Algorithms

Seeing Structure First

A reflection on eleven explorations in generic programming, and how algorithms arise from algebraic structure.

Alexander Stepanov: Efficient Programming with Components (A9 Lectures)

Notes

18-part lecture series on efficient programming. Covers the intellectual foundations behind STL.

Alexander Stepanov: Notes on Programming

Notes

Collected notes on programming philosophy. Free PDF.

Algorithm Design

Algorithms

Concrete Mathematics

Notes

Blends discrete mathematics with analysis and algorithm design.

Convex Optimization

Elements of Programming

Notes

Rigorous foundations of generic programming. Connects algebra and algorithms. Stepanov’s magnum opus.

From Mathematics to Generic Programming

Notes

History of mathematical ideas underlying generic programming. More accessible than EoP.

Introduction to Algorithms (CLRS)

Numerical Recipes: The Art of Scientific Computing

Notes

Broad coverage of numerical algorithms in science and engineering. Classic cross-topic numerical algorithms.

Pearls of Functional Algorithm Design

Programming Pearls

Sean Parent: C++ Seasoning (That's a Rotate)

Notes

Classic talk on recognizing algorithmic patterns. ‘No raw loops’ - shows how rotate solves many problems elegantly.

The Algorithm Design Manual

The Art of Computer Programming, Vol 1: Fundamental Algorithms

The Art of Computer Programming, Vol 2: Seminumerical Algorithms

The Art of Computer Programming, Vol 3: Sorting and Searching

The Art of Computer Programming, Vol 4A: Combinatorial Algorithms

AlgoGraph: Immutable Graph Library with Functional Transformers

AlgoGraph is an immutable graph library for Python with pipe-based transformers, declarative selectors, and lazy views.

CBT: Computational Basis Transforms

A C++17 header-only library that formalizes a pattern behind FFT, logarithmic arithmetic, and Bayesian inference: transform to a domain where your target operation is cheap.

Problem Set Solutions

Graduate problem set solutions in computational statistics and numerical methods from my math master's at SIUe. Implementing things from scratch teaches you what the libraries are hiding.

Is It Prime?

The Miller-Rabin primality test demonstrates how probabilistic algorithms achieve arbitrary certainty, trading absolute truth for practical efficiency.

One Algorithm, Infinite Powers

The Russian peasant algorithm computes products, powers, Fibonacci numbers, and more, once you see the underlying algebraic structure.

Bloom Filters

Bloom filters trade perfect recall for extraordinary space efficiency. How they work and why they matter.