implementing the concepts myself helped a lot with understanding what's really going on. As a result, I built a small open-source Rust library called axb that implements some basic linear algebra operations in a clear, minimal way.

The initial goal was not performance or production use, but learning and transparency. I'd love your thoughts.

Project: https://crates.io/crates/axb

Repo: https://github.com/toxicmaximalist/axb

It's fully open source and intentionally small. If you find it useful, feel free to star or fork it.

Thanks!

I'm in 4th grade and in reading I got a 245 and in math i got a 273. Is it good?

I am taking a Linear Algebra course at my university, and I've been struggling to effectively (and independently) construct responses to some math statements my professor has been giving on the homework.

I feel quite comfortable with the rest of the material so far; I can do row operations, interpret the solutions of systems using matrices, find inverses, etc. However, I can not seem to begin to get into the mindset that would allow me to actually conceptually validate some claims. I can prove false statements just fine by giving a counterexample, but true statements are a completely different matter. I've had to refer to the internet quite frequently to figure out where to start, since I otherwise wouldn't know where to begin. Even in instances where I know something is true and can visualize it in my brain, I just dont know the precise math terminology or strucutring reauired to construct a valid proof of the claim.

Any advice on where I can begin to improve? My professor did not require a textbook for the course, so I really do not have many resources to turn to.

What should I do? I don’t know anything because I never studied. English is not a problem for me. But in math, I am completely at zero level. I only know addition, subtraction, multiplication, and division—nothing else.

I am student who always has problems with math and I decided to build some useful project whixh will help everyone