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

I just cannot fathom interqactions or 3 dimensional geometry but ther are you people studying and develop[ing higher dimensional mathematics. But the question is how is it useful and how do we know it is correct. We know that the volume formula for a cube is correct becuase we can measure and see the amount of water put in it (please dont ask me he question 'how do we know that what we measured is exactly 1 liter , we have assigned the unit and water is something tangible so it feels intuitive), how do we know the shapes and how do we know its projection in lower dimensions is correct or not,

I am including the 4th dimension because I had watched a vide on theroy of relativity where time is the 4th dimension and for the fact that if we include time into the coordinateswe can assign a unique coordinate to each and every interaction.

Thanks in advance!

Hi,

I have always been a very stubborn when learning mathematics, I am willing to listen and to learn but I take a lot of convincing more so than the average person. I will spend weeks doing one thing if I do not understand something I can’t shake this negatively feeling until I do.

I fall behind very quickly because of this. There is no limit to how long I’m willing to struggle, even then I can admit some of this is “pointless struggle” as I’m not changing my approach or thoughts I am trying to tho as I’m doing this , though I find this quite hard to find the cut off between helpful struggle and pointless since sometimes time is what you need, I am still not comfortable moving on because I believe I need this done to understand the next thing.

A lot of what I’ve been confused about is quite simple things. Not concepts but reasoning. I think too much about the finer details that are probably irrelevant in my case. Especially since I am in very early days of my degree my mathematical maturity has not caught up.

I don’t believe I’m correct and have disproved some 5000 year old formula or method, I know I’m wrong and I know what I’m reading is correct but i can’t just accept something is true or semi understand it. I need to be 100% happy.

I talk to people, teachers or professors but only on rare occasions is this helpful because even if someone tells me a new approach new way of thinking I am still not convinced. I will listen to what they say and try to change my “understanding” but I can’t skip the process of getting there independently. A few problems when I have received external help they will say something that’s the catalyst to enabling me to understand something but I don’t understand in that moment, I need to organically get there myself.

I’m not sure how to structure my time. As this is clearly not sustainable. If my degree was 20 years maybe it would be but it’s not. I’ve got 30 hours of content to learn in a week. And a subject where everything is so intertwined if I move on from a proof or theorem not happy with it i just feel like I will be lost even more so.

I know undergrad maths esp the stuff im doing is not particularly hard as we are in wk4/5 so idk why im struggling to this level. I find in life though and previous mathematical learning experiences I struggle with the easy stuff more then what’s thought to be hard.

——

I’ve never been a gifted mathematician. I got top grades through hard work and passion. I was the dumbest in the room but got the best grades after putting in soooo much work. Sometimes I think there’s something fundamentally wrong with my mathematical “philosophy” and principles and I’m not made for this. Which makes me sad.

TLDR. Pointless vs Productive struggling. Falling behind due to my need for 100% clarity. Any tips?

A bit of background: instead of going to high school, I did a vocational training programme. I took maths-based classes, but they were entirely focused on electrical engineering topics (Maxwell’s equations, Ohm’s law, alternating current, direct current, low voltage, high voltage, and related topics). However, we never covered the usual high school curriculum.

Now I’ve started a telecommunications engineering degree, and I’m honestly struggling HARD with maths. Linear algebra is somewhat understandable. Matrices and complex numbers take a lot of work, but I do understand the logic behind them.

When it comes to Calculus I, though, I struggle to understand why and how we solve the exercises, as well as how to visualise the graphs, which makes everything extremely abstract and difficult for me to grasp.

My teachers teach in a very mechanical way: follow the standard steps for each type of exercise, repeat them 50 times, and you’re good to go. There’s no explanation of the underlying logic. If you can’t understand it, it’s your fault, and the class just moves on. This has made the whole process extremely difficult and unproductive. I spend hours and hours trying to understand a simple limit problem, and even then, I forget everything by the next day.

I also think I’m missing some key tricks or foundational concepts needed to understand Calculus I because of gaps in my previous education, but I can’t figure out exactly what I’m missing.

I’d like to know if anyone has any recommendations, whether they’re exercises, videos, guides, or anything else that might seem obvious but that I could be completely overlooking. My native language is Spanish, but I can understand English too, so either language works!

So far, I’ve been able to understand and solve exercises involving absolute values, inequalities, and some domain problems. However, I’m hitting a hard wall when trying to solve problems involving function analysis, continuity, differentiability, x- and y-intercepts, intervals of increase and decrease, and derivatives in general.

