In today's episode of "Let's Make #Math #Boring," Eli Bendersky attempts to dazzle us with #polynomial #magic and #convolution sorcery🤯. Spoiler alert: it's just #middle #school #math dressed in fancy terminology🎩📚. If you needed a nap, you're welcome. 💤
https://eli.thegreenplace.net/2025/convolutions-polynomials-and-flipped-kernels/ #Sorcery #HackerNews #ngated

`Cardan, in Ars Magna (1545), gives a rule for solving a system of two linear equations which he calls regula de modo and which [7] calls mother of rules ! This rule gives what essentially is Cramer's rule for solving a 2 × 2 system although Cardan does not make the final step. Cardan therefore does not reach the definition of a determinant but, with the advantage of hindsight, we can see that his method does lead to the definition.`

https://mathshistory.st-andrews.ac.uk/HistTopics/Matrices_and_determinants/

#matrix #linearAlgebra #polynomial

Why weren't you taught the cubic formula?
https://www.youtube.com/watch?v=N-KXStupwsc
#Mathologer #BurkardPolster @Mathologer
#NumberTheory #algebra #geometry
#quadratic #cubic #polynomial
#maths #mathematics #education
#math

Many may remember how to solve quadratic equations. For a long time, there have been known solutions for cubic and quartic equations as well, however, they are complicated. Similar solutions, just using roots do not exist for exponents higher than four, however. Now a general solution has been found using a completely different approach using Catalan numbers and power series. See http://www.neat-news.com/2025/05/88.php. #polynomial #zero

A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode

https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2460966#d1e523

#HackerNews #HyperCatalan #Series #Polynomial #Equations #Geode #Mathematics #Research

@catselbow
Astonishing! I hadn't come across this before - absolutely fascinating!
#maths #mathematics #polynomial #polynomials #CatalanNumbers #combinatorics #Galois #GaloisTheory
https://www.tandfonline.com/doi/epdf/10.1080/00029890.2025.2460966?needAccess=true

One day, one decomposition
A235035: Numbers n for which A234742(n) = n: numbers n whose binary representation encodes a GF(2)[X]-polynomial such that when its irreducible factors are multiplied together as ordinary integers (with carry-bits), the result is n

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A235035.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A235035.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #binary #representation #polynomial #factors #integers #graph #threejs #webGL

One day, one decomposition
A228183: Semiprimes generated by the Euler polynomial x^2 + x + 41

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A228183.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A228183.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #semiprimes #Euler #polynomial #graph #threejs #webGL

alte Tradition heute wieder aufleben lassen: Frühjahrsputz mit #AphexTwin #Classics - da lacht das Herz. Auch wenn Sie bis zum Ende noch einige male loopen wird, ich freue mic hauf jede Wiederholung. Einfach ne Frühlingsputz CD - und mit #Polynomial-C n Päuschen

I reviewed how Mizar formalizes the Polynomial ring (and, really, how it formalizes polynomials).

There's quite a bit to it, but every proof assistant appears to use the same strategy: it's basically the monoid algebra for the free monoid generated by monomials over the indeterminates.

#Mizar #ProofAssistant #Polynomial

https://thmprover.wordpress.com/2025/01/07/ring-of-polynomials-in-mizar/

One day, one decomposition
A145292: Composite numbers generated by the Euler polynomial x^2 + x + 41

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A145292.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A145292.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #composite #numbers #generated #Euler #polynomial #graph #threejs #webGL

polynomial:

https://codepen.io/fractalkitty/pen/ZEgaOrw

#wiggle #mathober #mathober2024 #polynomial

GraphOnShake

For Mathober Curated by @fractalkitty
Video: https://youtu.be/WB9Nm3H0P9s

Blogpost : https://blog.illestpreacha.com/mathober2024polynomial1

#mathober #mathart #mathober2024 #mathober23 #polynomial
For my sixth sketch of Mathober2024, GraphOnShake is coded in Desmos with Polynomial based equations. Polynomial is the 23rd Prompt for this year Mathober.

#poetry

Shaking and Flipping
Tilting and twisting
Spinning and Tipping
Over and Under,
As they wander,
Into a whole new listing

#creativecoding #coding #mathart #3d
#newmedia #diagram #animation

One day, one decomposition
A117223: Numbers n such that Phi(n,x) is a flat cyclotomic polynomial of order three

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A117223.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A117223.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #Phi #cyclotomic #polynomial #order #graph #threejs #webGL

Sometimes the shiny brand new thing is just as shiny a year and a half later..
Via arXiv:

Learning quantum #Hamiltonians at any temperature in #polynomial time
https://arxiv.org/abs/2310.02243

Линейная регрессия. Основная идея, модификации и реализация с нуля на Python

В машинном и глубоком обучении линейная регрессия занимает особое место, являясь не просто статистическим инструментом, но а также фундаментальным компонентом для многих более сложных концепций. В данной статье рассмотрен не только принцип работы линейной регрессии с реализацией с нуля на Python, но а также описаны её модификации и проведён небольшой сравнительный анализ основных методов регуляризации. Помимо этого, в конце указаны дополнительные источники для более глубокого ознакомления.

https://habr.com/ru/articles/804135/

#линейная_регрессия #linear_regression #polynomial #ridge #lasso #elasticnet #regularization #реализация_с_нуля #python #data_science

P versus NP

In Our Time: The venerable Melvyn Bragg struggles to understand the P v NP problem despite good explanations from (now Prof.) Colva Roney-Dougal from St Andrews, Prof. Tim Gowers then at Cambridge, and Prof. Leslie Ann Goldberg of Oxford.

https://www.bbc.co.uk/sounds/play/b06mtms8

Reading material and other links:
https://www.bbc.co.uk/programmes/b06mtms8

#math #maths #mathematics #pvnp #pure #computerscience #proof #polynomial #encryption #decryption #automation #bbc #audio

P vs. NP: The Biggest #Puzzle in #ComputerScience

"Are there limits to what #Computers can do? How complex is too complex for #Computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called #ComputationalComplexity."

https://www.youtube.com/watch?v=pQsdygaYcE4

#Philosophy #PhilosophyOfScience #Science #Information #InformationTechnology #PvsNP #Logic #BooleanLogic #Algorithm #Polynomial #Polymomials #NP #NondeterministicPolynomial #QuantaMagazine

🌗 利用Blueprint將PFR證明正式化在Lean4中：一個簡短的介紹
➤ 正式化PFR證明的一個快速導覽
✤ https://terrytao.wordpress.com/2023/11/18/formalizing-the-proof-of-pfr-in-lean4-using-blueprint-a-short-tour/
Terence Tao與其它作者在預印本中證明瞭Polynomial Freiman-Ruzsa (PFR) 猜想，並與Yael Dillies和Bhavik Mehta一起開始使用Lean4證明助手語言來正式化該證明。證明的大部分已經完成，而且使用了由Patrick Massot開發的Blueprint工具，該工具可以生成與Lean正式化相關聯的易讀的“藍圖”。文章提供了對項目的快速“導覽”，介紹了Blueprint藍圖的功能以及PFR證明的不同部分的狀態。
+ 很有趣的項目，對正式化數學證明的方法感到興奮。
+ Lean4似乎是一個很強大的工具，有望改變數學
#Blueprint #Lean4 #Polynomial Freiman-Ruzsa猜想

Accessible proofs of the transcendence of e and pi:
https://www.youtube.com/watch?v=WyoH_vgiqXM
#maths #e #pi #transcendental #polynomial #number #numbertheory #Mathologer #math