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

College freshman here, I have a passion for engineering and so obviously I want to get good at calculus. My first calc exam I studied a few days in advance for, took it, mind went blank, got a 30%. I decided this time around I would start studying 2 weeks in advance learning how to do each type of problem, practicing 3-4 similar problems, and so on and so forth. Just took the test and my mind went blank and I remembered basically nothing that I spent so long studying, even though when I studied it all the processes made sense to me. It feels as if calculus is like trying to learn another language off of just remembering past conversations, so I have no idea what to do. Any tips are massively appreciated.

I can learn and solve problems but I don’t understand the real world application of it. I struggle to visualize what is going on, and I want to understand the “why”. An example is trigonometric derivatives, 2nd order derivatives, or (Duf) directional derivatives, etc, super easy but I don’t know “why” it’s done that way. Right now, I just memorize the steps rather than understanding the real world application. I want to look at a question or solution and understand why it’s done that way. I couldn’t explain it to anyone. I just solve

I am a foundational learner. I need to understand why and how something works before I can use it properly, and having the basics behind them explained clearly helps me enormously. For example, I want a book that explains concepts and how and why that’s true, like a good physics or physical chemistry textbook (im a physics major). Any recommendations would be appreciated.

I have a question, maybe it's not a specific question, but... I think it'll be better if I explain whatever it is, I'm about to write.

Here is a question; what is the least common multiple of 2, 4, and 6?, obviously it's 12, because if you start the sum, you're going to find this: for 2 = 2, 4, 6, 8, 10 and 12, for 4 = 4, 8 and 12 and for 6 = 6 and 12. Or it can be like this: 2 = 2, 4 = 2*2 and 6 = 2*3; so the result will be 2*2*3. But there is something interesting between these two methods, they are the same, in the example of 2 (2 = 2, 4, 6, 8, 10, 12) the result is 2*6, and 2*6 is equal to 2*2*3, equally, for 4, it is the same (4 = 4, 8, 12), although it is different, because it is not 2*6, it is 4*3, but 4*3, it is equal to 2*2*3 (and for 6 it is the same; 6 = 6, 12, so 6 * 2 = 2*2*3). And here is a pattern; the distance between each multiplications is fundamentally (with fundamentally, i mean, when you factor the numbers; 2 = 2, 4 = 2*2 and 6 = 2* 3 ) the same (2*2*3).

My questions is: why ?, why does this happen ?, why the distance between each multiplications is fundamentally the same ?, why is the number raised to the greatest power the one that is multiplied by the other numbers (washed to the largest possible power in the same way) ?, how else can the problem be solved ?, what is the perspective from which you understand the problem ?.

I'm going to apologize, before anyone says that don't understand my question (because it already happened to me), so, sorry, I really tried to make it as clear as possible... sorry, again).

Reediting the text, I realize that it would be easier if I just said that I have several questions, instead of one...

Hey guys, so about 2-3 months ago I decided that I will try to master calculus 1 while self studying and having never taken calculus in high school. I’m still attending highschool tho. Since then I’ve made massive progress I would say. I’m currently reviewing everything I’ve learned in calculus 1 and polishing every skill. Looking back I think this is the best decision I’ve made in a couple of years, honestly. I have also decided that after I master calc 1, I will continue on to calc 2 and 3. And after that I’ll just keep learning math until I complete a full mathematics course that a math minor/major would. I have no idea how long this is going to take me but I’m sure I’ll love every second of it. I was wondering, is it as easy to find free lectures online for further maths such as real analysis as it for calc 1-3? I would greatly appreciate if you guys were able to drop a few link might help my endeavors. 👋

is this correct ok so we have a set X and a subset the set is partially ordered so both comparable and non comparable all of our subsets are organized by linear order so they have only comparable elements we find that an upper bound is in each subset so that greater than or equal to now we have a direct boundary now we look back at our set X and find the element that has no  element that comes after it making it our maximal element the rule for upper bound is greater than or equal to so we can have multiple upper bounds in any given subset but because we applied a bound is the reason why we can look at our set X and point out the maximal as it represents a boundary created through upper boundary if it wasn't for this both our set and subsets would be going on forever so the boundary stops them from going on forever because its a boundary.

according to this

0.2 Zorn's Lemma. If X is a partially ordered set and every linearly ordered subset of X has an upper bound, then X has a maximal element. Clearly the Hausdorff maximal principle implies Zorn's lemma: An upper bound for a maximal linearly ordered subset of X is a maximal element of X. It is also not difficult to see that Zorn's lemma implies the Hausdorff maximal principle. (Apply Zorn's lemma to the collection of linearly ordered subsets of X, which is partially ordered by inclusion.)

