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

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.

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.

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.

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 :(

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!

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. 🙌

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.

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?

College freshman here. I took Calc AB and BC in high school. I failed the BC exam last school year. I am retaking Calculus I as a result, and I failed my most recent midterm even with a lot of studying. I had a mental breakdown.

However, I was allowed to take Linear Algebra alongside Calculus I, and I find it very easy and fun to learn. The topics that took over two weeks of lectures to cover took me maybe 1 hour, tops. I'm genuinely not trying to be cocky whatsoever -- I thought I was bad at math ever since I started taking AP Calculus and I finally feel like myself again taking Linear Algebra. It's fun to do math with Lin Alg.

I was taking to Gemini AI about this math theory but wanted to see if anyone else has an idea? Either from a math/science or philosophical standpoint. I dont have any formal math training besides taking the normal math classes a STEM major takes, but have studied real analysis, proofs, topology, etc in my free time.

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No part of this publication (including text, original proofs, derivations, figures, and formatting) may be reproduced, distributed, reposted, or transmitted in any form or by any means without the prior written permission of the author.

I can say im actually decent at understanding math. However each week theres new lessons, and i have 3 subjects about math (Diffcal, math in modern world, and math for engineers.)

Heres how my study would go.

Id learn this new concept in math (like logarithms) then when i find that im weak at factoring, i spend so much time reviewing it to fully absorb it. Then when i return to logarithms, i find that i also have gaps in knwoledge when it comes to equations. So thats another thing that will eat up my time. Then my time has been fully eaten up and i havent even started to solve problems in logarithms and then its quiz day. I feel like i review so much and focus too much on fundamentals. Its so overwhelming and i feel dumb.

Any tips? ​

Retaking the pert test to skip remedial math. ( I should probably take them but I am trying to take my time and really focus on learning the fundamentals of math since I've always sucked at it and I also want to save money on courses)

I know I should do a lot of practice problems, but for the people who are taking more advanced math in college, how are you able to remember all the previous math you've taken? Ive been told all math just keeps building off previous math, so how does one continue to remember all the math they've learned? Say one is going to take college algebra, then calc, then maybe statistics ? Or whatever the order is lol

I'm just brushing up on what I learnt in school, basically I was curious to see if I could still do it and it turns out, yes, but also no. I can pretty easily just remember what I'm told and repeat it, I just need to know why lol. Also this has been asked before but the threads are pretty dormant now, so apologies for more of the same.

An example I found on YouTube asks you to:

Write x²+10x+28 as (x+a)²+b

Work this out by breaking x²+10x into (x+5)(x+5) = (x*x)+(x*5)+(5*x)+(5*5) which simplifies to

x²+10x+25

Therefore x²+10x = x²+10x+25 which can't be true

Having multiplied out those brackets which spits out 25, we then answer the question as (x+5)² - 25 + 28

So, (x+5)² + 3

What I don't understand is how that 25 appeared and once we've got it, why we just conveniently subtract it because x²+10x =/= x²+10x+25

Why is the final solution not (x+5)²+53 ? I can just remember to subtract ½b² but whyyy

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?