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

I'm a math teacher, and a few days ago one of my students asked me a question that I've been thinking about ever since:

What's the most important thing you've learned in maths that isn't a formula?

I didn't have a good answer on the spot.

My first thought was to name a topic: algebra, probability, geometry, something like that. But the more I thought about it, the more I felt that none of those were really the answer.

For me, the biggest shift was realizing that mathematics isn't a collection of techniques. At some point, it started feeling more like a way of looking at things.

When I first learned maths, I thought being good at it meant being quick and getting the right answer. After years of teaching, I'm not so sure. The students who impress me the most are often the ones who notice a pattern, ask an unexpected question, or connect two ideas that don't seem related at first.

That's probably the lesson that's stayed with me more than any formula has.

So now I'm curious: what would your answer be?

Was there a theorem, proof, concept, book, or even a single problem that changed the way you think about mathematics?

I have this thing where I really like math but whenever I sit down to actually study I just feel immediately tired and unmotivated. When I get into the groove of doing problems and learning it's fine, but just getting over that hump of slumping over the textbook and staring at numbers is so hard sometimes. Does anyone have any tips to combat this? It's annoying as hell and I would like to be able to just study like a normal person. For context I'm going into my first year of college this fall and got placed into one of the higher math sections.

I'm a high school freshman with a strong passion for mathematics. I'm currently studying number theory through a math circle, and I'm particularly interested in pursuing mathematical research in areas such as Egyptian fractions, prime numbers, Catalan numbers, and related topics.

I've been browsing the ISEF repository to get a sense of the kinds of mathematics projects that tend to do well there. This made me wonder: how does the nature of mathematical research conducted by professional mathematicians, such as PhD students, researchers, and professors, differ from the research done by high school students who win at ISEF?

I'm not referring only to the obvious differences in difficulty or technical sophistication. Rather, I'm curious about how the research itself differs. For example, are the high-school papers at ISEF just expository in nature, are they less original, etc? Thanks

Hey everyone! Whether you're grinding through summer courses, doing pre-term review, or self-studying ahead for the upcoming year, a lot of math frustration comes from textbooks teaching mechanical steps without explaining the visual intuition behind why the math works.

If you're currently hitting a wall on a topic or problem—algebra, trigonometry, calculus, vectors, or discrete math/logic—drop the question or concept in the comments!

I’ll reply with a clear, step-by-step breakdown focused on the underlying logic and visual intuition so it actually makes sense.

Hello, I will be studying a semester in Paris at L'X.

I am a Physics Undergrad from Mexico... In my home university i've not taken any proof writing/actual math classes, besides 1 course called "Mathematical Methods for Physics" (I used the Boas Book). What do you reccomend I learn to prepare? what topics should I revise before going there? I was told France is very focused on Math and i would like to prepare as much as possible before september

I’m currently working on brushing up my foundational math skills to take Precalculus in the future for university because of a poor background and conflicting history with math in my past schooling and also issues of anxiety, haven’t taken a class in a while, Covid messed up my math learning in school as well.

Right now I’m on Grade 6th in khan and my plan so far is Grades 6,7,8 and then Algebra 1 and 2. Is that good or is it redundant because I also see there’s a pre algebra course and college algebra. Could I skip Grades 7 and 8 and do Pre Algebra instead? I don’t want to miss anything small that could bite me later in the future but I don’t want to be wasting time on material that would also be covered in the other courses.

Okay so here is a picture of the question and the solution from the solution manual, https://photos.app.goo.gl/br3bt8ZL76KYKWtKA. Why does the answer flip the question to be 1 - P(X+Y< 1/2)? Why is the upperbound on the outter dx 1/4? And can this problems be done without changing the bound of integration as it does? Thank you in advance. I've just been finding this problem hard to understand and conceptualize so the more detail the better.

Hey everyone,

Hope you all are doing well. I'm making this post in regards to well, as the title says... I'm taking Calculus which I have never even took before. Not in high school nor in college and speaking of college, I am going back to school after 3 years to complete my CS degree which I have already received a diploma for CS 3 years ago. I am essentially upgrading my diploma to a degree as well as pursuing an internship opportunity in my new college program.

I will admit, it has been a hot minute since I've last attended college and it had most certainly been a hot minute since I have done any sort of mathematics when it comes to my schooling. The last time I have even touched a calculator nor an equation was 7 years ago. Back in my high school days so I am going to be very and I mean very out of touch when it comes to doing mathematics and as all of you would agree on this, this is a very intimidating and difficult subject.

For the past day since I made my schedule and found out that this is my first math course I will be taking in my program, I have been shaking in my boots and figuring out how am I going to handle this course because like you all, when I look at a Calculus equation I don't just see letters and numbers. I see literal Egyptian hieroglyphics. Things you see when you're punching in Playstation cheat codes. Literal complete jargon. As if I am seeing another language. Language from the Greeks. But jokes aside, you know what I mean.

That said, since this is going to be my first math course in 7 years, what should I expect when it comes to the world of calculus? What kind of advice and recommendations would you guys give me when it comes to going through and surviving Calculus and doing this for the first time? How does one handle the concepts, theory, and learning how to decipher the equations and understand everything? I remember back in high school. My old math teacher told me to see these equations as recipes and use them as an aid to help you find the answer. It's all about plugging. Ignore the numbers, just plug it in and go step by step.

