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.
Mathematics
-
Calculus for the Person Who Forgot -
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.
-
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.
-
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.
-
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.