Algorithms

Seeing Structure First

A reflection on eleven explorations in generic programming—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 brings functional programming elegance to graph algorithms with immutable data structures, pipe-based transformers, declarative selectors, and lazy views.

CBT: Computational Basis Transforms - A Unified Framework

A C++17 header-only library implementing Computational Basis Transforms - a unified framework for understanding how FFT, logarithmic arithmetic, and Bayesian inference are all instances of the same pattern.

Problem Set Solutions

A collection of graduate problem set solutions in computational statistics, numerical methods, and algorithm design from my mathematics master's program.

Is It Prime?

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

One Algorithm, Infinite Powers

The Russian peasant algorithm teaches us that one algorithm can compute products, powers, Fibonacci numbers, and more—once we see the underlying algebraic structure.

Bloom Filters and the Art of Probabilistic Certainty

An exploration of Bloom filters as elegant probabilistic data structures that trade perfect recall for extraordinary space efficiency.