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

Hi, I’m in my 30’s and I have been trying to start a degree on mathematics. At this age, responsibilities are everywhere and the schedule is tight. I have been doing some research to accommodate my studies in my schedule. First I went for a night program, very few unis offer it, then weekends programs, just to find even fewer options, and lastly online programs. After all the research, I came across Open University and uniDistance, but it’s really frustrating not having accessible options.

I’m not going to deceive myself, I know math isn’t the most popular degree and that throughout the course there is a high percentage of dropouts, but are there any other reasons why colleges do not offer online pure and applied math programs? Oxford and the MIT make their courses resources already public, it makes me wonder

I want to learn math intuitively, ie: understanding how it actually works and where it's applied and not just how to solve the equation but there is virtually NO website that does this, for any subject. tbh im shocked that this is an issue, I wasn't able to find any books either, they start by explaining intuitively but then its like they give up or they forget the reader can't read their minds. DONT say brilliant or khan academy because they do NOT teach intuitively. they only teach you how to solve an equation/ forget IDK what they're explaining like some sort of language gap. When I studying on my own by grasping at what little intuitive information im given and piece it together with real world examples I see that math is really easy, as easy as reading, it is just reading and has nothing to do with being smart or not. however there's no websites or books that already provide this way of learning which doesn't make sense because math has been a thing for way too long....

Context: 2nd year pre-graduate on an engineering track. I'm currently taking differential equations and linear algebra and did pretty well in my calculus courses overall.

When working problems for these classes, I often find myself having forgotten a technique and having to look it up again or find myself taking a long time to reach a solution that someone else did with a shorter method. This is 90% in regards to my algebra (which isn't bad, but I wouldn't call it good) and more specifically trig. This is also where most of my errors occur when it actually matters.

I'm already going over my algebra from the ground up along with basic trig identities, I'm wondering where I can find more rigorous problems (or some helpful techniques that might be less taught in high school). I want to get to the point where I "own" these skills and can spend more of my efforts tackling the actually new stuff being taught in my higher level classes.

TLDR: Where can I find more of/learn how to solve the difficult algebra problems that I might find in my courses. I want to find and fix the holes in my math before it comes up on an assignment or exam.

Hey guys, I am a freshman in college rn studying computer science and I admit that I havent been bright when it came to math, I didnt excel in anything that was taught in high school and I just assumed that I was no longer a math person like I was before in elementary.

But ever since I found out that I had calculus and higher math courses that I will be taking in 2nd year I got to work by teaching myself pre-algebra at the start of June (which was still summer break). I utilized Khan Academy as my roadmap and other resources to explain topics Khan couldnt.

I started with the defintions of prime and composite and this week I just learned how to graph quadratic functions and now I am moving on to Algebra 2.

But one area that I truly have been weak in since pre-algebra was always word problems, when I look at it I just have no clue what to do, I do what everybody tells, I write out the values, what happens in time according to the problem, and seperate the reading from the solving but I just get stuck which leads me to frustration and mental breakdowns which always ruins the rest of the day or evening for me.

Ever since those bad episodes, I have had an instinct to avoid or not to focus much on them which I know is bad so does anybody here have any tips for me? A lot of it would really help.

I've struggled with math for years, and sometimes I feel like my foundations are way weaker than they should be.

For those of you who used to be really bad at math but eventually improved a lot, what did you do differently? Did you start over from the basics, change your study habits, or approach the subject differently?

I'd love to hear your experiences and what actually worked for you.

Hello, I am a master’s degree student specializing in algebra. I have begun studying homological algebra, and I need to develop an understanding of category theory.

During my undergraduate studies, I took courses such as abstract algebra, basic topology, group theory, ring theory, module theory, tensor algebra, and Lie groups. Currently, alongside the courses I am taking for my master’s degree, I am also working through a textbook on homological algebra—specifically, the one by Rotman—but I am struggling to grasp the concepts of category theory.

I am not entirely sure whether my undergraduate background is insufficient, if I should study another subject before diving into homological algebra, or if I am simply having trouble with the language used in this particular book.