I’ll also add some examples of exercises that I’m having a particularly hard time with:

https://imgur.com/a/tmQLdFz

Any kind of help will be extremely apreciated

Im currently in my junior year and I still dont understand logs i can understand almost everything else but I haven't been to grasp logs and its numerous rules when its comes to solving log and exponents question. Would greatly appreciate any help

I’m reading “A Course in Calculus and Real Analysis” by Ghorpade and Limaye. it’s the first edition pdf, so maybe they updated this but I’ve noticed a couple of weird typos? But I’m not sure since I’m still pursuing an undergrad and maybe I’m missing something.

you can see the statement here

They state that:

aⁿ-b^{n =} a^n-1b + a^n-2b²+…+a²b^n-2+ab^n-1

Which, if you plug in n=3 you get

a³-b³=a³b-ab³

So that’s not right. I know the right series would also start with that first b term on the right hand side should have a “-1” tacked on to it and then the series makes sense.

is this a typo on their end or am I just not reading their series notation right?

I’ve seen people in this community mention they want to relearn math but don’t know where to start. Others remember the steps but never really understood why they worked. Others had math teachers that didn't care or were just bad teachers.

I've been helping students with math for over 15 years 

My name is Isaac. About 25 years ago, when I was in high school, my father started teaching math for free to children of friends and family. It began with a small group of 5 students and eventually reached more than 100 students motivating us to convert our family garage into a classroom.

I’ve continued teaching over the years and in 2018 I created Think! Before You Solve. A math program to help students understand math. Now I want to carry that into an online community, the reddit community lol. 

Below are the class conditions/rules:

- Free, live online classes: once a week for 90 minutes.

- 20 students maximum per class: if more people sign up, I’ll organize additional groups.

- Schedule: we’ll find a day and time with the people interested.

- Starting point (elementary math): basic addition and subtraction, including positive and negative numbers, fractions, and order or operations (PEMDAS).

- End goal (Trigonometry): we start with elementary math then pre-algebra, Algebra 1, Algebra 2, and eventually trigonometry.

- Length of Class: most classes are covered in 20-24 sessions. 

- Time Schedule: the time will be TBD based on the availability of most. Ideally it would be in the afternoon or evening.

The intent is to make it simple for busy people. Once a week for 90min is more than enough. 90 min are two episodes of your favorite series. 

If the majority wants to do twice a week instead of once we can also make that happen. 

I really mean it about one student. If one person wants to learn, that’s enough for me to start.

AI tools now provide students with the answers instantly. I feel learning math, now more than ever, is critical for reasoning, critical thinking, resiliency, and nurturs self-assurance. 

Because getting an answer and understanding it are different experiences.

Technology can be useful. But I want students to be able to look at a solution and ask: Does this make sense? Why does that work? Could I explain it to someone else?

The goal isn’t to grind through hundreds of problems. It’s to understand the concepts well enough to have the ability to reason through something unfamiliar.

When an answer is just a click away, it’s tempting to grab the answer just to complete the assignment and move on. I understand that. But with someone guiding you, working through that uncertainty is where confidence grows. You try, ask a question, adjust your approach, and realize you can figure it out.

That’s the type of classroom vibe my program creates. You can ask a basic question, get something wrong, or need another explanation. Those are all part of learning.

Adults starting over are welcome. You don’t need to remember what you learned in school, and you don’t need to consider yourself “a math person.”

If you’d like to see who you’d be learning with, here’s "my teaching journey"

https://www.thinkbeforeyousolve.com/v2/gallery/

and some "feedback from students"

https://thinkbeforeyousolve.com/v2/testimonials/

Interested? Just dm me it's that simple. 

Please share this with someone who’s been wanting to start again.

This isn't a scam or a joke this is for real. Education is at risk in the US the department of education is been cut, finding to schools is cut, and many other disadvantages our students face. 

I am literally doing this because it's my 2 cents to make the world a little better. Im only good in teaching math lol so I want to share it with you. 

Let's get cooking with math. 

I've been studying probability theory, particularly continuous probability density functions, and I came across something that I mathematically understand but still find logically and physically counterintuitive.

In a continuous uniform distribution, say a random variable (X) between 0 and 10, or for example a robot in a line of 10 m , i don't know where he is but i know he is within the 10 m yet the probability of any exact distance value of it is zero while in reality he is defenitly on a point that we said it's probablitiy is zero:

[
P(X=5)=0
]

This is because probability is calculated by integrating the density over an interval, and a single point has zero width, meaning zero area under the curve.

I understand the mathematics behind this. I also understand the distinction between countable and uncountable infinity, and how an interval can have a positive measure even though every individual point has measure zero.

