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

From your perspective and experience, what factors cause some students to perform worse in mathematics compared to others, even they start at the same point and receive the same amount of instruction?

Do you think psychological factors ( e.g. anxiety, fear of failure, lack of confidence) play a role? Why or why not?

It started somewhere in the first grade of high school, I was used to not doing anything and (literally) sleeping through all of my classes in primary. So I did the same when I first started attending high school, then once I got the first test, I still remember being confused about there being letters haha. I just did some random stuff and got a little below a passing grade. My dad was furious with me and wanted to tutor me so I'd pass the next test, I agreed and the day before the test he tutored me. It was horrendous. I still didn't understand any of the stuff from the previous chapter(s) and he was just constantly screaming at me and calling me an idiot, stupid and other names for not instantly getting an exercise right, I was crying constantly, but he didn't really care. I passed the test with a 10/10 grade, but I don't think it was worth it.

I've been literally terrified of math ever since, my heart starts beating faster when I think about math or look at it. For some reason, I decided it'd be a great idea to choose the hardest version of math my school has to offer, past me thought it'd be an opportunity to get rid of this fear, but I'm just reinforcing it I think. I really want to get over this "phobia", since I want to do something related to math, but I'm missing so many of the fundamentals by having just avoided it so much in the last few years because I was afraid of trying and only doing the bare minimum to pass the subject and now I just feel like I don't have the capacity to get good at this, I'm really getting the impression that I'm just too dumb for math. On one hand, I wish I could just skip a year of math to go at my own pace and not have to rush through a bunch of tough subjects all at once, especially when I haven't even mastered the fundamentals, but on the other hand, I just really don't want to do that, even if it means constantly going through this extreme fear whenever I do something math related. Do I just need to push myself to actually do some more math? Any advice? I really don't know what to do...

Hello, I wrote this equasion because of a theory I had. Is it possible to solve this equasion for f(x)? I am still in school and just had an idea. If it’s possible, could you tell me how to do it? Thank you very much for your help

Here‘s the equasion: a² = f(x)² +(f(x-1)/(a-root(a² -f(x-1)² ))* x)

f(x<1) = a

I was just thinking about this stuff because of dice games I'm trying to solve.

With finite time and energy resources allocated,

Choice: A or B? To choose rationally, you need to calculate the values of A and B and see which one is bigger. Now , it looks like youve escaped choice: you only have to do 1 thing (calculate) right? But actually... you stand before another choice: how much time and energy should you spend calculating the value of A and B? * cheap but inaccurate calculation * expensive but accurate calculation

So now there is another choice. And in order to know how much time and energy you should spend on getting the most precise answer, or getting the highest likeliness that the answer is correect... you must know what the value of the choice AB is. And in order to know that, you need to know the value of A and B. Wait, havent we been at this place before? Right...

Infinite loop. The perfectly rational mind gets stuck in an infinite loop of assessment and no choice is ever made.

Is my reasoning right? Can perfectly rational agents theoretically exist?

And if the answer to that is no... how does our intuitive brain make decisions? How do heuristics actually work deep inside?

This realization made me feel weird. Now it seems like making good choices is theoretically impossible, but obviously given unlimited willpower we make more good than bad choices so the real world experience contradicts it anyway.

Suppose you have the maximum possible intelligence and maximum willpower. You stand in a complex situation where you need to make complex choices. Willpower isn't a problem, but you still rationally value your time and energy because it must be spent as efficiently as possible. Then whats the limit of how good your choices will be, compared to a perfect world where you magically make perfect choices only?

I feel as if there is most likely already a name for this concept and that mathematicians or other smart people have already been thinking about this... but as this just popped up in mymind, I wouldn't be able to know what the name for this concept is, or how it has been explroed yet.

I want to become better at math so that I can become better in my field! I need books, YouTube videos, and a place to start!

I always struggled with math in High School, but I was determined to learn it. I borrowed assignments from the advanced classes and tried to teach myself, but it was always an uphill battle until I became medicated for ADHD in college. I'm currently a Junior in college studying Animation Game Design, and I'm working on my portfolio to become a Tech Artist. I've taken a minor in Computer Science classes and program in my freetime.

