Help haha..

ok so basically i can’t figure this out because math isn’t my forte, anyway- say i get paid roughly 200$ bi-weekly, and i need 2,600$ how long would it take me to get 2,600$? this is not a school or homework assignment, im genuinely trying to figure this out.

i am learning olympiad math, and my teacher asked me if i wanted to learn some abstract math.

so for the past 1 and 1/2 year ive been learning bits of group theory, ring theory etc.

i was just going through my group theory notes, and i was able to solve simple counting questions using the theorem, but couldn't find any thing online.

i was wondering if other people also use |||techniques for olympiad level questions

I am interested in learning about various analytical (not numerical) solution methods to differential equations (ODEs more so but PDEs perhaps as well) about irregular singular points. Most resources/textbooks do not discuss this topic in much detail or at all. I've found some stuff on Laurent series expansion and asymptotic methods but am not completely satisfied. If you have any recommended textbooks or maybe review articles please let me know, thanks in advance!

Does there exist at least two different knots, different from the unknot and also not mirror images of each other, such that they have the same p-coloring for all prime numbers p? Is this a solved problem or an open problem? What name does it go by? Thank you!

We all know we use decimals to represent dollars and cents. So this is my plan for my lesson.

Let's say you have 50 cents. You write it as $0.50 cents. Which means we don't care about the zero dollars, we only see 50 cents. And because we usually say 50 cents, the zero isn't significant. So that gives us 2 sig figs.

What about $501? The zero is important because without it, we couldn't have 501, it would just be 51. So that's 3 sig figs.

What if we have $50.00? This is a little more confusing, but in this case, we have $50 and 0 cents. The zero cents tells us that we have no cents. So that is 4 sig figs.

Is this method more congfusing or coud it work?

Im calculating what numbers have integers as their natural logs, these arent perfect, but theybare close enough where python spits out perfect integers when calculating their natural logs.

These are the ones i have so far ( will not be updated when i work out more)

In(2.718281828459045) ≈ 1

In(7.38905609893065) ≈ 2

In(20.08553692318767) ≈ 3

In(54.59815003314426) ≈ 4

In(148.4131591025766) ≈ 5

P.S. i dont know what a natural log is i just find calculating these incredibly relaxing

Edit: very very annoyed to know that what im doing in calculating the powers of e, & that ive wasted alot of timeo

I'm a complete novice to knot theory and the generalised question of embeddings of manifolds up to ambient isotopy. However, I know knot theory touches upon combinatorics, algebra and 3-manifolds. Do some of these (or other) areas also similarly depend on questions related to embeddings up to ambient isotopy?

Conservative vector fields can be described as the gradient for some potential function describing a surface in 3D space, and each vector at every point describes the highest slope of the tangent plane to the described surface at that point. Continuing with this reasoning, what kind of surface might a non-conservative vector field describe, for example <y,-x>? I imagine it would have some kind of helical structure, but couldn't be a function of two variables. Is there some way to determine the shape of this surface exactly, with some kind of implicit function maybe? apologies for any lack of clarity in how this question is posed, only in calc 3 so far!

Conservative vector fields can be described as the gradient for some potential function describing a surface in 3D space, and each vector at every point describes the highest slope of the tangent plane to the described surface at that point. Continuing with this reasoning, what kind of surface might a non-conservative vector field describe, for example <y,-x>? I imagine it would have some kind of helical structure, but couldn't be a function of two variables. Is there some way to determine the shape of this surface exactly, with some kind of implicit function maybe? apologies for any lack of clarity in how this question is posed, only in calc 3 so far!

I realized not that long ago that 2025 will be the first year since 414 that can be expressed in base 45 using only base ten digits. (2025 is 100 and 414 is 99). Sorry if this doesn't belong I'll delete it if not

I've started reading papers and books about a research area I'm thinking of going into for my thesis. Actually I've been reading about this area for the past 1.5 years because I did my masters thesis in it and I find it interesting so I'm not a complete beginner. Despite all this when I read papers or books I always feel like there's some background information that I'm missing and that I only understand some of the bigger picture. Of course it's gotten a lot better than when I first started but that feeling is always there to some extent when reading a new paper. What's made me nervous is other PhD students seem to have such a deep understanding on their area of research that I'm beginning to question if this is normal or if I'm just a little slower than everyone else.

I've found that Overleaf can become excruciatingly slow and even crash when a project grows too large, especially if you have:

- Too much content within a single `.tex` file

- Too many files or figures in the project

While Overleaf is good for collaboration, these performance issues have made it challenging to use for larger projects. I’ve started transitioning to VSCode with the TeX extension, which offers a smoother experience. I also push everything to GitHub.

