Approximation by prime powers

The well-known Weierstrass approximation theorem says that polynomials are dense in C [0, 1]. That is, given any continuous function f on the unit interval, and any ε > 0, you can find a polynomial P such that f and P are never more than ε apart. This means that linear

Logarithm approximation curiosity

I’ve written before about three simple approximations for logarithms, for base 10 log10(x) ≈ (x – 1)/(x + 1) base e, loge(x) ≈ 2(x – 1)/(x + 1) and base 2 log2(x) ≈ 3(x – 1)/(x + 1). These can be used to mentally approximate logarithms to moderate accuracy, accurate

Iterated Mersenne primes

A Mersenne number is a number of the form 2k − 1. A Mersenne prime is a Mersenne number which is also a prime. It turns out that if 2k − 1 is prime then k must be prime, so Mersenne numbers have the form 2p − 1 is prime.

Small probabilities add, big ones don’t

A video has been making the rounds in which a well-known professor [1] says that if something has a 20% probability of happening in one attempt, then it has a 40% chance of happening in two attempts, a 60% chance in happening in three attempts, etc. This is wrong, but

Between hyper-focus and burnout: Developing with ADHD

Eira and Ryan talk with Chris Ferdinandi, a front-end developer and ADHD advocate, about his diagnosis experience, the importance of accommodations for neurodivergent folks, and some advice for devs looking for the best tools and tactics for managing ADHD at work.

Python vs JavaScript: Most Important Differences

Margin vs Padding in HTML and CSS: Differences and How to Use

Logistic regression quick takes

This post is a series of quick thoughts related to logistic regression. It starts with this article on moving between logit and probability scales. *** Logistic regression models the probability of a yes/no event occurring. It gives you more information than a model that simply tries to classify yeses and

How a sound engineer builds coding skills on CodeSignal Learn

Whether you’re trying to break into tech, prepare for the job search, or level up in your current role, it helps to know that you’re not alone in your journey to build your technical skills. That’s why we’re sharing stories from learners like you: to motivate and inspire others in

Numerical application of mean value theorem

Suppose you’d like to evaluate the function for small values of z, say z = 10−8. This example comes from [1]. The Python code from numpy import exp def f(z): return (exp(z) - 1 - z)/z**2 print(f(1e-8)) prints -0.607747099184471. Now suppose you suspect numerical difficulties and compute your result to