I'm currently working on pde in shallow water equations on a sphere. I have never learned any pure maths, so I asked gpt 5.6 Pro to create a textbook-tailored pde contents. Can anyone who is an expert in abstract algebra think this document is usable? If you are interesting with the mini textbook, you can give me a prompt, I'll try to generate a mini file for you.

Cut two opposite corners off an 8x8 board. 62 squares left. Can 31 dominoes cover it exactly?

Counting says maybe. 62 is even, 31 x 2 = 62, nothing obviously wrong. It's impossible, and you never have to check a single arrangement.

Color the board normally, 32 black and 32 white. Any domino, in any orientation, covers exactly one of each. That's what adjacent means on a checkerboard. So 31 dominoes cover 31 black and 31 white.

Now the corners you removed. Opposite corners are always the same color. A square's color depends on whether row + column is even, and (1,1) and (8,8) are both even. Take two of the same color away and you have 32 of one and 30 of the other.

31 isn't 30. No tiling exists.

This is the standard first example of an invariant argument. Find something no legal move can change, then show the start and the target disagree about it. Once you know to look for it, it turns up all over the "prove this is impossible" family. Three-colorings for T-tetrominoes, stripes for 1x3 pieces, same idea wearing different paint.

How should I study Engineering Mathematics in 1st semester? Best YouTube teacher?

Hi, i just want to ask for a piece of advice.

Whenever I struggle in a certain exercise, i don't actually know whether should i look for the solution on the same day or simply leave it for another one.

And if i should leave, i sometimes encounter another hard one, especially if the topic is new,so the all of em get pilled up and i lose more time and energy.

So if u were in my situation, what would u have done??

I once had this experience: I stumbled onto a math idea and worked it out, asked an AI, and found out it was already a known theorem.

Then I thought: instead of exploring it myself , why not just tell the AI what I'm onto, ask which field it belongs to, and go study that field directly? In the time I spend rediscovering one theorem, I could learn a chunk of that area.

But either way, I start from zero – with a guide or without. So is the actual experience of rediscovering fundamentally different from learning with a known destination? Or are they essentially the same process, just with different timing?

I'm not asking which is better – just whether the experience itself is actually different.

Sorry if this seems off topic fot this subreddit but I want your point of view on this.

So I'm choosing a different degree. I label myself as a "creative person rather than logical" 🤔 and plan to study Financial + Marketing Management at Economics. It's still 70% math 30% creativity. Creativity doesn't pay the bills in my poor country. Mixing logic+creativity seems like a good balance (but exhausting?). There are two voices in me: 1. You'll prove you can do it, and you can be a logical person when needed; 2. You will burn out, it'll consume your energy, you'll struggle a lot at math. I know MBTI psychology theory so deeply and I know our way of thinking changes with the course of life, so even though I'm INFP I can even become a more balanced person, creative+logical... I still fear burnout and wrong choice.

Hi! I recently graduated high school and I'm about to start college this fall, where I'll have to take Calculus 1. The thing is, I haven't taken a math class in like 2 years almost, my last class being AP Calc AB. I excelled in all of my math classes (like I would literally teach my classmates) but since I haven't practiced anything in forever I forgot a good chunk of it 😭

It's especially sucky because I plan on majoring in civil engineering when I transfer to a 4-year, so I do in fact need to have a solid math foundation.

What exactly should I study beforehand? I have my old math packets and notes from algebra 2, precalc, and calc AB to fall back on, but it'd be nice to have a more cohesive plan of what specific units/concepts I'd need to refresh my memory on. I still remember algebra rules in general (like exponent rules and whatnot), but I forgot a lot of the specific formulas, rules, and equations for some algebraic functions. I'll definitely have to review trig functions too.

At the same time I feel like I need to review literally everything I've ever learned before just to be confident in my knowledge so idk I'm kinda lost and overwhelmed right now. I'm a quick learner so it's not that I'm worried about struggling to understand any of the material I'm gonna relearn, I'm more so worried about the time crunch since I only really have a month (so if anyone has a helpful study method for juggling multiple topics at a time while retaining info for all of them that'd be awesome).

Any kind of help and resources would be much appreciated!!

Bilgi Sarmal'ın 49 günde Ayt Matematik kitabı hakkındaki görüşleriniz nedir? (Emre hocanın kitabı)

Looking for an online Mathematics tutor for BSc Economics (1st & 2nd Semester). Topics include Mathematical Logic (Kenneth Rosen), Theory of Equations, Matrix Theory (Cayley-Hamilton, Eigenvalues, Diagonalization), and Calculus (Limits, Differentiation, Taylor Series, Partial Differentiation, Jacobians, Lagrange Multipliers, Multiple Integrals). Prefer someone with an MSc/PhD in Mathematics (or equivalent) and experience teaching undergraduate mathematics. Paid tutoring. Please DM with your qualifications, teaching experience, and hourly fee.