My problem isn't with the mathematics, but with its representation of physical reality.

If something has exactly 0% probability yet physically occurs, shouldn't that suggest the model might not perfectly describe reality?

We can't still say weather the universe is fundamentally continuous or discrete. But if space has some smallest resolution, wouldn't that change how we assign probabilities to exact positions?

I'm struggling to reconcile that with physical intuition.

So my question is: Is continuous probability merely a useful mathematical approximation of physical reality, or is there a deeper reason why zero-probability events can physically occur without contradicting the model?

Is it possible to study university-level math only with self-study and learn with YouTube videos, AI, and websites.

Hey! I've honestly never posted on Reddit before, but I thought I should after thinking about this for a long time. I am quite terrible at math, and yes, I know that's like preaching to the choir, but I really need some advice. I'll preface this by saying I have been extremely passionate about physics and astronomy since the 2nd grade; I'm totally enamored with the laws and theories of the universe and would adore to major in astronomy in college and make it my career. But I have an issue.

(sorry for all of this yapping)

My problem started around 4th grade when I couldn't quite wrap my head around writing out multiplication on a table, which was easy for everyone else. I was enrolled in tutoring until 6th grade, where I continued to not do the best in my math classes. Then came 8th grade, when I was given two math classes with two different teachers to help me catch up with my peers, but I was starting to give up completely! In high school, I stopped focusing on math and was passing with Ds until my junior year, when I finally enrolled myself in physics hoping that I could turn things around for myself, buuut I failed and dropped out. I would study whatever I could and was still failing all written sections on the exams. But get this!! I was passing the multiple-choice with flying colors. Though my teacher also did have a pretty rough reputation. I know that my lack of focus totally stunted me, and now I'm hoping to build the skill from scratch.

I am now enrolled in college, about to get my associates in general sciences, which only includes biology, so it's pretty easy for me. But my next step is deciding if I want to stop here or pursue astronomy like I've always wanted! I thought that there has to have been someone else on here that was kind of like me or anyone who could give some good advice. I'm mainly hoping for any guidance on where to start, or what material is most important to cover for physics-focused math?

(I'm not sure if people usually ramble like this on Reddit, so sorry if this is weird lol)

Just realized I misspelled physics

So I have started studying university in Slovenia in the faculty of geodesy and civil engineering. I am in the program for geodesy and real estate management. Most of my class are math related. The only things I understand when attending classes are some words (because I'm macedonian) and how they say the numbers. I try to translate everything and home and learn it but I can't grasp how to solve the problems and homework even with AI. When I was in highschool I could understand everything the teacher was saying and I learnt almost everything during the class and never had to study at home.

But here for some reason I cannot understand everything that is going on and I am having a lot of trouble on finishing homework and assignments, studying in general. Everything that they teach me here I can't seem to understand because there isn't somebody who can show me on how to actually solve the problems even though it doesn't seem that hard when the teacher is writing on the board.

What are some tips you the members from this subreddit would give me on better understanding the material and actually start properly learning the math that is taught here. (sorry if something is wrong with my english.)

I want to major in math, but I’m feeling completely lost in a proof-based linear algebra and multivariable calculus class I’m taking in the first year of university. To me, the class moves extremely quickly with little guidance and has introduced completely new ideas with real analysis topics used in the proofs we’re supposed to write. Even if I begin to understand things on a general, intuitive level, I get points docked for lacking rigor in my proofs (if I can think of any at all).

The requirements of the class were just that we had taken single variable calculus before with the recommendation of having taken linear algebra and mv before. Although I’ve taken all these classes before, they were mostly just doing computations, so I feel like I have no sense of proof-writing. We’re also supposed to essentially come up with everything ourselves with the teacher just showing some theorems in class.

I’m very willing to put in as much work as necessary to catch up, but I don’t even know where to start. I’ve watched real analysis videos online to try and catch up, but they’re much simpler examples than what we’re doing. I just have no clue what I should do, and I don’t want to drop.

If anyone has any video suggestions, books, or general advice, thank you in advance!

Hi guys,

I just finished a midterm for my abstract math class and my probability class. For my abstract math midterm I got a 48 and for my probability midterm I got a 24. These are by far the lowest scores I have ever gotten in any math class. In my proofs course I would sail through homework and class handouts, yet somehow despite studying for at least 30 hours and working through tons of practice problems I got a 48. Now in my probability class, I am just always confused. When I open my homework I don't even know how to start a problem. I just read the problem over and over again and I remain confused each time. I really am at a low point and its making me go crazy. I know I'm not stupid because I've come this far and I did good on my other 2 midterms. I am working on practice problems from the textbook as much as is available. I go to class and participate. I frequently attend my professors office hours. I am in study groups with classmates. I read the textbook albeit i have a hard time understanding the textbook. What else can one possibly do to study and understand a subject? I do not want to blame my professors, although my probability professor just reads off of his notes. I should be able to learn regardless of who is teaching me and how they are teaching me. I am so lost and angry at myself. This is like such a low point for me. I need advice, help, and guidance.

