Bayes' theorem in the form that actually matters day to day: why a 99%-accurate test on a rare condition is still usually wrong, why doctors and juries fall for the same reasoning error, and how the same math runs underneath spam filters and alert triage. Priors, likelihoods, and posteriors made concrete with natural-frequency arithmetic instead of symbol-pushing.
Mathematics for Engineers
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Bayes' Theorem for Engineers: The Base-Rate Trap That Fools Doctors, Juries, and Alert Dashboards -
Bayesian Statistics for Engineers Bayesian and frequentist statistics answer different questions, and engineers benefit from knowing which question they are actually asking. This post walks through priors, conjugate posteriors, a worked Bayesian A/B test, MCMC at a working level, and where Bayesian reasoning genuinely beats classical inference.
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Calculus for the Person Who Forgot A working engineer's guide to the calculus that actually earns its keep: derivatives as sensitivity, gradients for optimization, the chain rule as backpropagation, and integrals as accumulation. Plus the curriculum you can safely forget.
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Game Theory in System Design Game theory is not a curiosity for economists. It is the design language for any system where independent parties act in their own interest — ad auctions, blockchains, consensus protocols, congested networks — and this post works through the math and the places it genuinely predicts, and fails to predict, real engineering behavior.
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Error-Correcting Codes: From Hamming to Reed-Solomon Data does not survive storage and transmission by accident. Error-correcting codes — from the elegant simplicity of Hamming(7,4) to the polynomial algebra of Reed-Solomon — are what stand between your bits and a noisy, unreliable physical world. This post works through the mathematics that keeps your RAID array, NVMe drive, QR code, and deep-space telemetry intact.
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Monte Carlo Methods: Simulating Your Way Out of Hard Math When a closed-form solution does not exist or is not worth finding, random sampling is the most practical path forward. This post covers the core theory of Monte Carlo estimation — convergence, variance reduction, PRNG discipline — and applies it to portfolio Value at Risk, infrastructure reliability, and capacity planning, with a full Python walkthrough using numpy.
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Queueing Theory for Capacity Planning: Why Latency Explodes at 80% Queueing theory gives engineers a rigorous foundation for capacity planning. Little's Law, the M/M/1 utilization-latency formula, and the hockey-stick curve explain why latency degrades catastrophically near saturation — and exactly where to set thresholds for thread pools, connection pools, and HPA.
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Shannon and Information Theory: The 1948 Paper That Named the Bit Claude Shannon's 1948 paper defined the mathematical foundation of every digital communication system on earth. This post unpacks entropy as surprise, the source and channel coding theorems, the Shannon-Hartley limit, and the unexpected appearances of Shannon entropy in machine learning and the Kelly criterion.
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The Fourier Transform, Finally Intuitive Any signal is a sum of sinusoids — that one sentence unlocks audio codecs, Wi-Fi, 5G, oscilloscopes, and JPEG. This post builds the Fourier transform from first principles, explains why the naive DFT is impractical and the FFT fixes it, covers windowing and spectral leakage, and shows the whole thing in working Python.