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SymPy makes math fun again
An introduction into symbolic computations in Python. Don't worry, it's much simpler than it sounds. It's about making Python do your math for you with very little investment in the technology.
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3Blue1Brown Calculus Blog Series
Mathematics with a distinct visual perspective. Linear algebra, calculus, neural networks, topology, and more.
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Hashing
A visual, interactive introduction to hash functions.
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BB(3, 3) is Hard
I’m excited to share a 3 state, 3 symbol Turing Machine that cannot be proven to halt or not (when starting on a blank tape) without solving a Collatz-like problem. Therefore, solving the \(BB(3, 3)\) problem is at least as hard as solving this Collatz-like problem, a class of problem for which Paul Erdős famously…
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Estimating square roots in your head
Imagine we want to compute the square root of a number n n n . The basic idea of Heron’s method , named after the mathematician and engineer, Heron of Alexandria, is to find a number g g g that is close to n \sqrt{n} n and to then average that with the number n / g n/g n / g , which corrects for the fact that g g g…
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Thoughts about what worked in math circles
Thoughts about what worked in math circles After about 7 months of math circles with a group of 7- turning 8-year-old boys and girls, I decided to take a...
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California needs real math education, not gimmicks
A guest post by Armand Domalewski.
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Every possible Wordle solution visualized
Every Wordle solution laid out at once. Filter all 2,309 by letter, position, and gray/yellow/green clues to narrow down today's answer.
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Why we don’t generate elliptic curves every day
Elliptic curves are standardized, instead of being generated like Diffie-Hellman parameters. There's good reasons!
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The Art of LaTeX: Common mistakes and advice for typesetting proofs
When was the first time you had to use LaTeX? If you are like most people, it was probably suddenly forced upon you during your first math or CS class where you had to start writing proofs, with minimal guidance on how to get started. Unfortunately, this meant that while many people have good operational knowledge of…
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Superrational
“Will Vicktoreya Keyneslee Beauxpensees please come see the principal right now?” said the voice over the intercom.
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Breaking RSA with a quantum computer?
A group of Chinese researchers have just published a paper claiming that they can—although they have not yet done so—break 2048-bit RSA. This is something to take seriously. It might not be correct, but it’s not obviously wrong. We have long known from Shor’s algorithm that factoring with a quantum computer is easy…
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Problems harder than NP-Complete
People always talk about "P vs NP" like P problems are easy and NP problems are hard. This is a useful day-to-day model but also an oversimplification....
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Lerp
Lerp is the nickname for Linear Interpolation between two points. It's a fairly simple effect to implement but can really improve the look of your animations if you're moving an object from a point A to point B.
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Subtraction is functionally complete
To be precise, IEEE-754 floating point subtraction is functionally complete . That means you can construct any binary circuit using nothing but floating point subtraction.
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Formally modeled Dreidel for no good reason
I can mathematically prove the game's not fun.
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2048 Bit RSA and the Year 2030
The Call of the Open Sidewalk [The Call of the Open…2023239 points149 commentsSecurity & Privacy details
Update: NIST released a draft that modified their recommendations (Oct 2024) 1) . RSA 2048 is to be only considered “deprecated” after 2030. The draft states:
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Circles do not exist
Many logos, drawings and other graphical designs have the following shape in it. What is this shape? If you thought: "Ah-ha! I'm smart and r...
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Causal Trees
Projects and Ramblings
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How far can you jump from a swing?
In this post I derive the physics of pumping a swing and the physics of jumping from a swing. Then, using both pieces I compute the optimal strategy of jumping from a swing to maximize the traveled distance. I propose this game as a new Olympic sport.
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A tutorial quantum interpreter in 150 lines of Lisp
a personal blog
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Cargo Cult Quantum Factoring
Just days after we celebrated my wife’s 40th birthday, she came down with COVID, meaning she’s been isolating and I’ve been spending almost all my time dealing with our kids. But …
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Is the reversal curse in LLMs real?
A recent paper The Reversal Curse points out an apparent failure in large large language models like GPT-4. From the abstract: We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is