Thank you !

IGNORING ALL COEFFICIENTS

How is all of this so connected?

Let's consider the homologous series of c, x, x^2, x^3, x^4... and so on: x^n where n belongs to a non negative integer only

Why is it that the graph for a particular expression not only explain the graph for the expression itself, but also the graph of literally *EVERY OTHER MEMBER IN THE SERIES*.

for example, the graph of x^3 (or simply x^3 itself, as graph is that thing itself) explain the graph of x^3 itself, but also x^4 (how f' graph explains a graph of f), and x^5 (how f'' graph explains for f)

How the graph for f' of x^3 is same as f'' of x^5 and f''''''' of x^10

How the graph for f' of x^8, f'' of x^9 and f of x^7 is all the same. A single graph is doing all of it

Yes, on paper, I know, and can prove this with my pen (I know the limit definition of derivative and what it is in terms of slope, in terms of rate of change in area/volume etc). But it still seems out of grasp on how this is possible.

[Only considering for the homologous series highlighted to keep it simple for now]

I started making animated maths lessons mainly for my daughter (Grade 4).

Sample: Fractions: https://youtu.be/bHL4Z3UbvAc

Each video has a free printable worksheet with an answer key. Here's the one for this video (PDF, no sign-up):

https://drive.google.com/file/d/1O_lK7tNx0iW_36udZzcJr7ayLdBb8Bjy/view?usp=sharing

The narration uses an AI voice. Feedback from teachers is very welcome!

I've got some doubts about the properties of the neutral element and of the inverse in general, and in particolar about about a property of vector spaces.

Firstly, when you consider the neutral element in, for example, a group or in a ring, the neutral element must be commutative. So it must satisfy: a + e = e + a = a? Or can there be a left neutral and right neutral? I've got the same doubt with the inverse. I get that if you have an abelian group that is guaranteed by axiom, for example in a ring that is obvious. But what if you have a group.

Secondly I don't get how you can prove this:

Let be V a vector space on K.

If l is a scalar and v a vector =\ 0 and

lv = 0, then l = 0.

I don't understand how is proofed that there isn't any scale diverse from 0 that gives 0 as a result. I don't seem to find any axiom of the vector space that assures this.

İ found out that we can use the formula that i found out to while calculating degrees we dont even need to use any geometry (my english isnt that good dud im Turkish). So with this formula im pinning is helps for that.

Just wanted to introduce Limerse (https://limerse.com), a new style of math textbooks built around visual explanations and interactive examples. I was really inspired by 3Blue1Brown and wanted to bring that level of deep intuition to full math textbooks.

So far, I have launched Calculus, which includes 950+ animations (over 50 hours of videos), and 150 interactives. Will be adding more subjects like Multivariable Calculus, Linear Algebra, and Differential Equations soon, and I would really love to hear what you all think. Thanks.

Hey guys, I got into college for Networking and it turns out we learn electronics (math/physics) when I was younger I made the mistake of not paying attention in class, like never.. and now I have trouble with stuff like fraction divisions, rearranging formula, and more.. I feel lost when It gets to some points, like I have holes I need to fill, I can maybe bang my head to learn a formula and copy paste it like a parrot but I can also forget it due to not understanding and at times in class(like rearranging formula and fraction division) I get confused.

This is kinda embarrassing because this is considered simple math

Now my question is: how do I approach it? There seems to be a lot of rules I don't know of, any tips?

I really gotta learn that quickly before studying for the subject itself

Thanks for the help

I’m a high schooler. My school doesn’t distribute any textbooks to students, so I want to know something that can help my understanding. Website, book, or anything else is fine.

Transferred from a community college with As in everything up until calc 3 and differential equations.

First term and I’m taking proof and logic and a proof based linear algebra course(and probability theory but it’s been easy thus far) and I’m debating if this is for me.

I genuinely enjoy math, and have systemized my way of studying it but I feel like I’m not yet accustomed to the jump from computational to proof based mathematics

Do I just accept my B/C’s? Will that affect my graduate/postgraduate applications and what if I retake the class?

I’d be appreciative of any and all tips.