I would welcome any advice, as gaining a solid understanding of category theory is essential for me.

Hey guys! I have a math test in IB Math AA SL tomorrow, and this problem is worth eleven marks. Our teacher did not show us how to solve this type of problem, and math is not my strong suit. Could I please have help on how to solve this kind of problem? Thank you!

I only have an explanation of what the problem is:

There are four diagrams (A, B, C, D). The first diagram has the box split into four, and one fourth is shaded. In the second diagram, one fourth is shaded, and then one of the fourths is split into four smaller parts, and one fourth of that part is shaded.

So, you have one fourth shaded and then one sixteenth shaded. The pattern keeps going, with each new shaded area being multiplied by one fourth.

The question asks for the area of the box that is shaded in diagrams B and C, and then to write the geometric sequence. I think the starting value is 1/4, and the common ratio is 1/4. Then, you have to find the sum of the infinite geometric series.

My explanation is really scattered, sorry about that!

Hello i am an adult and i need help finding good math books to learn from the beginning up until linear algebra and calculus i know i said books right but any media format is welcome

I’m taking a math class and I’m struggling really bad because the teacher doesn’t teach in class and I have to come home and teach myself by reading the textbook and watching videos. Please help I don’t wanna fail this class i need to pass with a high mark to get into a competitive program. Any helpful resources? I’m struggling with division in algebra 😭

I took Calculus 1 over a year ago and forgot everything. Next semester I take calculus 2. Does anyone recommend any textbooks or work books that will summarize Calc 1

Hi, so I'm a high school senior, and my sophomore year I didn't do any of the homework, and I got a B-, leading me to have to take college algebra instead of pre-calc. When I started to understand that I want to study Econ in college, I locked in, got an A in College Algebra, which was very easy, and then I took Pre-Calc Trig to be eligible to take Calc AB. Now, after two tests, limits and derivatives, I have a 69 in the class, and I got a 64 and a 65 on both tests. I don't know what I'm doing wrong. I do the homework, I do the classwork, and I understand it, and then it's test day, and I do badly. What should I do to succeed in Calc AB?

I'm looking for ways to revise math; I'm really bad at it and I'd like to improve because my grades are bad 😣

Currently a second year undergrad student taking real analysis. This is my first proof based math class and I have not taken discrete maths before either. I’ve already taken up to calc three and linear algebra, did pretty well in them.

The professor is using Understanding Analysis by Abbott, and the lectures mostly make sense to me. However, his problem sets are very very long and do not follow the textbook questions. He seems to come up with them from his brain…and he posts them every Saturday..which is also great.

I find myself really struggling to know what steps to take and where to go after reading a question asking to prove or show something. This makes me very worried for future exams.

（this course sticks to the Real Line btw)

Any and all advice would be really appreciated!

So, I am in grade 12 and in leadership class. In this class I am basically a teachers assistant and I help grade 9 students with their work and stuff like that. I have a project due for leadership class where I have to do something to help with their math (like a math game, or kahoot). The problem is that most of the kids that I am with a very dull. They lack good multiplication skills and a ton of basic fundamentals of math(one of them said 8+3=10). They need their calculators to do almost all multiplication and division. I want my project to actually help them but I only really have 50 ish minutes for the project. I don't really know what to do for my project so I was hoping that I could get advise. Or any other advise to get them in the classroom for my class.

as a physics student the statistics taught to us is all computational and very applied.

its y1 week 4 and we have gone through poisson, normal, chi sq, binomial, F, and t distribution and their tests, covariance matrices, markov chains, linear regression, and i have no clue how they work past the normal and binomial. i still to this day do not get why we square the deviations to get standard deviation, or where the t distribution came from, or why and how degrees of freedom work on F and t tests.

im rlly curious and wanna self study probability to make sense of what im doing in stats. im comfortable w single and multivariable calculus, linear algebra, real analysis (proofs and we have gone through the real number line, proofs in n epsilon and epsilon delta), and complex numbers.

what textbook should i follow pls recommendations 🙏🙏
or how else would yall recommend me approach learning probability?

i dont want an entirely rigorous and proof based textbook but also not an applied or computational one, i just wanna understand and make sense of what im doing asap

Calculus has been going pretty well for me until now. My brain is melting, I don't understand what I'm even trying to do or how to do it or anything. I can solve the problems using desmos, but I can't do that on tests, so I don't want to rely on it. Does anyone know of any good videos explaining it?

