Wiki: https://en.wikipedia.org/wiki/Mandelbrot_set

Here are a bunch of other visualizations: I don't know how artistic or data-driven some of these are, but they look very interesting. I think the nebula-looking one measures how often a point is visited?

!Black and Green mandelbrot set

The Bulbic Mandelbrot Set

!Bulbic Mandelbrot Set

https://www.deviantart.com/metafractals/art/The-Bulbic-Mandelbrot-Set-811453986

A Nebulabrot

!Nebula looking mandelbrot set

https://mathematica.stackexchange.com/questions/89458/how-to-make-a-nebulabrot

So I'm gearing up to take a calculus 1 exam, and this question is on the sample test. My initial thought was that since we are looking for F(9), and F(x) is an antiderivative of f(x), I can just use the integral of the equation of f(x) at 9, which is f(x) = -2x/3 + 5, which, when integrated, becomes -x^2/3 + 5x + 2 (C = 2 because F(0) = 2). Thing is, though, that won't give me any of the answers listed. And even after taking the integral of all of the equations of f(x), I still have no idea how to produce any of the answers in the multiple choice.

I'm super stumped on this one. Any help would be welcome!

BOINC is a free tool you can download to participate in several different math research projects. It runs on Windows, MacOS, Linux, and even Android. Each project gives you fun stats and graphs about your participation, many of them will even credit you individually for your discoveries (such as finding a new prime) on their website or in their published papers.

Here's a few of the projects available (emoji legend at bottom of post):

🏆💚❤️✖️✒️🔓 Amicable Numbers Independent research project that uses Internet-connected computers to find new amicable pairs. Currently searching the 10^20 range.

🎓🔓✖️ NFS@Home - Lattice sieving step in Number Field Sieve factorization of large integers. Many public key algorithms, including the RSA algorithm, rely on the fact that the publicly available modulus cannot be factored. If it is factored, the private key can be easily calculated.

🏆🎓💚❤️✖️🔓 Numberfields@home - Research in number theory. Number theorists can mine the data for interesting patterns to help them formulate conjectures about number fields.

🔓 ODLK1 - Building a database of canonical forms of diagonal Latin squares of the 10th order

🔓💚❤️ SRBase - Attempting to solve Sierpinski / Riesel Bases up to 1030.

🔓✖️PrimeGrid - Find new prime numbers!

Gerasim@home - research in discrete mathematics and logic control. Testing and comparison of heuristic methods for getting separations of parallel algorithms working in the CAD system for designing logic control systems

🔓✖️ Loda@home - LODA is an assembly language, a computational model, and a distributed tool for mining programs. You can use it to generate and search programs that compute integer sequences from the On-Line Encyclopedia of Integer Sequences® (OEIS®). The goal of the project is to reverse engineer formulas and efficient algorithms for a wide range of non-trivial integer sequences.

🔓🎓Rakesearch - The enormous size of the diagonal Latin squares space makes it unfeasible to enumerate all its objects straightforwardly in reasonable time. So, in order to discover the structure of this space, sophisticated search methods are needed. In RakeSearch project, we implement an application that picks up separate pairs of mutually orthogonal DLSs, which allows to reconstruct full graphs of their orthogonality.

🔓✒️ Ramanujan machine - Discover new mathematical conjectures

Legend:

🔓 - Publishes data openly and regularly. Note many projects publish papers detailing the results of their work, this icon means that they regularly publish the source materials as well/the results of the computation in an open fashion.

🏆 - Credits individual crunchers for discoveries, such as finding a new black hole or prime number

🎓 - Sponsored by major university or research institute.

💚 - Supports NVIDIA GPU/graphics card (all projects should be assumed to support CPU unless otherwise stated)

❤️ - Support AMD GPU (all projects should be assumed to support CPU unless otherwise stated)

✖️ - Supports OS X (all projects should be assumed to support Windows & Linux unless otherwise stated)

ChatGPT will gobble up every symbolic manipulation task I give to it. At worst, sometimes I have to check its output and point out anything weird, then it'll correct it.

I'm writing pages over pages of scary differential equations and the damn thing is saving me lots of time on it. And everything checks out! I wonder about GPT 4, since it is supposed to give correct answers without help as often as the average calculus student...

The regular elo formula is complicated.

The most basic elo formula is win = 1 points, draw = 0, lose = -1. Which is a little too basic.

I looked around and couldn't find a 'medium difficulty' elo formula. Anyone have a medium difficulty proposal?

Regular elo formula:

The Elo rating system embodies this by using a formula that changes a player's rating by adding K(S-E) to his rating each time. K is a constant that is the same for all players; the higher it is, the more easily your rating changes. S is the score of the player in a match (+1 for a win, 0 for a loss). E is the expected score of the player in the match. Against a weak player, it is close to 1 since you expect a strong player to beat a weak player most of the time. Conversely, against a stronger player, it is close to 0. You can calculate E using the formula E_A = 1/(1+10(R_B-R_A/400)), where E_A is the expect score of player A with rating R_A when faced with player B with rating R_B.

Beginner-friendly derivation of an alternative expression of the gamma function.

Walk around a house that exists in a non-Euclidean space called a 3-sphere.

A math channel by a Field's Medalist having really good explainations of undergrad and grad topics.

Since the spaces feature for matrix has entered open beta, I've created a mathematics space that brings together (most) of the mathematics related rooms on matrix.org.

I was burned out on math for a very long while after failing out of my phd, just now starting to get back into it. This paper is not something a professional mathematician would take seriously, but I'm really happy with it still and wanted to share.

I'm waiting for the day I get all the references in the video! Also If u peeps could recommend a math oriented peertube instance that'd be great!

It's the first and best piece of math fiction I've read, it's inspiring and such an amazing commentary on society during the Victorian Era. What are your thoughts? Any similar readings?