Currently a grad student on track to get a math PhD, but I've hit a brick wall and realized I have ADHD with a recent diagnosis. It's been hard to adjust to focusing for long periods of time in grad school, since somehow I got by in undergrad. Any tips?

So I'm here to ask if anybody knows how do I study or continue my study of Linear Algebra. I know like very basics of math.

Currently I'm watching the Esceene of Linear Algebra by 3Blue1Brown but I don't know what to do after, should I do practice qns or watch any other course.

I also want to add that purchasing any books will be hard task for me because they aren't locally available and shipping isn't also a major option.

Hi everyone,

I’m writing from Turkey! I’m currently taking a gap year to prepare for our university entrance exams. I work hard every day, but I’ve hit a huge wall when it comes to math word problems.

When I study the concepts or watch video solutions, everything makes total sense. I get the logic and the formulas easily. However, as soon as I sit down with a practice book by myself, I struggle to translate the text/story into a mathematical equation.

Because I fail to make that initial connection, I get demotivated very quickly, feel bad about myself, and end up giving up or walking away from my desk. It feels like a total mental block.

For those who have gone through this and overcome it:

1.How did you train your brain to step-by-step convert story problems into math?

2.How do you deal with the frustration and demotivation when you get stuck repeatedly

Any advice, mental frameworks, or practical study tips would mean a lot to me right now. Thanks in advance!

How do I prepare to an Olympiad from a high school math level?

Hi! I'm currently in fifth grade of high school (I'm Mexican, as far as I know is like 11th grade in the US) and want to start keeping in math. I always liked it and in the last year I started learning a bit more, specially on proves, understanding why instead of just copying the teachers formulas.

This year I want to try the olimpiad, my school (the UNAM) makes a yearly math olimpiad and I want to participate in it. It's not top level including deep props, real Analysis, complex analysis, calculus, etc. It is more basic but still impossible for most regular students. I try to solve some problems and solve half of one exam, I really love this kind of problems.

I really want to win an keep learning, not only for the contest, but for my future. I want to study math, so I want to prepare from know into pure math.

What is the path to go from mechanic thinking into abstract logic? I love this kind of thinking but I'm kinda stuck into how to improve my knowledge.

I'm 31 and based in the UK (sorry we call it maths here) and I've struggled with numbers and the whole subject my whole life. I excelled in most of my other subjects at school, however when it came to mathematics, I just couldn't get my head around it. I was extremely fortunate that I received extra help at school and that my parents recognised my struggles and had me going to personal maths tutor, but despite all this I still only got a C in maths (I'm fairly convinced that the grade boundaries were heavily lowered though due to our school year doing so badly).

During college, the tutors recognised my struggles and organised some sort of dsycalculia assessment type thing along with other students who were struggling. Stupidly, I never finished the assessment (turns out I had undiagnosed ADHD which I've only had diagnosed this year), so I never found out.

I have a degree in Biology which thankfully doesn't have too much maths involved, but I've had enough of just getting by trying to avoid the subject, so the last few months I've been trying to re-learn it starting from the very basics. My partner is a maths whizz and he offered to help me, claiming that I probably just had bad teachers, but then he said he was finding it difficult because I just can't grasp basic stuff and I ask weird questions like "but why is a 7, 7"? or "but why is this number on top during a fraction?". Just getting really deep into it, it's like a whole different language for me. I can't visualise numbers and calculations, even when I write it down and my brain just gets muddled so easily. I couldn't figure out 20/1=20.. because I can't visualise it, I just see a different language that I need to try memorise, so I don't know the difference between 20/1 or 1/20. It's embarrassing because I still need to do basic maths in my job and I can't do simple stuff because I just don't understand it, or I know the answer but I don't understand why that's the answer. Sometimes I overthink a correct asnwer so much that I end up making it incorrect.

I'm so embarassed and sad about this. I feel like no matter how hard I try, I just can't get it. When I was learning basic fractions, I had to draw pictures of pizza slices and stuff and I was still getting it wrong. I'm 31 years old and I can't do basic fractions or times tables or literal primary school maths. No matter which method I try, I get confused. I've tried books, youtube videos, mock tests, my partner going through questions with me.

I don't know what to do, I really want to keep trying to learn but it's just making me feel depressed and stupid :(

Keeping it short; I'm applying to (applied) math PhD programs in the US, and I'm sorta doing some guided reading on dynamic programming, and connections to mean field theory right now. Also, some optimal transport. I'm concerned never taking intro to PDEs is gonna really hinder me beyond the whole applications part.