Unfortunately, though, I’m not aware of an autosave feature in VSCode, so if you forget to push your work to GitHub or your computer crashes, you risk losing a lot of progress.

By the way, I feel a BURNING hatred in my heart for dealing with inserting figures in Beamer presentations and I absolutely hate making Tikz figures, but I have a fondness for the Madrid theme because the first math class I ever took used it.

The feature that VSCode extension lacks is not having a side panel showing the sections when viewing the raw tex.

I know this would sound weird or not welle explained. but i remember where a teacher showed us a sequence which will be easily predicting (without like the formula or something)... i think it was something like (not sure if it was up to 3 or if that was the sequence)

f1=1

f2=2

f3=3

f4=1231312312 (very high number). And then showed us the formula

It was to prove like implictions can't be written sometimes ... I have some class and i want to give this example as why we need to be very accurate etc..

Question is in the title :)

This is the competition I'm referring to: https://globalolympiadsacademy.com/fmo/

Are there any numbers that follow this pattern:- a^b + b^c + c^d = d^n (where n can be anything)

The logic behind this is choosing one number, raising it to the power of another number, and now the power becomes the base (the power becomes the second number). Repeat this 3 times (find the sum of 3 different such exponentiated numbers) and the sum should be the power of the last number raised to the power of n (where n can be an arbitrary real number). I haven’t had done any computation regarding this so far, but has there been any research paper / mathematical theory regarding such a relationship?

Thank you, and have an awesome day!

Hey guys:

https://preview.redd.it/vpzzmua3ggyd1.jpg?width=914&format=pjpg&auto=webp&s=68010d8af97764b6df6f6b0be9a40b296da9bb1b

I feel like this question might relate to approximation theory, but I’m not very familiar with the topic. Any insights would be appreciated!

I'm studying basic PDE techniques like separation of variables, Fourier series and Fourier transform. The examples they always give are the classics: Laplace's equation, the heat equation and the wave equation. Does anyone know any different PDEs (not necessarily corresponding to any particular physical phenomenon) that can be solved by these methods? If you play around with creating new PDEs you realize why they always stick to the classics - other easy examples are hard to come by. Any suggestions?

A basic calculus result is that \sum 1/n diverges.

A result of Euler has that \sum 1/p_n diverges where p_i is the i-th prime.

Does this generalize? Does \sum 1/p_{p_n} diverge too?

The first 100 terms of this sum are:

1/3,1/5,1/11,1/17,1/31,1/41,1/59,1/67,1/83,1/109,1/127,1/157,1/179,1/191,1/211,1/241,1/277,1/283,1/331,1/353,1/367,1/401,1/431,1/461,1/509,1/547,1/563,1/587,1/599,1/617,1/709,1/739,1/773,1/797,1/859,1/877,1/919,1/967,1/991,1/1031,1/1063,1/1087,1/1153,1/1171,1/1201,1/1217,1/1297,1/1409,1/1433,1/1447,1/1471,1/1499,1/1523,1/1597,1/1621,1/1669,1/1723,1/1741,1/1787,1/1823,1/1847,1/1913,1/2027,1/2063,1/2081,1/2099,1/2221,1/2269,1/2341,1/2351,1/2381,1/2417,1/2477,1/2549,1/2609,1/2647,1/2683,1/2719,1/2749,1/2803,1/2897,1/2909,1/3001,1/3019,1/3067,1/3109,1/3169,1/3229,1/3259,1/3299,1/3319,1/3407,1/3469,1/3517,1/3559,1/3593,1/3637,1/3733,1/3761,1/3911, ...

That seems too slow to converge. But maybe not.

What about \sum 1/p_{p_{p_n} ?

The first 100 terms are:

1/5,1/11,1/31,1/59,1/127,1/179,1/277,1/331,1/431,1/599,1/709,1/919,1/1063,1/1153,1/1297,1/1523,1/1787,1/1847,1/2221,1/2381,1/2477,1/2749,1/3001,1/3259,1/3637,1/3943,1/4091,1/4273,1/4397,1/4549,1/5381,1/5623,1/5869,1/6113,1/6661,1/6823,1/7193,1/7607,1/7841,1/8221,1/8527,1/8719,1/9319,1/9461,1/9739,1/9859,1/10631,1/11743,1/11953,1/12097,1/12301,1/12547,1/12763,1/13469,1/13709,1/14177,1/14723,1/14867,1/15299,1/15641,1/15823,1/16519,1/17627,1/17987,1/18149,1/18311,1/19577,1/20063,1/20773,1/20899,1/21179,1/21529,1/22093,1/22811,1/23431,1/23801,1/24107,1/24509,1/24859,1/25423,1/26371,1/26489,1/27457,1/27689,1/28109,1/28573,1/29153,1/29803,1/30133,1/30557,1/30781,1/31667,1/32341,1/32797,1/33203,1/33569,1/33967,1/35023,1/35311,1/36887

Is there a finite k where \sum 1/p^{(k)}_n converges?