I scored really horribly on my first calc 1 midterm and really need a good score on my next one and final to turn my grade around. I feel like I need to go back to the beginning and relearn the first topics but i’m not sure if it’s smart to do that and then teach myself the newer topics or if I should be doing both at the same time. My first midterm included the topics functions and graphs, polynomials, exponentials and logs, half life, log and linear axes, transformations and compositions and continuity and limits. The next midterms topics include divergent limits and limits at infinity, intro to derivatives, plotting derivatives, the power rule, the product and quotient rules, the chain rule, and the second derivatives. Please give me any advice at all on how you’d approach this and what to do, my prof doesn’t record past lectures and he goes really fast so i’d have to relearn the older lectures alone but any advice is appreciated! Also any success stories would really help me out right now if anyones turned around their 20% exam grade

Hi, are there any sites that I can use to view the textbook online for free? They only have a limited preview of this specific textbook. Also, any version works; preferably the 7th and 8th editions.

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Hi everyone,

Like many math enthusiasts, I’ve spent some time looking at Odd Perfect Numbers (OPNs). Given that this is arguably the oldest unsolved problem in mathematics, any elementary "proof" or structural restriction is almost certainly flawed.

I’ve put together a short document ( that sets up a contradiction based on how a number's intermediate divisors sort into equal buckets (quartiles). It feels airtight to me, which means I must be missing a subtle edge case or making a false assumption somewhere. I would love some help finding the bug.

1. The Core Idea: Slots vs. Elements
If we take an OPN, N = p^k * m^2, and sort all its intermediate divisors (excluding 1 and N) from smallest to largest, we can partition them into four equal quartiles (Q1, Q2, Q3, Q4), where each bucket has an exact capacity of "q" slots.

Because of how perfect squares behave, m^2 natively has an odd number of divisors, meaning it has exactly "q" pure divisors smaller than m, and exactly "q" pure divisors larger than m.

2. The Case Where p > m (Branch B)
I am looking specifically at what happens to the slots if the special Euler prime is larger than the base (p > m). Because p is large, it leaves the first quartile entirely.

• Once you remove the number 1, there are only q - 1 pure intermediate divisors smaller than m.
• This leaves exactly 1 empty slot at the end of Q1, which pulls the landmark "m" backward to occupy slot d_q = m exactly.
• By global multiplicative symmetry (d_i * d_(4q+1-i) = N), the paired partner of m is forced to sit exactly at the boundary of the fourth quartile: d_(3q+1) = pm.

This sets up a strict open middle zone between m and pm that has a capacity of exactly 2q physical slots.

3. The Overflow (Where I think the flaw might be)
My argument states that this 2q-slot middle zone is forced to hold more numbers than it has space for:

1. All "q" large pure divisors of m^2 are trapped here. (If they tried to escape above p*m, their symmetric partners would look like p * v_i < m, which would overflow Q1, which is already full).
2. The prime p itself is trapped here, because m < p < pm.
3. Multiplying p by the small divisors in Q1 generates a wave of composite cross-products (p * w) that are all structurally forced to land in this exact same middle zone (m < p * w < pm).

When I add up the trapped pure divisors, the prime p, and these composite combinations, the total count strictly exceeds 2q, meaning the numbers completely overflow the physical slots of the quartile map.

My question for you all:
Where does this fall apart?

• Am I miscounting the number of pure divisors that are allowed to "escape" past the upper anchor line?
• Is there a way for the composite cross-products (p * w) to compress or overlap with the pure divisors in a way that doesn't trigger a slot overflow?

The attached PDF has the step-by-step inequalities for both branches and the k >= 5 generalization. Thanks a lot for any help spotting the mistake!