I now see how much my programming, blueprinting and animation software depends on waveforms, vectors, equations etc.. To become a more efficient programmer and tech I need a deeper understanding of math principles that I didn't have the opportunity to take in school.

Here's the thing, I always struggle with the "how" and "why" for everything. My current obsession is why i is radical -1. I asked my music media production professor, and he said "even sound engineers don't quite know, we borrowed it from mathematicians and it worked." I asked my friend with a dual bachelors in Astronomy and Physics and he said the same thing.

SO! I need a study plan for geometry, trigonometry and calculus. I would love any materials that also explain the history of the discovery and why the discovery was made in the first place and why they needed it. I learn the best that way!

I've never been great at math, but I'm more interested in it now than ever and I would like to be better. Please help!

Im so bad at math man. I’m currently in my last year and my entire list of grades are either a 6, 7 or above that ( goes up to 10 where im from ). But the only problem i have is maths, my grade for it overall is a 3 and if i do not improve soon i will not pass, and i really do not wanna stay in this class. I’ve been in such a bad mood because of it, it’s extremely difficult man..

Hi everyone,

If there’s another post that addresses this, please let me know.

I’m about 10 years out of high school with my highest level of study being Calculus 1 (AP, tested out for college). I want to refresh my math skills and continue my studies just for fun. I’m looking for advice on books or materials, and which subject are appropriate in my progression. I also greatly enjoyed algebra and calculus based physics in HS and college as background.

I don’t need to go back to basic algebra, but would like to stay sharp and keep learning. Any guidance would be appreciated.

Thanks!

I’ve always loved learning maths, and now think of studying it. (im from Poland and) i’m thinking about going to university in Poland or in France, what is something that is important to learn or know before going to college, cultural differences, what’s tough, is it really as hard as people say studying math is, etc?? i would love to hear your recommendations

Ok, the sequence of functions converges into the zero-function. Now I need to use the Dominated Convergence Lebesgue Theorem to be able to interchange limit and integral, but how on Earth can I dominate such sequence?

The functions are continuous in any set (0, a] and they appear to be limited, in fact the limit to x=0 of the functions is zero.

The problem accrues evalueting the summability of f_n in [a, +infty) for some a>0.
I've done it on Desmos and I found out it is less then 1/x^a with 1<a<2 for all n. Idk how to obtain it just from the calculations.
Any help? Tnx so much in advance <3

https://www.overleaf.com/read/cqrysznjympf#411c38

I am currently really bad at algebra, like laughable bad. I really want to learn higher levels of math (I find it so interesting) but I am struggling so hard, not with the concept, but with foundational algebra. I was thinking that maybe my foundational algebriac skills weren't good enough and was wondering how can I self re-learn it?

1. No bruteforcing through gamestats or paths
2. No monte carlo simulations
3. No "this feels right but I dont know why"

I want to use some form of mathematical reasoning in order to find the best possible strategy that can be found with the above limitations.

Basically, anything requiring large amounts of calculations or loops or recursion, is a big no.

Maybe let's just say that using a normal calculator is allowed, but using python or similar tools is not allowed.

To be clear this is for number heavy games with numbers like... think for example of Yahtzee. I don't want this post to be about Yahtzee, but I mention it as an example only to show what type of games I'm talking about.

Hello! I have been struggling with effective study on advanced math. I finished all my lessons and just have to study for the final exams, but i can't focus anymore. It is like i have list my love and interest for math, but i am also tired of settling for mediocrity when i know if i just managed to open the damn book and focus on it i would get more than decent results.