The thing is, I'm kind of faking the fact that I'm familiar with PDE theory; like I never took the course because I had a bad experience in my intro to ODEs class (full of engineers), but I've been realizing that I kinda need it to talk about most of the results in the readings. I'm more comfortable with being unfamiliar with measure theory, which does come up a lot in OT; the PDE stuff, which I feel I should be familiar with by now, is the more troubling part.

My prof is OK teaching me this cus I took his Stochastic Calc course and I had some exposure to PDEs there, but honestly I've always had a bit of a lousy understanding past the simple classifications of PDEs, and the qualitative descriptions of them. I'm concerned that I'm not going to be able to work with more complicated SDEs (HJB, Mckean Vlasov, Fokker-Planck) if this keeps up, and I can't take a PDE sequence until grad school (a year from now).

Also, I kind of don't enjoy how PDEs are motivated with physics; could just be a personal preference.

I've considered picking up a traditional intro to PDE book, but that's lowkey a BIG time commitment I'd have to carve out.

Any tips on what I should do?

I have an exam coming up on Friday. I was just wondering if anyone was familiar with ODE’s and would help me study since none of my classmates seem to be available.

I’m about to transfer to a 4-year university, but I’ve already been at community college for two years. I unfortunately got interested in math very late, and due to my performance in high school, I had to take precalculus my first semester. I’m in my second year and I’m currently taking calculus 3.

I’m already aware how incredibly behind I am and I wanted to try and learn stuff now so I can try to
hopefully catch up. I also wanted to go grad school and I’m
pretty sure taking graduate classes as an undergraduate is pretty important.

I just kind of don’t know what to do. I feel like I’ve forgotten how to do some elementary things so I’m sure I should review that. I think I should also learn proofs. I was thinking about reading through apostol to refresh my memory on calculus 1 & 2 to prepare for advanced calculus 1 and 2 which I think is proof based.

Any advice?

I also have a pretty open schedule as I was forced to drop 2 classes (and possibly one more). The only class I’ll stick with for the semester is calc 3 and I will probably take differential equations next semester, and maybe linear algebra if my scholarship will cover the cost (it’s a long story on how it works).

The cardinality of the set of real numbers is the same as the cardinality of the set of continuous real functions. Is there a relatively comprehensible bijection we can construct, or is it more of a "we've proven it's possible to do, but there's no pretty way to do it" kind of situation? Like, I want to have something where I can plug in exp or sin and come back with some unique real number.

Hi! I'm working on Nabla, a free math tutor: Nabla

Type your working or snap a photo of your notebook, and it marks the line where your first mistake is and what kind of mistake it is. It doesn't give you the answer, just a hint. It also tells you when you got the right result with wrong working.

It covers equations through derivatives, including the topics on university entrance exams. If it gets something wrong, you can send your exercise to a teacher who'll explain it.

It's still in testing, so if you try it with your homework and tell me what breaks, that helps a ton. 🙌

can someone please help me find a good yt channel for BCA maths? im in my first semester and they don't teach us anything in clg😭

in school im used to a part of subtracting polynomials being distributing the subtraction sign, the "negative sign" into the parentheses. i understand that doing so is the same as multiplying everything by -1 (well why do i have to do that?) as a positive sign multiples everything by 1 which just equals itself.

in the ordinary integer simplifying question: 7−(−4−3)−9 we do not distribute the subtraction sign into (-4-3). but if this was a polynomial we totally would.

the book im using to self study (Openstax but ive switched to a different open source) explains that - outside of a negative number by itself is actually a positive number because the - sign is asking for the opposite of the number within parentheses. i could get that if it was consistent.

i know the answer to the question, im not really asking how to solve it, im asking what is with this weird rule that applies situationally i cant find much about online?

is "distributing the negative sign" some sort of law? a shortcut for something else? why is it necessary, why cant we keep everything the same? is it related to when we have a variable-- how?

I’ll keep it short and simple. During sixth grade, he had a 100 in math straight up.
But he’s now in 12th grade and his brain completely shuts down when he has to do math.

He’s had around three awful math teachers
One was obsessed with homework every day and you had to get a 100 just to turn it in. Meaning he had to do hours of constant correcting.

Another one just had another student teach for him, which made it awkward and he eventually stopped trying.

And then the third one was that kind of teacher that just told you to Google it instead of actually teaching

I just feel like there’s nothing I can do to help and he feels like he’s hopeless that his brain is completely shot when it comes to this.

Is it true that you can have trauma from bad math to where your brain will shut down from it?