With automated proof-checkers, a problem can be broken up into small chunks, solved bit-by-bit, then reassembled with confidence that every piece is correct. For some, this heralds a new area in ...

So, you want to learn Python, and you’re thinking YouTube is the place to do it. Smart move! The internet is packed with video lessons that can take you from zero to coding hero. But with so many ...

The tipping point came in the summer of 2025. That July, several artificial intelligence models solved five out of six problems at the International Mathematical Olympiad, an annual challenge for some ...

Traditional statistical and machine learning methods mostly focus on correlations, but causal models allow researchers to infer mechanisms and predict the effects of interventions. Nevertheless, the ...

Numerov’s numerical method is developed in a didactic way by using Python in its Jupyter Notebook version 6.0.3 for three different quantum physical systems: the hydrogen atom, a molecule governed by ...

In 2005, Travis Oliphant was an information scientist working on medical and biological imaging at Brigham Young University in Provo, Utah, when he began work on NumPy, a library that has become a ...

Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

Introductory text for Kalman and Bayesian filters. All code is written in Python, and the book itself is written using Jupyter Notebook so that you can run and modify the code in your browser. What ...

But in many cases, it doesn’t have to be an either/or proposition. Properly optimized, Python applications can run with surprising speed—perhaps not as fast as Java or C, but fast enough for web ...

HP calculators, slide rules, and Forth all have something in common: reverse polish notation or RPN. Admittedly, slide rules don’t really have RPN, but you work problems on them the same way you do ...