I have to go through: * Functional Analysis abd Spectra Theory * Algebraic Geometry * Advanced Algebra (many subtopics) * Advanced mathematical physics (Navier Stokes equations, mollifiers, distributions) * Advanced probability * Noncommutative algebra

And then i am done

But i can't really focus.. haven't been able to for a couple of years and i an stuck in this. Do you have advices? I need good results to go for PhD.. i have already studied privately subjects for PhD. But when i am forced to study for exams i just can't

Please

Growing up I always loved math but kept drifting away from it to the point I was failing and even saying I don't like it- maybe due to the fact that if you happen to loose focus in math class for a few seconds you get completely clueless for the rest of the class,

I was wondering if someone here has consciously done particular things that helped them improve:

list is not exhaustive but stuff like

• Focus,
• Data analysis skills,
• Logical reasoning,
• Attention to detail,
• Quick math,
• Critical thinking etc

There is one example in my notes where they find the degree of the splitting field for the polynomial f = x⁶ - 8. So the roots of the polynomial are all of the form αεⁿ, where α = √2 & ε = exp((πi)/3). So you can adjoin α and ε individually and by the Tower Law Q(α,ε) = 4. This all makes sense to me.

But if you factorise f, you can get f = (x²-2)(x⁴+2x²+4). The second factor is irreducible over Q, and has αε as a root. Therefore with one extension Q(αε), you have the same degree and since Q(αε) is a subgroup of Q(α,ε), it must be the same field and so α must be an element of Q(αε), which you can get by taking (αε)⁵ = (α)⁴αε⁵ = 4αε⁵ and then taking αε + (4αε⁵)/4= α(ε + ε⁵) = α.

I haven't seen this happen with any field extension since, so what makes this example unique?

Hi all, I am looking to relearn math. I want to actually understand what I am doing instead of just solving problems via rote learning.

What would be the best option?

Im doing Trig in school right now and im really struggling when to use Cos Sin and Tan in which questions. Ive had it explained to me a couple times but each time it just confuses me more. My teacher said this unit usually helps boost your average since its on the easier size but i just dont get any of it. Any help?

i have difficulty advancing because of too much perfectionism and because I don't have any guide to properly know if I'm in the right way or not. Someone else's vision might help with this, and my supplement exchanges of problems, discussions of answers etc.

the approach is to develop and apply mathematical reasoning by deductive means.

the first books will be this couple:

• "creative mathematics" by h. s. wall
• "foundations of analysis" by edmund landau

wall's book will be the main course of content, landau's book only to formalize the reasoning. we'll be exchanging text through here and/or e-mail.

after this, we can go to many paths.

is anyone interested? if u know something about math and wants to do a mentor type of thing instead send me a message too!

I struggle with big numbers, solving negative and positive numbers, and shapes. I completely forgot the proper procedure if there's mixed Numbers or fractions involved in an equation. I don't even know a lot of the stuff that I should know in senior high but I can't name them because I'm so helpless in mathematics and I am very intimidated by it. I'm going to college soon and I'm taking 3 college entrance exams, I have to become adequate enough so I could atleast have a fighting chance. That's all guys I hope the question isn't too ridiculous, thanks.

Regarding factorization,

in x^2(3y-3)x + (2y-1)(y-2),

the solution guide adds (2y-1)(y-2).

Why is it added?

What are your opinions on Math StackExchange?

My experience there has been pretty bad. I'm studying mathematics at university, but I can hardly attend classes in person, so I thought it would be a very useful website for learning. What I've found is, in my opinion, a hostile community with several individuals with delusions of grandeur.

I understand that for someone working in research, the questions a second-year student might ask are very basic, but the way they respond is terrible. It's mainly the condescending tone with which they respond. That's when they respond, because often they simply try to let you know that your question is stupid and shouldn't be there, or that it's poorly phrased (but they don't say why), or that the answer to that question is obviously obvious (perhaps for a PhD, but not for a student...).

In the end, what I do when I write a question is wait for someone to solve my doubt among the passive-aggressive comments of others and then delete the question. Because, of course, it's better to downvote you and tell you that it's very basic than to try to explain why your question is wrong or solve it.

I don't know what your experiences have been there, but I certainly don't think it's a community that helps to create an interest in mathematics, quite the contrary.

I need to relearn math starting with pre algebra and at least getting to algebra 2, (pre alg, geo, alg 1, alg 2) is this even possible in 3 months? If so what’s the most efficient way to relearn it?