Count from one as this begins a counting sequence! 0 divided by 0 equals 1infinity! Mathematics generates Love Magic! You cannot start a count with 0. You can count multiple times as much as you need! Credit: Lucifer of the Satanic Temple, Eazy-G, and Moses.

For starters, I'm gonna need this ELI5...

If you zoom out far enough on an exponential curve, would it turn into a right angle? This is, of course providing the line thickness remains constant in the field of view (ie. 1 pixel).

I have no reason for needing an answer other than I can't figure out how to word this in a search engine to achieve an answer and it's been in my head for a whole day.

My calc 1 teacher told us that dy/dx isn’t a fraction but in calc 2 when we do U subs we end up treating du/dx as a fraction, when we multiply dx on both sides to substitute for the remaining x in the integral or something

So which one is it? Why do we treat it like a fraction despite it being a technically symbol?

I'm specifically looking for an analogue to cos(2x)=2cos^(2)(x)-1 in the p-norm of p=3.

Every proof of the cosine double angle formula that I could find uses either (1) triangle-angle geometry or (2) Euler's identity, and I haven't found a suitable parallel for the squine-3 and cosquine-3.

I need either (1) a squigonometric analogue to Euler's identity or (2) a method to derive the angle identities from either (i) the IVP {x'=-y, y'=x, x(0)=1, y(0)=0} or (ii) the parametrized equation x^(2)+y^(2)=1.

I’ve been working on a project to build an interactive web of mathematics and physics—a kind of hierarchical map that shows how different concepts and theories connect. I’ve been documenting chains of inclusions between mathematical objects to highlight relationships and potential “gaps” in knowledge, hoping it could be useful for students, educators, and researchers.

Here’s the thing: I’ve become completely obsessed with this project. I can’t stop working on it, and I even lose sleep because my mind keeps drifting back to it. It’s pulled me away from my usual work in writing, and I’m constantly thinking about these connections and jotting them down.

But now, after discovering TGView, which already does something similar with visualizing mathematical relationships, I’m wondering if my project brings enough unique value to keep going. Maybe my focus on mapping “gaps” and inclusion chains could make it different enough, but I’m honestly not sure. I’m starting to think that maybe I should step back and go back to my writing.

Any advice or perspectives would be so appreciated—especially if you’ve been in a similar situation.

This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!

Hi everyone, I’m trying to find a closed formula for

sum[k=0,∞] x^k!

where |x|<1. WolframAlpha gives exact values for inputs, e.g

x=1/2 leads to sum=1.26563

x=1/3 leads to sum=0.77915

x=1/4 leads to sum=0.562744

x=1/10 leads to sum=0.210001

and so on. I tried different techniques of manipulating the expression, for example writing it as an integral with bounds 0 and x but never got anywhere.

I've been thinking about the set theory multiverse and its philosophical implications, particularly regarding mathematical truth. While I understand the pragmatic benefits of the multiverse view, I'm struggling with its philosophical implications.

The multiverse view suggests that statements like the Continuum Hypothesis aren't absolutely true or false, but rather true in some set-theoretic universes and false in others. We have:

• Gödel's Constructible Universe (L) where CH is true
• Forcing extensions where CH is false
• Various universes with different large cardinal axioms

However, I find myself appealing to basic logical principles like the law of non-contradiction. Even if we can't currently prove certain axioms, doesn't this just reflect our epistemological limitations rather than implying all axioms are equally "true"?

To make an analogy: physical theories being underdetermined by evidence doesn't mean reality itself is underdetermined. Similarly, our inability to prove CH doesn't necessarily mean it lacks a definite truth value.

Questions I'm wrestling with:

1. What makes certain axioms "true" beyond mere consistency?
2. Is there a meaningful distinction between mathematical existence and consistency?
3. Can we maintain mathematical realism while acknowledging the practical utility of the multiverse approach?
4. How do we reconcile Platonism with independence results?

I'm leaning towards a view that maintains objective mathematical truth while explaining why we need to work with multiple models pragmatically. But I'm very interested in hearing other perspectives, especially from those who work in set theory or mathematical logic.

Mathematics seems to be independent of reality, it has its own storytelling styles, and one usually proves some things in order to prove the follow-ups, which reminds me of having a narrative structure.