John D. Cook provides expert consulting in applied mathematics and data privacy, helping clients from tech, biotech, and legal industries—including Amazon, Google, Microsoft, and Amgen—solve complex problems efficiently.
76 articles from this blog
Explores the exact closed-form solution to the nonlinear pendulum equation using Jacobi elliptic functions, comparing it with numerical and linearized solutions.
Explores the formula for the nth derivative of a quotient, a lesser-known counterpart to the product rule.
A mathematical approximation for solving oblique triangles without inverse trig functions, with Python code example.
A developer shares personal experiences with AI coding agents, noting significant improvements in capability and efficiency, while discussing limitations and best practices.
Explores Newton's diameter theorem using a fifth-degree polynomial, showing centroids of intersections fall on a line.
Explores NF4 and FP4 4-bit floating point formats for LLM weight quantization, focusing on Gaussian-distributed weights.
Explores 4-bit floating point (FP4) numbers, their formats, and use in neural networks for reduced precision.
Explores Newton's theorem of diameters for algebraic curves, using elliptic curves as an example.
Explains how GPS uses intersecting spheres from satellite distances to determine location, including error corrections and linear algebra.
Solving for a parabola through two points with given slopes using conic section constraints.
Explores a mathematical paper showing how to derive all elementary functions from just the function e^x and the constant 1.
Explores the distribution of digits in decimal fractions of prime denominators, with examples in Python.
Exploration of a random hexagon fractal process, comparing barycenter and incenter triangle centers.
Analysis of Artemis I and Apollo 12 orbits, exploring three- and four-body gravitational problems in space missions.
Explores Toffoli gates as reversible computing building blocks, their energy efficiency, and how they can simulate NAND gates.
Explains why running AI locally on your own hardware is the best way to maintain HIPAA compliance, avoiding costly and restrictive cloud options.
Explains how updating an average grade relates to Bayesian statistics and Kalman filtering, using weighted averages and gain.
Explores the hyperbolic analog of Napier's mnemonic for spherical trigonometry, comparing circular and hyperbolic functions.
Comparison of Artemis II mission trajectory with Apollo 8 and Apollo 13, highlighting lunar free-return and orbit details.
Explores the relationship between pentagonal and triangular numbers through visual and algebraic proofs.