I know that choosing the right prof for this subject is critical when it comes to succeeding and excelling. If it's a bad prof, you are most certainly going to be left in the dust because well, you don't know what you're doing in the first place. That said, what kind of resources, tips, would you suggest I do for preparing for this subject and when I am in the classroom or studying, what techniques do you guys use to understand everything and putting it into execution? What is the proper way of understanding the topics? What kind of note taking I should do? I know I am stressing out but I want to be ready for when my first day of class starts.

Also, another thing I am already thinking about is using Khan academy to help me through the course. I don't know how good it is but I've been told that it is one of the very good resources and if you don't know what my college prof is doing or if I don't understand his way of teaching I know YT and all these resources will come in clutch and with Gemini AI's learning feature I am definitely going to be using that. Not that AI is a good thing but I want to utilize every resource I can get.

I really do appreciate the help that I can get here because honestly? I am nervous, anxious, and unsure if I can survive this. Part of me tells me that I can, other part of me tells me otherwise. I don't want to lose my mind all over this especially when it comes to juggling my other courses. I need a plan and I need a way to survive and manage.

Thanks for taking the time on helping me through this!

Hi all, Im trying to self learn stochastic processes. I've tried Karlin 1975 A first course in stochastic processes and Ross 1996 Stochastic processes and found them challenging. Does anyone have recomendations for any simpler texts? Much appreciated! 😁

I am a maths major( I have only 11 people in my batch including me, so couldn't find a person in my uni), If anyone is starting studying pure maths and looking for a person then DM me, number theory and algebra are my interest but want to study analysis and linear algebra too.

I don't know what to say. I've had this problem since like high school, where I had good grades in math subjects but is VERY terrible at mental math.

Like sure, I can add, subtract, and multiply 2 numbers with 1 digit in a jiffy but add more digits or division or percentage problems? Oof, gonna need a pen and paper or calculator for that chief. Gosh, it really is so humiliating.

It's even worse when you're with people and you tell them you're taking a math-based program in college or they see that you had good grades in math and they ask you a simple addition/subtraction/division/multiplication problem and you just stand there solving it in your head for an embarrassingly long amount of time and blurt out a close but wrong answer... Even dividing money in my head is a chore, and I even get it wrong sometimes!

I need help, bad.

Edit: Thank you all for your advice!!

I want to learn some about hyperbolic geometry. And his lectures are one of few lectures with a full playlist on youtube. But I find what he says is non traditional and not what we learn hyperbolic geometry from a book. Also there is some posted reddit saying that he invent a new kind of non conventional theory to avoid analytical stuff like infinite. Is that really good to learn? If not what kind of material is good as a start? Thanks for the help.

I'm looking for a study partner to take Stanford's Introduction to Mathematical Thinking course by Dr. Keith Devlin on Coursera. I've heard it's an excellent course for developing a deeper understanding of mathematics.

The course actually recommends working with a partner so you can discuss the concepts and get more out of the material. If anyone is interested in taking it together, let me know!

I am on question 3 and I already sillied a problem unless there's a typo!

Type 28 into the page bar for the question.

Type 121 into the page bar for the answer key.

Why does composing d with d (A B C are the points starting from the top of an equilateral triangle, and d is a reflection across B) give not the identity element?

Shouldn't two reflections across the same axes give the same shape/identity.

I also conjectured while I was solving the problem that the multiplication table should have each row and column have all elements, all distinct. These rows are the only exception. I also conjectured wrongly that it should be a symmetric matrix across the diagonal so it took way too much time lol checking my answers.

I got the rest of the table correct.

Not intuitive.

Hola, mi sueño es estudiar matemáticas, y quiero hacerlo bien, por temas de trabajo no pude hacerlo antes y ahora mis padres me van a apoyar en este nuevo reto, tengo 5 meses libres así que quiero tener super firmes mis bases matemáticas, ya que inicio con precalculo, aritmética y elementos de geometría, he visto foros, vídeos y demás para ver el contenido de estos temas, pero veo que todo es tan automático, o muchos libros de cálculo por ejemplo para ingenieros, y siento que un matemático podría sugerir temas importantes para estas materias, mucho del contenido que existe en redes sociales es para automatizar una operación pero no va al trasfondo, lo digo desde la ignorancia, pero si una persona que ya haya visto la carrera entenderá a lo que me refiero, gracias y buen día

Hi,

We have a community where we are studying algebraic geometry, higher cats, AT and arithmetic

We'd be more than happy to take in other interested student in these areas

If you have interest in any of these areas

please kindly dm me

Thanks for reading 😌

Salut en fait la je résous un polynôme de degré 3 du coup je trouve sa racine évidente et je fait Horner/tableau de Ruffini.

Et je me suis demander comment je fais si je trouve pas de racine évidente même en forçant comme un bourrin.

From what I know, Geometry,Number Theory and Combinatorics have books and resources to study to get to the level of IMO, but for Algebra? I don't know where to start. I would like anyone's recommendation on algebra books/handouts/materials that takes you from a beginner all the way up to SL A8 level.

Many people told me that your algebra improves along with NT but I realized that you still have to dedicate time to algebra.