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.
162 articles from this blog
A user describes a text encoding issue where apostrophes become garbled characters when syncing files between laptop and phone, due to UTF-8 and Windows-1252 misinterpretation.
Explains why power series are inefficient for computing trig functions like cosine, using cos(200) as an example, and discusses range reduction.
Explores why Python's math library can compute logarithms of huge numbers like 200! but not cosines, due to digit sensitivity and range reduction.
Explores methods to calculate log(1000!) without modern computing, using math, tables, and manual techniques.
Exploring Python's math.log handling of large integers and float overflow quirks, revealing surprising behavior with scientific notation.
Explores the correspondence between rooted trees and non-overlapping circles, showing how tree structures map to circle configurations with examples.
Explores algebraic relationships between metallic ratios, showing when one can be derived from another via field theory and quadratic forms.
Explores metallic ratios (golden, silver, bronze) and demonstrates approximating any real number using ratios of these ratios, with Python code for pi approximation.
Explores holonomic functions, which solve linear differential equations with polynomial coefficients, and their prevalence among special functions in Abramowitz and Stegun.
Deriving an asymptotic estimate for the cumulative sum of unlabeled rooted trees, with code to visualize convergence.
Explains why second order linear differential equations with polynomial coefficients are important in physics and applications, linking to separable PDEs.
Explores the surprising link between counting unlabeled rooted trees and designing Runge-Kutta methods for differential equations.
Explains why Runge-Kutta methods need more stages than order for p≥5, known as the Butcher barrier, with examples like Dormand-Prince.
Exploring the derivation of Runge-Kutta method coefficients by solving the RK4 design equations using Mathematica, including variations like the 3/8 rule and Gill's method.
Improving inverse factorial computation using Newton's method and log gamma function for better accuracy and performance.
Explores using card deck permutations to store cryptographic keys, from Bitcoin to post-quantum ML-KEM.
Explores hiding cryptographic keys in card permutations, covering ranking/unranking algorithms and SymPy implementation.
Explores counting permutations with kth roots using generating functions in Mathematica and SymPy.
Explains how to convert floating point numbers to binary using Python's hex method.
Explores permutation square roots, cube roots, and their existence conditions using Python code and mathematical theorems.
