Algorithms from THE BOOK [Lange]

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Algorithms from THE BOOK, Second Edition by Kenneth Lange is a broad, mathematically oriented introduction to important algorithms drawn from many areas rather than a conventional computer-science textbook focused on one application. The book begins with ancient algorithms and progresses through sorting, graph algorithms, primality testing, linear systems, Newton's method, linear programming, eigenvalues and eigenvectors, optimization, data mining, the fast Fourier transform, Monte Carlo methods, and numerical/automatic differentiation. Its central theme is that powerful algorithms are often built on elegant mathematical ideas, and understanding those ideas helps readers understand what algorithms are doing “under the hood.” 

The second edition (2025) expands and updates the original work, adding a chapter on automatic differentiation and neural-network modeling, correcting errors, improving explanations, adding worked exercises, and introducing additional algorithms. Most algorithms are accompanied by Julia code, making the book suitable for experimentation as well as theoretical study; exercises and appendices with background material and selected solutions also make it usable as a textbook. 

Overall, it presents algorithms as a meeting point between mathematics, numerical computation, optimization, statistics, graph theory, number theory, data science, and machine learning, aimed at students and professionals in quantitative fields.

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