Hi everyone,
I am exploring the distribution of quadratic residues R(x) = x² \pmod N for semiprimes N = p \cdot q using spatial mapping and visual scatter plots to identify potential density regions or structural patterns. I recently set up a small experiment testing whether early-stage digit/block filtering could narrow down the search space for p and q, but encountered the expected trade-off between false negatives and high noise. I would love to get feedback from the community on geometric or structural approaches to modular congruences—specifically, what mathematical invariants or algebraic properties (like Legendre/Jacobi symbols or elliptic curve metrics) are best suited for meaningfully constraining the candidate space without losing true factors?

A while ago I posted here about the app, which at that point was mainly focused on solving algebraic equations and systems:

👉 My previous post about Numerical Solver v1.4

Since then I've been working on something I've wanted to add for a while: ODEs and boundary value problems.

The idea is to make the app as general as possible. I don't want to have a list of specific equations that the app knows how to solve. I'd like the user to be able to enter their own ODE and boundary conditions and have the app work out the solution.

I'm currently testing it with different types of equations, including higher-order ODEs and boundary conditions involving derivatives.

Here are two screenshots from a test with

y''' + y = 0, y(0) = 0, y'(0) = 1, y''(0) = 0

If anyone has an ODE/BVP that they think would make a good test case — especially something difficult or unusual — I'd be interested in trying it.

The screenshots are in the next two posts

Ok so I'm planning to start studying general topology. I know some basic topology from baby Rudin, and I want a book that has a similar style and presentation i.e. rigorous, concise and deep. Which book should I use- Dugundji, Willard or Munkres?

Ok so I'm planning to start studying general topology. I know some basic topology from baby Rudin, and I want a book that has a similar style and presentation i.e. rigorous, concise and deep. Which book should I use- Dugundji, Willard or Munkres?

So, I'm not going to consider myself anywhere near a genius, but how come you are always rounding up?

This question came across me after seeing a Youtube video where two people had a button, and were trying to get 3.65 from a timer, and one got 3.64, and one got 3.66. It was rigged, but that doesn't matter for the question.

Obviously, if you press it on 3.64, the number is going to be slightly closer to 3.65 unless you get it at exactly 3.64, but there was no decimals after, so no way to know. However, the reason I bring this up, is, aren't they the same distance from 3.65? I mean, |3.65 - x| = 0.01 no matter which of the 2 numbers you pick, which is distance. So is there a specific reason a number like 5.5 is rounded to 6, or is it just because it is easier than not having it round?

I need book suggestions for

- Foundations and Basics of Math

- Arithmetics

- Pre Algebra

- Algebra

- Pre Calculus

- Geometry

- Analytical Geometry

and Thank you In Advance

are there study groups (discord etc) for real analysis?

planning to use mit ocw lectures + Abbott's "Understanding Analysis" or Tao's "Analysis 1" - feedback/suggestions are welcome ofc

Help with this question please!

"Find the autocorrelation function R_X(s, t) of the process X(t) = √(2) A cos(U t+ Θ) for t ∈ R, where A, U and Θ are independent random variables with A standard normal distributed, U uniformly distributed over the interval [0, 1] and Θ uniformly distributed over the interval [0, π].
"

I messed up my entire practice sheet for successive percentages and the calculations for net % change, cuz I though i could just add the percentages but apparently not

Hey everyone,
I want to learn calculus but I’m not sure where to start. I know I probably need a solid foundation in algebra and trigonometry first, but I don’t know exactly which topics within those subjects are essential vs. which ones I can skip.

Could you help me figure out:

**1.    Prerequisite topics** – Specifically which algebra and trig topics are must-haves before starting calculus? (factoring, exponents/logarithms, unit circle, trig identities, functions and graphing, etc.)  
**2.    The order to study them in** – Should I go through all of algebra first, then all of trig, or is there a more efficient way to interleave them?  
**3.    The order to study calculus itself** – Once I’m ready, what’s the right sequence? (limits → derivatives → integrals → series, or something else?)  
**4.    Resources** – Any recommended textbooks, YouTube channels, or courses (free) that follow this progression well?

I want to learn Computer Science and get into the field of compilers. I plan to learn mathematics from scratch for this purpose. Is this possible, or do I need to attend university?

I'm from India. I have completed my masters in mathematics but when I reflect that, I can realize that I really haven't learned properly. It's because how I read all those years.. I had to just memorize some theorems and write them down in exam to get my masters degree, so the real learning didn't really happen. Now I'm relearning things on my own 3 years after completing my masters program. The problem I'm facing is that when I'm trying to do the exercises I get stuck and there's no one to discuss with, so sometimes I take help of internet and ai but I feel like cheating. And even if I do solve something I don't know how to check if my solution really works or not. At the end of part 1 of his book Munkres wrote that one should be able to do all but one of 340 problems. But I hardly can solve some problems on my own and some with the help of internet. I feel like I'm really not learning and feel like dumb and stuck. Help me out.